Bruce R Barrett

Interests

Research

I am interested in developing a microscopic theory of the structure of atomic nuclear starting only from the basic strong interactions among the protons and neutrons in the nucleus and using the quantum mechanical nuclear many-body theory.

Teaching

I want to inspire students to pursue a career in science, in general, and in physics, in particular.

Courses

Scholarly Contributions

Journals/Publications

• Barrett, B., & Giraud, B. (2015). Testing for Parity Violation in Nuclei using Spin Density Matrices for Nuclear Density Functionals. Physica Scripta, 90, 065301.
• Dikmen, E., Lisetsky, A., Barrett, B., Maris, P., Shirokov, A., & Vary, J. (2015). Ab initio effective interactions for sd-shell valence nucleons. Phys. Rev. C, 91(064301), 064301-1 to 064301-12. doi:10.1103/PhysRevC.91.064301
• Barrett, B. R. (2013). Microscopic calculations of nuclear structure beyond the 0p-shell. Journal of Physics: Conference Series, 445(1).
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  Abstract: Significant progress has been made in our microscopic understanding of the properties of light nuclei, starting from the basic nucleon-nucleon and three-nucleon interactions among the particles inside the nucleus. The main challenge now is to extend these successes for light nuclei (A ≤ 16) to heavier mass nuclei. Here we discuss three recent approaches within the No Core Shell Model for possibly going beyond the 0p-shell.
• Barrett, B. R., Barrett, B. R., Navratil, P., & Vary, J. P. (2013). Ab initio no core shell model. Prog. Part. Nucl. Phys, 69, 131.
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  Published online December 20, 2012
• Barrett, B. R., Navrátil, P., & Vary, J. P. (2013). Ab initio no core shell model. Progress in Particle and Nuclear Physics, 69(1), 131-181.
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  Abstract: Motivated by limitations of the Bloch-Horowitz-Brandow perturbative approach to nuclear structure we have developed the non-perturbative ab initio no core shell model (NCSM) capable of solving the properties of nuclei exactly for arbitrary nucleon-nucleon (NN) and NN+ three-nucleon (NNN) interactions with exact preservation of all symmetries. We present the complete ab initio NCSM formalism and review highlights obtained with it since its inception. These highlights include the first ab initio nuclear-structure calculations utilizing chiral NNN interactions, which predict the correct low-lying spectrum for 10B and explain the anomalous long 14C β-decay lifetime. We also obtain the small quadrupole moment of 6Li. In addition to explaining long-standing nuclear structure anomalies, the ab initio NCSM provides a predictive framework for observables that are not yet measured or are not directly measurable. For example, reactions between short-lived systems and reaction rates near zero energy are relevant to fusion research but may not be known from experiment with sufficient precision. We, therefore, discuss, in detail, the extension of the ab initio NCSM to nuclear reactions and sketch a number of promising future directions for research emerging from the NCSM foundation, including a microscopic non-perturbative framework for the theory with a core. Having a parameter-free approach, we can construct systems with a core, which will provide an ab initio pathway to heavier nuclei. © 2012 Elsevier B.V. All rights reserved.
• Kruse, M. K., Jurgenson, E. D., Navrátil, P., Barrett, B. R., & Ormand, W. E. (2013). Extrapolation uncertainties in the importance-truncated no-core shell model. Physical Review C - Nuclear Physics, 87(4).
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  Abstract: Background: The importance-truncated no-core shell model (IT-NCSM) has recently been shown to extend theoretical nuclear structure calculations of p-shell nuclei to larger model (Nmax) spaces. The importance truncation procedure selects only relatively few of the many basis states present in a "large" Nmax basis space, thus making the calculation tractable and reasonably quick to perform. Initial results indicate that the procedure agrees well with the NCSM, in which a complete basis is constructed for a given Nmax. Purpose: An analysis of uncertainties in IT-NCSM such as those generated from the extrapolations to the complete Nmax space have not been fully discussed. We present a method for estimating the uncertainty when extrapolating to the complete Nmax space and demonstrate the method by comparing extrapolated IT-NCSM to full NCSM calculations up to Nmax=14. Furthermore, we study the result of extrapolating IT-NCSM ground-state energies to Nmax=∞ and compare the results to similarly extrapolated NCSM calculations. A procedure is formulated to assign uncertainties for Nmax=∞ extrapolations. Method: We report on 6Li calculations performed with the IT-NCSM and compare them to full NCSM calculations. We employ the Entem and Machleidt chiral two-body next-to-next-to-next leading order (N3LO) interaction (regulated at 500 MeV/c), which has been modified to a phase-shift equivalent potential by the similarity renormalization group (SRG) procedure. We investigate the dependence of the procedure on the technique employed to extrapolate to the complete N max space, the harmonic oscillator energy (âΩ), and investigate the dependence on the momentum-decoupling scale (λ) used in the SRG. We also investigate the use of one or several reference states from which the truncated basis is constructed. Results: We find that the uncertainties generated from various extrapolating functions used to extrapolate to the complete Nmax space increase as Nmax increases. The extrapolation uncertainties range from a few keV for the smallest N max spaces to about 50 keV for the largest Nmax spaces. We note that the difference between extrapolated IT-NCSM and NCSM ground-state energies, however, can be as large as 100-250 keV depending on the chosen harmonic oscillator energy (âΩ). IT-NCSM performs equally well for various SRG momentum-decoupling scales, λ=2.02 fm-1 and λ=1.50 fm-1. Conclusions: In the case of 6Li, when using the softened chiral nucleon-nucleon N3LO interaction, we have determined the difference between extrapolated Nmax=∞ IT-NCSM and full NCSM calculations to be about 100-300 keV. As âΩ increases, we find that the agreement with NCSM deteriorates, indicating that the procedure used to choose the basis states in IT-NCSM depends on âΩ. We also find that using multiple reference states leads to a better ground-state description than using only a single reference state. © 2013 American Physical Society.
• Kruse, M., Navratil, P., Barrett, B., & Ormand, W. (2013). Extrapolation uncertainties in the importance- truncated no-core shell model. Phys. Rev. C, 87, 044301.
• Papadimitriou, G., Rotureau, J., Michel, N., Ploszajzak, M., & Barrett, B. (2013). Ab initio No-Core Gamow Shell Model calculations with realistic interactions. Phys. Rev. C, 88, 044318.
• Papadimitriou, G., Rotureau, J., Michel, N., Płoszajczak, M., & Barrett, B. R. (2013). Ab initio no-core Gamow shell model calculations with realistic interactions. Physical Review C - Nuclear Physics, 88(4).
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  Abstract: No-core Gamow shell model (NCGSM) is applied to study selected well-bound and unbound states of helium isotopes. This model is formulated on the complex energy plane and, by using a complete Berggren ensemble, treats bound, resonant, and scattering states on equal footing. We use the density matrix renormalization group method to solve the many-body Schrödinger equation. To test the validity of our approach, we benchmarked the NCGSM results against Faddeev and Faddeev-Yakubovsky exact calculations for 3H and 4He nuclei. We also performed ab initio NCGSM calculations for the unstable nucleus 5He and determined the ground-state energy and decay width, starting from a realistic N3LO chiral interaction. © 2013 American Physical Society.
• Barrett, B. R. (2012). Extending the No Core Shell Model to heavier mass nuclei. Progress in Particle and Nuclear Physics, 67(2), 521-525.
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  Abstract: The No Core Shell Model (NCSM) is an ab initio method for calculating the properties of light nuclei, up to about A=20, in which all A nucleons are treated as being active and interacting through realistic nucleonnucleon (NN) and three-nucleon (NNN) forces. It is difficult to go to larger A values due to the rapid growth of the basis spaces required in order to obtain converged results. In this talk we discuss three techniques, still in development, for extending the NCSM to heavier mass nuclei. © 2012 Elsevier B.V. All rights reserved.
• Barrett, B. R. (2012). The no core shell model in an effective field theory framework. Journal of Physics: Conference Series, 403(1).
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  Abstract: One of the outstanding problems in nuclear-structure theory is the construction of two-body (and higher-body) effective interactions in a model (or basis) space. In this presentation we discuss a recently developed approach to this problem, where one starts with an effective field theory (EFT), which contains only nucleonic fields and is formulated directly in a No-Core-Shell-Model (NCSM) space. Such an approach helps us to understand the gross features of nuclear systems from a QCD perspective. It also leads to a new method for the construction of effective interactions suitable for NCSM calculations. We then present applications to light nuclei within the pionless EFT and obtain reasonable results. Finally, we discuss future applications and extensions, such as testing the limits of the pionless EFT and extending the formalism to the pionfull EFT. © Published under licence by IOP Publishing Ltd.
• Rotureau, J., Stetcu, I., Barrett, B. R., & Kolck, U. V. (2012). Erratum: Two and three nucleons in a trap, and the continuum limit (Physical Review C (2012) 85 (034003) DOI:10.1103/PhysRevC.85.034003). Physical Review C - Nuclear Physics, 85(3).
• Rotureau, J., Stetcu, I., Barrett, B. R., & Kolck, U. V. (2012). Two and three nucleons in a trap, and the continuum limit. Physical Review C - Nuclear Physics, 85(3).
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  Abstract: We describe systems of two and three nucleons trapped in a harmonic-oscillator potential with interactions from the pionless effective field theory up to next-to-leading order (NLO). We construct the two-nucleon interaction using two-nucleon scattering information. We calculate the trapped levels in the three-nucleon system with isospin T=1/2 and determine the three-nucleon force needed for stability of the triton. We extract neutron-deuteron phase shifts, and show that the quartet scattering length is in good agreement with experimental data. © 2012 American Physical Society.
• Rotureau, J., Stetcu, I., Barrett, B., & van, K. U. (2012). Two and Three Nucleons in a Trap, and the Continuum Limit. Phys. Rev. C, 85, 034003.
• van Kolck, U., Rotureau, J., Barrett, B. R., & Stetcu, I. (2012). Two and Three Nucleons in a Trap and the Continuum Limit. Phys. Rev. C, 85, 034003.
• Barrett, B. R. (2011). Beyond the no core shell model: Extending the NCSM to heavier nuclei. AIP Conference Proceedings, 1355, 130-137.
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  Abstract: The No Core Shell Model (NCSM) is an ab initio method for calculating the properties of light nuclei, up to about A=20, in which all A nucleons are treated as being active. It is difficult to go to larger A values due to the rapid grow of the basis spaces required in order to obtain converged results. In this presentation we briefly discuss three new techniques for extending the NCSM to heavier mass nuclei. © 2011 American Institute of Physics.
• Barrett, B. R., Navrátil, P., & Vary, J. P. (2011). Ab initio no core shell model. Nuclear Physics News, 21(2), 5-12.
• Barrett, B., Kruse, M., Lisetskiy, A., Navratil, P., Stetcu, I., & Vary, J. (2011). Ab initio shell model with a core: Extending the no core shell model to heavier nuclei. Journal of Physics: Conference Series, 312(SECTION 9).
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  Abstract: The No Core Shell Model (NCSM) is an ab initio method for calculating the properties of atomic nuclei, starting with the fundamental interactions among the nucleons and treating all A nucleons as being active. This approach has been successfully applied to nuclei with A ≤ 20, but it is difficult to treat heavier mass nuclei with existing computer technology, because of the extemely large basis spaces required to obtain converged results. In this presentation we outline a new formalism for extending the NCSM to heavier mass nuclei. It involves using the NCSM approach to determine the core, one-body and two-body (and perhaps also three-body) terms, which are the usual input for standard shell model (SSM) calculations. Such SSM calculations can be easily performed for sd- and pf-shell nuclei. As a test of this new formalism, we apply it to nuclei in the 0p-shell, for which exact NCSM calculations can also be performed for making comparisons. Results are given both for energy spectra and electromagnetic properties.
• Barrett, B., Lisetskiy, A., Kruse, M., Navratil, P., Stetcu, I., & Vary, J. (2011). Ab initio shell model with a core. Journal of Physics: Conference Series, 267(1).
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  Abstract: The No Core Shell Model (NCSM) has been successful in describing the properties of light nuclei, A ≤ 16, starting from the fundamental interactions among the A nucleons, but it is currently difficult to extend the NCSM to heavier nuclei, because of the extremely large model spaces involved in the calculations. We present a new procedure, based on performing two unitary transformations on the Hamiltonian, so as to obtain the core, one-body, two-body and perhaps three-body input necessary for performing Standard Shell Model (SSM) calculations for nuclei. Such SSM calculations can be easily performed for sd- and pf-shell nuclei. We demonstrate the accuracy of our approach by applying to it nuclei within the 0p-shell. © Published under licence by IOP Publishing Ltd.
• Barrett, B. R., Bürki, J., Cardamone, D. M., Stafford, C. A., & Stein, D. L. (2010). Determining the energy barrier for decay out of superdeformed bands. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 688(1), 110-113.
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  Abstract: An asymptotically exact quantum mechanical calculation of the matrix elements for tunneling through an asymmetric barrier is combined with the two-state statistical model for decay out of superdeformed bands to determine the energy barrier (as a function of spin) separating the superdeformed and normal-deformed wells for several nuclei in the 190 and 150 mass regions. The spin-dependence of the barrier leading to sudden decay out is shown to be consistent with the decrease of a centrifugal barrier with decreasing angular momentum. Values of the barrier frequency in the two mass regions are predicted. © 2010 Elsevier B.V. All rights reserved.
• Barrett, B. R., Giraud, B. G., Jennings, B. K., & Toberg, N. P. (2010). Concavity for nuclear bindings. CERN-Proceedings, 1, 267-272.
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  Abstract: Sequences of experimental ground-state energies for both odd and even A are mapped onto concave patterns cured from convexities due to pairing. These patterns yield improved estimates by interpolation or extrapolation (as appropriate) of ground-state energies for nuclei, which have not yet been measured. An example of this procedure, using the tin isotopes is given. The same patterns, completed by a list of excitation energies, give numerical estimates of thermodynamical functions, which lead to the average nucleon number (A) (β,μ) becoming a continuous variable at low to moderate temperatures, allowing extrapolations towards nuclear masses closer to drip lines. Estimates of the free energy and the average energy, as functions of (A), provide upper and lower bounds, respectively, to ground-state energy. Finally, we discuss extensions to a two-dimensional analysis and how concavity and universality are related to the theory of the nuclear density functional.
• Rotureau, J., Stetcu, I., Barrett, B. R., Birse, M. C., & Kolck, U. V. (2010). Three and four harmonically trapped particles in an effective-field-theory framework. Physical Review A - Atomic, Molecular, and Optical Physics, 82(3).
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  Abstract: We study systems of few two-component fermions interacting via short-range interactions within a harmonic-oscillator trap. The dominant interactions, which are two-body interactions, are organized according to the number of derivatives and defined in a two-body truncated model space made from a bound-state basis. Leading-order (LO) interactions are solved for exactly using the formalism of the no-core shell model, whereas corrections are treated as many-body perturbations. We show explicitly that next-to-LO and next-to-next-to-LO interactions improve convergence as the model space increases. We present results at unitarity for three- and four-fermion systems, which show excellent agreement with the exact solution (for the three-body problem) and results obtained by other methods (in the four-body case). We also present results for finite scattering lengths and nonzero range of the interaction, including (at positive scattering length) observation of a change in the structure of the three-body ground state and extraction of the atom-dimer scattering length. © 2010 The American Physical Society.
• Stetcu, I., Rotureau, J., Barrett, B. R., & Kolck, U. V. (2010). Effective interactions for light nuclei: An effective (field theory) approach. Journal of Physics G: Nuclear and Particle Physics, 37(6).
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  Abstract: One of the central open problems in nuclear physics is the construction of effective interactions suitable for many-body calculations. We discuss a recently developed approach to this problem, where one starts with an effective field theory containing only fermion fields and formulated directly in a no-core shell-model space. We present applications to light nuclei and to systems of a few atoms in a harmonic-oscillator trap. Future applications and extensions, as well as challenges, are also considered. © 2010 IOP Publishing Ltd.
• Stetcu, I., Rotureau, J., Barrett, B. R., & Kolck, U. v. (2010). An effective field theory approach to two trapped particles. Annals of Physics, 325(8), 1644-1666.
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  Abstract: We discuss the problem of two particles interacting via short-range interactions within a harmonic-oscillator trap. The interactions are organized according to their number of derivatives and defined in truncated model spaces made from a bound-state basis. Leading-order (LO) interactions are iterated to all orders, while corrections are treated in perturbation theory. We show explicitly that next-to-LO and next-to-next-to-LO interactions improve convergence as the model space increases. In the large-model-space limit we regain results from a pseudopotential. Arbitrary scattering lengths are considered, as well as a generalization to include the non-vanishing range of the interaction. © 2010 Elsevier Inc.
• van Kolck, U., Rotureau, J., Stetcu, I., Barrett, B. R., & Birse, M. C. (2010). Three and Four Harmonically Trapped Particles in an Effective Field Theory Framework. Phys. Rev. A, 82, 032711.
• van Kolck, U., Stetcu, I., Rotureau, J., & Barrett, B. R. (2010). An Effective Field Theory Approach to Two Trapped Particles. Ann. Phys., 325, 1644-166.
• van Kolck, U., Stetcu, I., Rotureau, J., & Barrett, B. R. (2010). Effective Interactions for Light Nuclei: An effective (field theory) approach. J. Phys. G, 37, 064033.
• Barrett, B. R., Giraud, B. G., Jennings, B. K., & Toberg, N. P. (2009). Concavity for nuclear bindings, thermodynamical functions and density functionals. Nuclear Physics A, 828(3-4), 267-282.
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  Abstract: Sequences of experimental ground-state energies for both odd and even A are mapped onto concave patterns cured from convexities due to pairing and/or shell effects. The same patterns, completed by a list of excitation energies, give numerical estimates of the grand potential Ω (β, μ) for a mixture of nuclei at low or moderate temperatures T = β- 1 and at many chemical potentials μ. The average nucleon number 〈 A 〉 (β, μ) then becomes a continuous variable, allowing extrapolations towards nuclear masses closer to the drip lines. We study the possible concavity of several thermodynamical functions, such as the free energy and the average energy, as functions of 〈 A 〉. Concavity, which always occurs for the free energy and is usually present for the average energy, allows easy interpolations and extrapolations providing upper and lower bounds, respectively, to binding energies. Such bounds define an error bar for the prediction of binding energies. Finally we show how concavity and universality are related in the theory of the nuclear density functional. © 2009 Elsevier B.V. All rights reserved.
• Lisetskiy, A. F., Kruse, M. K., Barrett, B. R., Navratil, P., Stetcu, I., & Vary, J. P. (2009). Effective operators from exact many-body renormalization. Physical Review C - Nuclear Physics, 80(2).
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  Abstract: We construct effective two-body Hamiltonians and E2 operators for the p shell by performing 16 Ω ab initio no-core shell model (NCSM) calculations for A=5 and A=6 nuclei and explicitly projecting the many-body Hamiltonians and E2 operator onto the 0 Ω space. We then separate the effective E2 operator into one-body and two-body contributions employing the two-body valence cluster approximation. We analyze the convergence of proton and neutron valence one-body contributions with increasing model space size and explore the role of valence two-body contributions. We show that the constructed effective E2 operator can be parametrized in terms of one-body effective charges giving a good estimate of the NCSM result for heavier p-shell nuclei. © 2009 The American Physical Society.
• Navrátil, P., Quaglioni, S., Stetcu, I., & Barrett, B. R. (2009). Recent developments in no-core shell-model calculations. Journal of Physics G: Nuclear and Particle Physics, 36(8).
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  Abstract: We present an overview of recent results and developments of the no-core shell model (NCSM), an ab initio approach to the nuclear many-body problem for light nuclei. In this approach, we start from realistic two-nucleon or two- plus three-nucleon interactions. Many-body calculations are performed using a finite harmonic-oscillator (HO) basis. To facilitate convergence for realistic inter-nucleon interactions that generate strong short-range correlations, we derive effective interactions by unitary transformations that are tailored to the HO basis truncation. For soft realistic interactions, this might not be necessary. If this is the case, the NCSM calculations are variational. In either case, the ab initio NCSM preserves translational invariance of the nuclear many-body problem. In this review, we, in particular, highlight results obtained with the chiral two- plus three-nucleon interactions. We discuss efforts to extend the applicability of the NCSM to heavier nuclei and larger model spaces using importance-truncation schemes and/or use of effective interactions with a core. We outline an extension of the ab initio NCSM to the description of nuclear reactions by the resonating group method technique. A future direction of the approach, the ab initio NCSM with continuum, which will provide a complete description of nuclei as open systems with coupling of bound and continuum states, is given in the concluding part of the review. © 2009 IOP Publishing Ltd.
• Cardamone, D. M., Barrett, B. R., & Stafford, C. A. (2008). Universality of decay-out of superdeformed bands in the 190 mass region. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 661(2-3), 233-238.
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  Abstract: Superdeformed nuclei in the 190 mass region exhibit a striking universality in their decay-out profiles. We show that this universality can be explained in the two-level model of superdeformed decay as related to the strong separation of energy scales: a higher scale related to the nuclear interactions, and a lower scale caused by electromagnetic decay. Decay-out can only occur when separate conditions in both energy regimes are satisfied, strongly limiting the collective degrees of freedom available to the decaying nucleus. Furthermore, we present the results of the two-level model for all decays for which sufficient data are known, including statistical extraction of the matrix element for tunneling through the potential barrier. © 2008 Elsevier B.V. All rights reserved.
• Giraud, B. G., Jennings, B. K., & Barrett, B. R. (2008). Existence of a density functional for an intrinsic state. Physical Review A - Atomic, Molecular, and Optical Physics, 78(3).
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  Abstract: A generalization of the Hohenberg-Kohn theorem for finite systems proves the existence of a density functional (DF) for a symmetry violating intrinsic state, out of which a physical state with good quantum numbers can be projected. © 2008 The American Physical Society.
• Lisetskiy, A. F., Barrett, B. R., Kruse, M. K., Navratil, P., Stetcu, I., & Vary, J. P. (2008). Ab-initio shell model with a core. Physical Review C - Nuclear Physics, 78(4).
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  Abstract: We construct effective two- and three-body Hamiltonians for the p-shell by performing 12 Ω ab initio no-core shell model (NCSM) calculations for A=6 and 7 nuclei and explicitly projecting the many-body Hamiltonians onto the 0 Ω space. We then separate these effective Hamiltonians into inert core, one- and two-body contributions (also three-body for A=7) and analyze the systematic behavior of these different parts as a function of the mass number A and size of the NCSM basis space. The role of effective three- and higher-body interactions for A>6 is investigated and discussed. © 2008 The American Physical Society.
• Stetcu, I., Barrett, B. R., Kolck, U. V., & Vary, J. P. (2008). Erratum: Effective theory for trapped few-fermion systems (Physical Review A (2007) 76 (063613)). Physical Review A - Atomic, Molecular, and Optical Physics, 77(3).
• Barrett, B. R. (2007). Three nucleon forces and nuclear structure. International Journal of Modern Physics A, 22(27), 4883-4889.
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  Abstract: The author's earlier research with Professor Bruce McKellar, some 30 years ago, led to the Tucson-Melbourne three-nucleon interaction, which is still relevant today. The new significance of three-nucleon forces in determining the structure of atomic nuclei will be discussed. This has led to increased efforts to learn more about the nature of these three-nucleon interactions, both experimentally and theoretically. The recently developed no-core shell model (NCSM) has the ability to test different theoretical models for three-nucleon forces by making direct comparisons of results produced by these forces with experimental data. © World Scientific Publishing Company.
• Quaglioni, S., Stetcu, I., Bacca, S., Barrett, B. R., Johnson, C. W., Navrátil, P., Barnea, N., Leidemann, W., & Orlandini, G. (2007). Benchmark calculation of inclusive responses in the four-body nuclear system. Nuclear Physics A, 790(1-4), 372-375.
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  Abstract: This paper reports on a recent benchmark calculation in the four-nucleon system, aimed at investigating the reliability of the no-core shell model (NCSM) approach to the description of inclusive response functions via the Lorentz integral transform (LIT) method. © 2007 Elsevier B.V. All rights reserved.
• Stetcu, I., Barrett, B. R., & Kolck, U. v. (2007). No-core shell model in an effective-field-theory framework. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 653(2-4), 358-362.
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  Abstract: We present a new approach to the construction of effective interactions suitable for many-body calculations by means of the no-core shell model (NCSM). We consider an effective field theory (EFT) with only nucleon fields directly in the NCSM model spaces. In leading order, we obtain the strengths of the three contact interactions from the condition that in each model space the experimental ground-state energies of 2H, 3H and 4He be exactly reproduced. The first (0+ ; 0) excited state of 4He and the ground state of 6Li are then obtained by means of NCSM calculations in several spaces and frequencies. After we remove the harmonic-oscillator frequency dependence, we predict for 4He an energy level for the first (0+ ; 0) excited state in remarkable agreement with the experimental value. The corresponding 6Li binding energy is about 70% of the experimental value, consistent with the expansion parameter of the EFT. © 2007 Elsevier B.V. All rights reserved.
• Stetcu, I., Barrett, B. R., Kolck, U. V., & Vary, J. P. (2007). Effective theory for trapped few-fermion systems. Physical Review A - Atomic, Molecular, and Optical Physics, 76(6).
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  Abstract: We apply the general principles of effective field theories to the construction of effective interactions suitable for few- and many-body calculations in a no-core shell model framework. We calculate the spectrum of systems with three and four two-component fermions in a harmonic trap. In the unitary limit, we find that three-particle results are within 10% of known semianalytical values even in small model spaces. The method is very general, and can be readily extended to other regimes, more particles, different species (e.g., protons and neutrons in nuclear physics), or more-component fermions (as well as bosons). As an illustration, we present calculations of the lowest-energy three-fermion states away from the unitary limit and find a possible inversion of parity in the ground state in the limit of trap size large compared to the scattering length. Furthermore, we investigate the lowest positive-parity states for four fermions, although we are limited by the dimensions we can currently handle in this case. © 2007 The American Physical Society.
• Stetcu, I., Quaglioni, S., Bacca, S., Barrett, B. R., Johnson, C. W., Navrátil, P., Barnea, N., Leidemann, W., & Orlandini, G. (2007). Benchmark calculation of inclusive electromagnetic responses in the four-body nuclear system. Nuclear Physics A, 785(3-4), 307-321.
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  Abstract: Both the no-core shell model and the effective interaction hyperspherical harmonic approaches are applied to the calculation of different response functions to external electromagnetic probes, using the Lorentz integral transform method. The test is performed on the four-body nuclear system, within a simple potential model. The quality of the agreement in the various cases is discussed, together with the perspectives for rigorous ab initio calculations of cross sections of heavier nuclei. © 2006 Elsevier B.V. All rights reserved.
• Barrett, B. R., Navratil, P., Stetcu, I., & Vary, J. P. (2006). Effective interactions and operators in nuclei within the no-core shell model. AIP Conference Proceedings, 819, 504-508.
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  Abstract: We review the application of effective operator formalism to the ab initio no core shell model (NCSM). For short-range operators, such as the nucleon-nucleon potential, the unitary-transformation method works extremely well at the two-body cluster approximation and good results are obtained for the binding energies and excitation spectra of light nuclei (A ≤ 16). However, for long-range operators, such as the radius or the quadrupole moment, performing this unitary transformation at the two-body cluster level does not include the higher-order correlations needed to renormalize these long-range operators adequately. Usually, such correlations can be obtained either by increasing the order of the cluster approximation or by increasing the model space. We will discuss the difficulties of these approaches as well as alternate possible solutions for including higher-order correlations in small model spaces. © 2006 American Institute of Physics.
• Barrett, B. R., Navrátil, P., Nogga, A., Ormand, W. E., Quaglioni, S., Stetcu, I., & Varyd, J. P. (2006). New developments within the no-core shell model. Journal of Physics: Conference Series, 49(1), 1-6.
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  Abstract: We review recent developments in the ab initio no-core shell model, such as the influence of 3NFs on the binding energies and excitation spectra of light nuclei. Our calculations permit us to compare the effect of different choices for the theoretical 3NF on the properties of light nuclei. This is of particular interest in determining the best choice of the values for the contact terms in 3NFs derived from Chiral Perturbation Theory. Other recent developments in the NCSM include an investigation of the renormalization properties of physical operators, besides the nuclear Hamiltonian, as well as the Lorentz integral transform approach to the description of select reaction observables in light nuclei. © 2006 IOP Publishing Ltd.
• Barrett, B. R., Stetcu, I., Navrátil, P., & Vary, J. P. (2006). From non-Hermitian effective operators to large-scale no-core shell model calculations for light nuclei. Journal of Physics A: Mathematical and General, 39(32), 9983-9992.
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  Abstract: No-core shell model (NCSM) calculations using ab initio effective interactions are very successful in reproducing experimental nuclear spectra. The main theoretical approach is the use of effective operators, which include correlations left out by the truncation of the model space to a numerically tractable size. We review recent applications of the effective operator approach, within a NCSM framework, to the renormalization of the nucleon-nucleon interaction, as well as scalar and tensor operators. © 2006 IOP Publishing Ltd.
• Negret, A., Adachi, T., Barrett, B. R., Bäumer, C., Van, A., Berg, G. P., Brentano, P. V., Frekers, D., Frenne, D. D., Fujita, H., Fujita, K., Fujita, Y., Grewe, E. -., Haefner, P., Harakeh, M. N., Hatanaka, K., Heyde, K., Hunyadi, M., Jacobs, E., , Kalmykov, Y., et al. (2006). Gamow-Teller strengths in the A=14 multiplet: A challenge to the shell model. Physical Review Letters, 97(6).
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  Abstract: A new experimental approach to the famous problem of the anomalously slow Gamow-Teller (GT) transitions in the β decay of the A=14 multiplet is presented. The GT strength distributions to excited states in C14 and O14 were studied in high-resolution (d,He2) and (He3,t) charge-exchange reactions on N14. No-core shell-model calculations capable of reproducing the suppression of the β decays predict a selective excitation of Jπ=2+ states. The experimental confirmation represents a validation of the assumptions about the underlying structure of the N14 ground state wave function. However, the fragmentation of the GT strength over three 2+ final states remains a fundamental issue not explained by the present no-core shell model using a 6 ω model space, suggesting possibly the need to include cluster structure in these light nuclei in a consistent way. © 2006 The American Physical Society.
• Nogga, A., Navrátil, P., Barrett, B. R., & Vary, J. P. (2006). Spectra and binding energy predictions of chiral interactions for Li7. Physical Review C - Nuclear Physics, 73(6).
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  Abstract: Using the no-core shell model approach, we report on the first results for Li7 based on the next-to-next-to-leading order chiral nuclear interaction. Both two-nucleon and three-nucleon interactions are taken into account. We show that the p-shell nuclei are sensitive to the subleading parts of the chiral interactions including three-nucleon forces. Though chiral interactions are soft, we do not observe overbinding for this p-shell nucleus and find a realistic description for the binding energy, excitation spectrum, and radius. © 2006 The American Physical Society.
• Stetcu, I., Barrett, B. R., Navrátil, P., & Vary, J. P. (2006). Long- and short-range correlations in the ab-initio no-core shell model. Physical Review C - Nuclear Physics, 73(3).
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  Abstract: In the framework of the ab-initio no-core shell model (NCSM), we describe the longitudinal-longitudinal distribution function, part of the inclusive (e,e') longitudinal response. In the two-body cluster approximation, we compute the effective operators consistent with the unitary transformation used to obtain the effective Hamiltonian. When short-range correlations are probed, the results display independence from the model space size and length scale. Long-range correlations are more difficult to model in the NCSM and they can be des-cribed only by increasing the model space or increasing the cluster size. In order to illustrate the model space independence for short-range observables, we present results for a large set of model spaces for He4, and in 0-4 Ω model spaces for C12. © 2006 The American Physical Society.
• Barrett, B. R. (2005). Effective operators in nuclear-structure calculations. Journal of Physics: Conference Series, 20(1), 48-50.
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  Abstract: A brief review of the history of the use of many-body perturbation theory to determine effective operators for shell-model calculations, i.e., for calculations in truncated model spaces, is given, starting with the ground-breaking work of Arima and Horie for electromagnetic moments. The problems encountered in utilizing this approach are discussed. New methods based on unitary-transformation approaches are introduced and analyzed. The old problems persist, but the new methods allow us to obtain a better insight into the nature of the physics involved in these processes. © 2005 IOP Publishing Ltd.
• Barrett, B. R. (2005). Theoretical approaches to many-body perturbation theory and the challenges. Journal of Physics G: Nuclear and Particle Physics, 31(8), S1349-S1355.
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  Abstract: A brief review of the history of many-body perturbation theory (MBPT) and its applications in nuclear physics is given. Problems regarding its application to nuclear-structure calculations are discussed and analysed. It is concluded that the usefulness of nuclear MBPT in terms of an expansion in the nuclear reaction matrix G for the calculation of effective interactions in shell-model investigations is severely challenged and restricted by the problems and uncertainties connected with this approach. New methods based on unitary transformation approaches have proven to be more accurate and reliable, particularly for light nuclei. © 2005 IOP Publishing Ltd.
• Barrett, B. R., Cardamone, D. M., & Stafford, C. A. (2005). Exactly solvable model for the decay of superdeformed nuclei. International Journal of Modern Physics E, 14(1), 157-164.
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  Abstract: The history and importance of superdeformation in nuclei is briefly discussed. A simple two-level model is then employed to obtain an elegant expression for the branching ratio for the decay via. the E1 process in the normal-deformed band of superdeformed nuclei. From this expression, the spreading width Γ↓ for superdeformed decay is found to be determined completely by experimentally known quantities. The accuracy of the two-level approximation is verified by considering the effects of other normal-deformed states. Furthermore, by using a statistical model of the energy levels in the normal-deformed well, we can obtain a probabilistic expression for the tunneling matrix element V. © World Scientific Publishing Company.
• Barrett, B. R., Navrátil, P., Nogga, A., Ormand, W. E., Stetcu, I., Vary, J. P., & Zhan, H. (2005). Ab initio large-basis no-core shell model. AIP Conference Proceedings, 769, 1257-1262.
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  Abstract: We discuss the motivation, theory, and formulation of the ab initio No-Core Shell Model (NCSM). In this method the effective Hamiltonians are derived microscopically from realistic nucleon-nucleon (NN) and theoretical three-nucleon (NNN)potentials, as a function of the finite harmonic-oscillator (HO) basis space. We present converged results for the A = 3 and 4 nucleon systems, which are in agreement with results obtained by other exact methods, followed by results for p-shell nuclei. Binding energies, rms radii, excitation spectra, and electromagnetic properties are discussed. The favorable comparison with available data is a consequence of the underlying NN and NNN interactions rather than a phenomenological fit. © 2005 American Institute of Physics.
• Stetcu, I., Barrett, B. R., Navrátil, P., & Johnson, C. W. (2005). Electromagnetic transitions with effective operators. International Journal of Modern Physics E, 14(1), 95-103.
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  Abstract: In the no-core shell model formalism we compute effective one- and two-body operators, using the Lee-Suzuki procedure within the two-body cluster approximation. We evaluate the validity of the latter through calculations in reduced model spaces. In particular, we test the results for the two-body system and find that indeed the effective operators in the reduced space reproduce the expectation values or transition strengths computed in the full space. On the other hand, the renormalization for operators in the case of 6Li is very weak, suggesting the need for higher-body clusters in computing the effective interaction. © World Scientific Publishing Company.
• Stetcu, I., Barrett, B. R., Navrátil, P., & Vary, J. P. (2005). Effective operators in the NCSM formalism. European Physical Journal A, 25(SUPPL. 1), 489-490.
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  Abstract: No-core shell model (NCSM) calculations using ab initio effective interactions are very successful in reproducing the experimental nuclear spectra. While a great deal of work has been directed toward computing effective interactions from bare nucleon-nucleon (NN) and three-nucleon forces, less progress has been made in calculating the effective operators. Thus, except for the relative kinetic energy, the proton radius, and the NN pair density, all investigations have used bare operators. We apply the Lee-Suzuki procedure to general one-body operators, investigating the importance of the approximations involved. In particular we concentrate on the limitations of the two-body cluster approximation. © Società Italiana di Fisica and Springer-Verlag 2005.
• Stetcu, I., Barrett, B. R., Navrátil, P., & Vary, J. P. (2005). Effective operators within the ab initio no-core shell model. Physical Review C - Nuclear Physics, 71(4).
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  Abstract: We implement an effective operator formalism for general one- and two-body operators, obtaining results consistent with the no-core shell model (NCSM) wave functions. The Argonne V8' nucleon-nucleon potential was used in order to obtain realistic wave functions for 4He, 6Li, and 12C. In the NCSM formalism, we compute electromagnetic properties using the two-body cluster approximation for the effective operators and obtain results which are sensitive to the range of the bare operator. To illuminate the dependence on the range, we employ a Gaussian two-body operator of variable range, finding weak renormalization of long range operators (e.g., quadrupole) in a fixed model space. This is understood in terms of the two-body cluster approximation which accounts mainly for short-range correlations. Consequently, short-range operators, such as the relative kinetic energy, will be well renormalized in the two-body cluster approximation. © 2005 The American Physical Society.
• Vary, J. P., Atramentov, O. V., Barrett, B. R., Hasan, M., Hayes, A. C., Lloyd, R., Mazur, A. I., Navráti, P., Negoita, A. G., Nogga, A., Ormand, W. E., Popescu, S., Shehadeh, B., Shirokov, A. M., Spence, J. R., Stetcu, I., Stoica, S., Weber, T. A., & Zaytsev, S. A. (2005). Ab initio no-core shell model for light nuclei and other applications. Journal of Physics: Conference Series, 20(1), 71-76.
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  Abstract: The ab initio No-Core Shell Model (NCSM) begins with an intrinsic Hamiltonian for all nucleons in the nucleus. Realistic two-nucleon and tri-nucleon interactions are incorporated such as those recently developed from effective-field theory and chiral perturbation theory. We then derive a finite basis-space dependent Hermitian effective Hamiltonian that conserves all the symmetries of the initial Hamiltonian. The resulting finite Hamiltonian matrix problem is solved by diagonalization on parallel computers. Applications range from light nuclei to multiquark systems and, recently, to quantum-field theory including systems with bosons. We present this approach with a sample of recent results. © 2005 IOP Publishing Ltd.
• Vary, J. P., Atramentov, O. V., Barrett, B. R., Hasan, M., Hayes, A. C., Lloyd, R., Mazur, A. I., Navrátil, P., Negoita, A. G., Nogga, A., Ormand, W. E., Popescu, S., Shehadeh, B., Shirokov, A. M., Spence, J. R., Stetcu, I., Stoica, S., Weber, T. A., & Zaytsev, S. A. (2005). Ab initio no-core shell model - Recent results and future prospects. European Physical Journal A, 25(SUPPL. 1), 475-480.
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  Abstract: The ab initio No-Core Shell Model (NCSM) adopts an intrinsic Hamiltonian for all nucleons in the nucleus. Realistic two-nucleon and tri-nucleon interactions are incorporated. From this Hamiltonian, an Hermitian effective Hamiltonian is derived for a finite basis space conserving all the symmetries of the initial Hamiltonian. The resulting finite sparse matrix problem is solved by diagonalization on parallel computers. Applications range from light nuclei to multiquark systems and, recently, to similar problems in quantum field theory. We present this approach with a sample of recent results. © Società Italiana di Fisica / Springer-Verlag 2005.
• Barrett, B. R., Navrátil, P., Nogga, A., Ormand, W. E., & Vary, J. P. (2004). No-core shell-model calculations in light nuclei with three-nucleon forces. Nuclear Physics A, 746(1-4 SPEC.ISS.), 579c-582c.
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  Abstract: The ab initio No-Core Shell Model (NCSM) has recently been expanded to include nucleon-nucleon (NN) and three-nucleon (3N) interactions at the three-body cluster level. Here it is used to predict binding energies and spectra of p-shell nuclei based on realistic NN and 3N interactions. First results show that NN plus 3N interactions based on chiral perturbation theory lead to a realistic description of 6Li. © 2004 Elsevier B.V. All rights reserved.
• Nogga, A., Epelbaum, E., Navrátil, P., Glöckle, W., Kamada, H., Meißner, U., Witała, H., Barrett, B. R., & Vary, J. P. (2004). Probing chiral interactions in light nuclei. Nuclear Physics A, 737(SUPPL.), 236-240.
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  Abstract: Chiral two- and three-nucleon interactions are studied in few-nucleon systems. We investigate the cut-off dependence and convergence with respect to the chiral expansion. It is pointed out that the spectra of light nuclei are sensitive to the three-nucleon force structure. As an example, we present calculations of the 1+ and 3+ states of 6Li using the no-core shell model approach. The results show contributions of the next-to-next-to leading order terms to the spectra, which are not correlated to the three-nucleon binding energy prediction. © 2004 Elsevier B.V. All rights reserved.
• Vary, J. P., Barrett, B. R., Lloyd, R., Navrátil, P., Nogga, A., & Ormand, W. E. (2004). Shell model in a first principles approach. Nuclear Physics A, 746(1-4 SPEC.ISS.), 123c-129c.
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  Abstract: We develop and apply an ab-initio approach to nuclear structure. Starting with the NN interaction, that fits two-body scattering and bound state data, and adding a theoretical NNN potential, we evaluate nuclear properties in a no-core approach. For presently feasible no-core model spaces, we evaluate an effective Hamiltonian in a cluster approach which is guaranteed to provide exact answers for sufficiently large model spaces and/or sufficiently large clusters. A number of recent applications are surveyed including an initial application to exotic multiquark systems. © 2004 Elsevier B.V. All rights reserved.
• Zhan, H., Nogga, A., Barrett, B. R., Vary, J. P., & Navrátil, P. (2004). Extrapolation method for the no-core shell model. Physical Review C - Nuclear Physics, 69(3), 034302-1.
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  Abstract: Nuclear many-body calculations are computationally demanding. An estimate of their accuracy is often hampered by the limited amount of computational resources even on present-day supercomputers. We provide an extrapolation method based on perturbation theory, so that the binding energy of a large basis-space calculation can be estimated without diagonalizing the Hamiltonian in this space. The extrapolation method is tested for 3H and 6Li nuclei. It will extend our computational abilities significantly and allow for reliable error estimates.
• Aroua, S., Navrátil, P., Zamick, L., Fayache, M. S., Barrett, B. R., Vary, J. P., & Heyde, K. (2003). Allowed Gamow-Teller excitations from the ground state of ¹⁴N. Nuclear Physics A, 720(1-2), 71-83.
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  Abstract: Motivated by the proposed experiment 14N(d,2He) 14C, we study the final states which can be reached via the allowed Gamow-Teller mechanism. Much emphasis has been given in the past to the fact that the transition matrix element from the Jπ=1+, T=0 ground state of 14N to the Jπ=0+, T=1 ground state of 14C is very close to zero, despite the fact that all the quantum numbers are right for an allowed transition. We discuss this problem, but, in particular, focus on the excitations to final states with angular momenta 1+ and 2+. We note that the summed strength to the Jπ=2+, T=1 states, calculated with a wide variety of interactions, is significantly larger than that to the Jπ=1+, T=1 final states. We investigate the relative influences of the two-particle spin-orbit and tensor forces. © 2003 Published by Elsevier Science B.V.
• Cardamone, D. M., Stafford, C. A., & Barrett, B. R. (2003). How to Measure the Spreading Width for the Decay of Superdeformed Nuclei. Physical Review Letters, 91(10), 1025021-1025024.
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  PMID: 14525475;Abstract: A new expression for the branching ratio for the decay via the E1 process in the normal-deformed band of superdeformed nuclei was presented within a simple two-level model. The tunneling matrix element V from the measured value of γ↓ and a statistical model of the energy levels was also determined. The accuracy of two-level approximation was verified by considering the effects of the normal-deformed states.
• Barrett, B. R., Navratil, P., & Vary, J. P. (2002). Large-basis no-core shell model. Nuclear Physics A, 704(1-4), 254c-263c.
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  Abstract: We discuss both the translationally invariant and the standard formulation of the nocore shell-model approach. In this ab initio method the effective Hamiltonians are derived microscopically from realistic nucleon-nucleon (NN) potentials as a function of the finite harmonic-oscillator (HO) basis space. We present results for three and four nucleon systems interacting by the CD-Bonn or several other NN potentials in model spaces that include up to 50ℏΩ and 18ℏΩ HO excitations, respectively. Our results for these light systems are in agreement with results obtained by other exact methods. Also, we calculate properties of 12C using the CD-Bonn and the Argonne V8' NN potentials for model spaces up to 5ℏΩ. Binding energies, rms radii, excitation spectra and electromagnetic properties are discussed. The favorable comparison with available data is a consequence of the underlying NN interaction rather than a phenomenological fit.
• Barrett, B. R., Navrátil, P., Ormand, W. E., & Vary, J. P. (2002). Ab initio large-basis No-Core Shell Model and its application to light nuclei. Acta Physica Polonica B, 33(1), 297-311.
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  Abstract: We discuss the ab initio No-Core Shell Model (NCSM). In this method the effective Hamiltonians are derived microscopically from realistic nucleon-nucleon (NN) potentials, such as the CD-Bonn and the Argonne AV18 NN potentials, as a function of the finite Harmonic Oscillator (HO) basis space. We present converged results, i.e., up to 50ℏΩ and 18ℏΩ HO excitations, respectively, for the A = 3 and 4 nucleon systems. Our results for these light systems are in agreement with results obtained by other exact methods. We also calculate properties of 6Li and 6He in model spaces up to 10ℏΩ and of 12C up to 6ℏΩ. Binding energies, rms radii, excitation spectra and electromagnetic properties are discussed. The favorable comparison with available data is a consequence of the underlying NN interaction rather than a phenomenological fit.
• Cardamone, D. M., Stafford, C. A., & Barrett, B. R. (2002). Coherence and decoherence in tunneling between quantum dots. Physica Status Solidi (B) Basic Research, 230(2), 419-423.
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  Abstract: Coupled quantum dots are an example of the ubiquitous quantum double potential well. In a typical transport experiment, each quantum dot is also coupled to a continuum of states. Our approach takes this into account by using a Green's function formalism to solve the full system. The time-dependent solution is then explored in different limiting cases. In general, a combination of coherent and incoherent behavior is observed. In the case that the coupling of each dot to the macroscopic world is equal, however, the time evolution is purely coherent.
• Deveikis, A., Kalinauskas, R. K., & Barrett, B. R. (2002). Calculation of coefficients of fractional parentage for large-basis harmonic-oscillator shell model. Annals of Physics, 296(2), 287-298.
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  Abstract: A new procedure for large-scale calculations of the coefficients of fractional parentage (CFPs) for a single j-orbit with isospin is presented. The approach is based on a simple enumeration scheme for antisymmetric A-particle states and an efficient method for constructing the eigenvectors of an idempotent matrix. We investigate the characteristics of the introduced CFP basis and the application of this procedure to the ab initio harmonic-oscillator shell-model approach. The results of CFP calculations for the j = 1/2, ⋯, 41/2 orbits are presented (the full sets of one-particle and two-particle CFPs up to the j = 9/2 orbit are obtained). The new computer code for calculation of the CFPs proves to be very quick, efficient, and numerically stable and produces results possessing only small numerical uncertainties. © 2002 Elsevier Science (USA).
• Marsden, D. C., Navrátil, P., Coon, S. A., & Barrett, B. R. (2002). Feasibility study of a three-nucleon force in the no-core shell model: ³H binding energy. Physical Review C - Nuclear Physics, 66(4), 440071-4400711.
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  Abstract: We investigate the three-nucleon system with a realistic nucleon-nucleon potential and the Tucson-Melbourne (TM) two-pion exchange three-body interaction using a translationally invariant harmonic oscillator basis. In the calculations, the no-core shell-model two-body effective interaction replaces the nucleon-nucleon potential, while the three-nucleon interaction is added without any renormalization. We study the convergence of the approach by changing the basis size. Also the dependence of the binding energies on the TM cutoff parameter Λ is examined. The results show promise for the construction of three-body effective interactions including a three-nucleon interaction, for use in future ab initio no-core shell-model nuclear structure calculations for A > 3 systems.
• Nogga, A., Kamada, H., Glöckle, W., & Barrett, B. R. (2002). The α particle based on modern nuclear forces. Physical Review C - Nuclear Physics, 65(5), 540031-5400318.
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  Abstract: The Faddeev-Yakubovsky equations for the a particle are solved. Accurate results are obtained for several modern nucleon-nucleon (NN) interaction models, which include charge-symmetry breaking effects in the NN force, nucleon mass dependences as well as the Coulomb interaction. These models are augmented by three-nucleon forces of different types and adjusted to the 3N binding energy. Our results are close to the experimental binding energy with a slight overbinding. Thus there is only little room left for the contribution of possible 4N interactions to the α-particle binding energy. We also discuss model dependences of the binding energies and the wave functions.
• Kamada, H., Nogga, A., Glöckle, W., Hiyama, E., Kamimura, M., Varga, K., Suzuki, Y., Viviani, M., Kievsky, A., Rosati, S., Carlson, J., Pieper, S. C., Wiringa, R. B., Navrátil, P., Barrett, B. R., Barnea, N., Leidemann, W., & Orlandini, G. (2001). Benchmark test calculation of a four-nucleon bound state. Physical Review C - Nuclear Physics, 64(4), 440011-440018.
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  Abstract: In the past, several efficient methods have been developed to solve the Schrödinger equation for four-nucleon bound states accurately. These are the Faddeev-Yakubovsky, the coupled-rearrangement-channel Gaussian-basis variational, the stochastic variational, the hyperspherical variational, the Green's function Monte Carlo, the no-core shell model, and the effective interaction hyperspherical harmonic methods. In this article we compare the energy eigenvalue results and some wave function properties using the realistic AV8′ NN interaction. The results of all schemes agree very well showing the high accuracy of our present ability to calculate the four-nucleon bound state.
• Kamuntavičius, G., Kalinauskas, R. K., Barrett, B. R., Mickevičius, S., & Germanas, D. (2001). The general harmonic-oscillator brackets: Compact expression, symmetries, sums and Fortran code. Nuclear Physics A, 695(1-4), 191-201.
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  Abstract: We present a very simple expression and a Fortran code for the fast and precise calculation of three-dimensional harmonic-oscillator transformation brackets. The complete system of symmetries for the brackets along with analytical expressions for sums containing products of two and three brackets is given. © 2001 Elsevier Science B.V.
• Navrátil, P., Vary, J. P., Ormand, W. E., & Barrett, B. R. (2001). Six-nucleon spectroscopy from a realistic nonlocal hamiltonian. Physical Review Letters, 87(17), 1725021-1725024.
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  PMID: 11690268;Abstract: Ab initio no-core nuclear shell model was used to solve a six-nucleon system interacting by realistic nucleon-nucleon potentials. The effective interaction was obtained from the decoupling condition between the model space and the excluded space for the two-nucleon transformed Hamiltonian. A semirealistic Minnesota (MN) potential was used to test the proposed method. Comparison of calculated Li spectra with experimental results showed slip-flip transitions to be concentrated at about 4 MeV.
• Diallo, A. F., Barrett, B. R., Navrátil, P., & Gorrichategui, C. (2000). The spdf IBA analytical description of odd parity states in the actinide region. Annals of Physics, 279(1), 81-103.
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  Abstract: An extension of the IBA 1/Λ asymptotic scheme to the description of odd parity states via the introduction of odd l bosons in the condensate is presented. The new features that are thereby introduced into the system are highlighted and the advantages of using such an approach are discussed. A standard minimization routine is used to determine the structure coefficients for the wavefunctions of the system and to obtain a fit to the spectra and the electromagnetic transition rates of 11 nuclei in the actinide region with a rather small number of variable parameters, namely the single-particle energies and the multipole interaction strengths. Reasonable results are obtained and are compared to the results of exact numerical calculations and earlier 1/N calculations. © 2000 Academic Press.
• Navratil, P., Vary, J. P., & Barrett, B. R. (2000). Properties of¹²C in the Ab Initio nuclear shell model. Physical Review Letters, 84(25), 5728-5731.
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  PMID: 10991040;Abstract: We obtain properties of 12C in the ab initio no-core nuclear shell model. The effective Hamiltonians are derived microscopically from the realistic CD Bonn and the Argonne V8I nucleon-nucleon (NN) potentials as a function of the finite harmonic oscillator basis space. Binding energies, excitation spectra, and electromagnetic properties are presented for model spaces up to 5Ω. The favorable comparison with available data is a consequence of the underlying NN interaction rather than a phenomenological fit. © 2000 The American Physical Society.
• Navrátil, P., Kamuntavičius, G., & Barrett, B. R. (2000). Few-nucleon systems in a translationally invariant harmonic oscillator basis. Physical Review C - Nuclear Physics, 61(4), 440011-4400116.
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  Abstract: We present a translationally invariant formulation of the no-core shell model approach for few-nucleon systems. We discuss a general method of antisymmetrization of the harmonic-oscillator (HO) basis depending on Jacobi coordinates. The use of a translationally invariant basis allows us to employ larger model spaces than in traditional shell-model calculations. Moreover, in addition to two-body effective interactions, three-or higher-body effective interactions as well as real three-body interactions can be utilized. In the present study we apply the formalism to solve three and four nucleon systems interacting by the CD-Bonn nucleon-nucleon (NN) potential in model spaces that include up to 34ℏΩ and 16ℏΩ HO excitations, respectively. Results of ground-state as well as excited-state energies, rms radii, and magnetic moments are discussed. In addition, we compare charge form factor results obtained using the CD-Bonn and Argonne V8′ NN potentials.
• Navrátil, P., Vary, J. P., & Barrett, B. R. (2000). Large-basis ab initio no-core shell model and its application to ¹²C. Physical Review C - Nuclear Physics, 62(5), 543111-543114.
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  Abstract: We present the framework for the ab initio no-core nuclear shell model and apply it to obtain properties of 12C. We derive two-body effective interactions microscopically for specific model spaces from the realistic CD-Bonn and the Argonne V8' nucleon-nucleon (NN) potentials. We then evaluate binding energies, excitation spectra, radii, and electromagnetic transitions in the 0ℏΩ, 2ℏΩ£l, and 4ℏΩ model spaces for the positive-parity states and the 1ℏΩ, 3ℏΩ, and 5ℏΩ model spaces for the negative-parity states. Dependence on the model-space size, on the harmonic-oscillator frequency, and on the type of the NN potential, used for the effective interaction derivation, are studied. In addition, electromagnetic and weak neutral elastic charge form factors are calculated in the impulse approximation. Sensitivity of the form-factor ratios to the strangeness one-body form-factor parameters and to the influence of isospin-symmetry violation is evaluated and discussed. Agreement between theory and experiment is favorable for many observables, while others require yet larger model spaces and/or three-body forces. The limitations of the present results are easily understood by virtue of the trends established and previous phenomenological results.
• Barrett, B. R. (1999). Effective operators in shell-model calculations. Czechoslovak Journal of Physics, 49(1), 1-34.
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  Abstract: After a brief review of the properties of the nucleon-nucleon interaction and of basic shell-model theory, the microscopic theory for determining effective interactions and operators for use in shell-model calculations is given. Difficulties in applying the usual formalism are discussed. Finally, a new large-basis, no-core shell-model approach is presented, which is able to handle these difficulties.
• Barrett, B. R., Kuyucak, S., Navrátil, P., & Isacker, P. V. (1999). Is there a proton-neutron interacting boson model rule for M1 properties?. Physical Review C - Nuclear Physics, 60(3), 373021-373024.
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  Abstract: We investigate the robustness of the purported correlation between the g-factor ratios in the y and ground bands and the corresponding E2/M1 mixing ratios in the proton-neutron interacting boson model. We show that this correlation is dependent on the choice of the Hamiltonian and can be transgressed, when the parameters are chosen appropriately. The recent M1 data in 168Er, which do not exhibit such a correlation, are analyzed in the light of these results.
• Davis, E. D., Barrett, B. R., & Diallo, A. F. (1999). Importance of the hexadecapole-hexadecapole interaction. Physical Review C - Nuclear Physics, 59(1), 200-209.
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  Abstract: Motivated by the sensitivity of collective M 1 excitations to the hexadecapole-hexadecapole interaction, we explore the influence of this and other features of sdgIBM on the ground-state band properties of deformed rare-earth nuclei. We adopt microscopically motivated choices of the Hamiltonian parameters and work within the angular-momentum-projected intrinsic state formalism, deriving analytic expressions for observables in which the dependence on wave functions and parameters of the model is explicit. We find that energies of ground-state band excitations are insensitive to the hexadecapole-hexadecapole interaction. On the other hand, its contribution to the deformation energy term in the nuclear binding energy is substantial. Our results indicate that angular momentum projection is important even for well-deformed nuclei and that at least two g bosons should be utilized in the corresponding sdgIBM calculations.
• Kamuntavičius, G., Navrátil, P., Barrett, B. R., Sapragonaite, G., & Kalinauskas, R. K. (1999). Isoscalar Hamiltonians for light atomic nuclei. Physical Review C - Nuclear Physics, 60(4), 443041-4430411.
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  Abstract: The charge-dependent realistic nuclear Hamiltonian for a nucleus, composed of neutrons and protons, can be successfully approximated by a charge-independent one. The parameters of such a Hamiltonian, i.e., the nucleon mass and the NN potential, depend upon the mass number A, charge Z, and isospin quantum number T of state of the studied nucleus.
• Navrátil, P., & Barrett, B. R. (1999). Four-nucleon shell-model calculations in a Faddeev-like approach. Physical Review C - Nuclear Physics, 59(4), 1906-1918.
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  Abstract: We use equations for Faddeev amplitudes to solve the shell-model problem for four nucleons in a model space that includes up to 14ℏΩ harmonic-oscillator excitations above the unperturbed ground state. Two- and three-body effective interactions derived from the Reid93 and Argonne V8' nucleon-nucleon potentials are used in the calculations. Binding energies, excitation energies, point-nucleon radii, and electromagnetic and strangeness charge form factors for 4He are studied. The structure of the Faddeev-like equations is discussed and a formula for the matrix elements of the permutation operators in a harmonic-oscillator basis is given. The dependence on harmonic-oscillator excitations allowed in the model space and on the harmonic-oscillator frequency is investigated. It is demonstrated that the use of three-body effective interactions improves the convergence of the results.
• Navrátil, P., Barrett, B. R., & Glöckle, W. (1999). Spurious states in the Faddeev formalism for few-body systems. Physical Review C - Nuclear Physics, 59(2), 611-616.
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  Abstract: We discuss the appearance of spurious solutions of few-body equations for Faddeev amplitudes. The identification of spurious states, i.e., states that lack the symmetry required for solutions of the Schrödinger equation, as well as the symmetrization of the Faddeev equations is investigated. As an example, systems of three and four electrons, bound in a harmonic-oscillator potential and interacting by the Coulomb potential, are presented.
• Orosa, A. M., Heyde, K., Coster, C. D., Decroix, B., Wyss, R., Barrett, B. R., & Navratil, P. (1999). Shape coexistence in the light Po isotopes. Nuclear Physics A, 645(1), 107-142.
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  Abstract: The systematics of the even light Po isotopes (N ≤ 126) are studied in the framework of the Particle-Core Model. The strong perturbation of the systematics in the very light isotopes is interpreted as arising from the interaction between regular and intruder structures. Results of Potential Energy Surface (PES) calculations and predictions of the Pairing Vibration Model support this interpretation. The mixing between the regular and intruder structures is studied within the IBM-2 and in a simple two-state mixing picture. Matrix elements of the interaction and their spin dependence are extracted. The 'reconstructed systematics' show the coexistence of a spherical structure, which varies little with the neutron number, with an intruder band, strongly lowered in energy as the neutron number approaches midshell. The crossing of the two configurations takes place over a few isotopes; the intruder band becomes the ground-state configuration in 192Po. © 1999 Elsevier Science B.V.
• Stafford, C. A., & Barrett, B. R. (1999). Simple model for decay of superdeformed nuclei. Physical Review C - Nuclear Physics, 60(5), 513051-513054.
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  Abstract: Recent theoretical investigations of the decay mechanism out of a superdeformed nuclear band have yielded qualitatively different results, depending on the relative values of the relevant decay widths. We present a simple two-level model for the dynamics of the tunneling between the superdeformed and normal-deformed bands, which treats decay and tunneling processes on an equal footing. The previous theoretical results are shown to correspond to coherent and incoherent limits of the full tunneling dynamics. Our model accounts for experimental data in both the A ∼ 150 mass region, where the tunneling dynamics are coherent, and in the A ∼ 190 mass region, where the tunneling dynamics are incoherent.
• Barrett, B. R., Navrátil, P., & Ormand, W. E. (1998). Large-basis no-core shell-model calculations and their application to ¹⁰C →¹⁰B fermi beta decay. Czechoslovak Journal of Physics, 48(6-7), 691-696.
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  Abstract: We use a 4Ω shell-model calculation with a two-body effective interaction derived microscopically from the Reid93 potential to calculate the isospin-mixing correction for the 10C→10B superallowed Fermi transition. The effective interaction takes into account the Coulomb potential as well as the charge dependence of T = 1 partial waves. Our results suggest the isospin-mixing correction δC ≈ 0.1%, which is compatible with previous calculations obtained by other methods. The obtained δC correction is about a factor of four too small to obtain unitarity of the Cabibbo-Kobayashi-Maskawa matrix with the present experimental data.
• Navrátil, P., & Barrett, B. R. (1998). Large-basis shell-model calculations for p-shell nuclei. Physical Review C - Nuclear Physics, 57(6), 3119-3128.
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  Abstract: Results of large-basis shell-model calculations for nuclei with A = 7-11 are presented. The effective interactions used in the study were derived microscopically from the Reid93 potential and take into account the Coulomb potential as well as the charge dependence of T = 1 partial waves. For A = 7, a 6ℏΩ model space was used, while for the rest of the studied nuclides, the calculations were performed in a 4ℏΩ model space. It is demonstrated that the shell model combined with microscopic effective interactions derived from modern nucleon-nucleon potentials is capable of providing good agreement with the experimental properties of the ground state as well as with those of the low-lying excited states.
• Navrátil, P., & Barrett, B. R. (1998). Shell-model calculations for the three-nucleon system. Physical Review C - Nuclear Physics, 57(2), 562-568.
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  Abstract: We use Faddeev's decomposition to solve the shell-model problem for three nucleons. The dependence on harmonic-oscillator excitations allowed in the model space, up to 32ℏΩ in the present calculations, and on the harmonic-oscillator frequency is studied. Effective interactions derived from Nijmegen II and Reid93 potentials are used in the calculations. The binding energies obtained are close to those calculated by other methods. The structure of the Faddeev equations is discussed and a simple formula for matrix elements of the permutation operators in a harmonic-oscillator basis is given. The Pauli principle is properly treated in the calculations.
• Thoresen, M., Navrátil, P., & Barrett, B. R. (1998). Comparison of techniques for computing shell-model effective operators. Physical Review C - Nuclear Physics, 57(6), 3108-3118.
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  Abstract: Different techniques for calculating effective operators within the framework of the shell model using the same effective interaction and the same excitation spaces are presented. Starting with the large-basis no-core approach, we compare the time-honored perturbation-expansion approach and a model-space truncation approach. Results for the electric quadrupole and magnetic dipole operators are presented for 6Li. The convergence trends and dependence of the effective operators on differing excitation spaces and Pauli Q-operators are studied. In addition, the dependence of the electric-quadrupole effective charge on the harmonic-oscillator frequency and the mass number, for A = 5,6, is investigated in the model-space truncation approach.
• Weidenmüller, H., Brentano, P. V., & Barrett, B. R. (1998). Spreading width for decay out of a superdeformed band. Physical Review Letters, 81(17), 3603-3606.
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  Abstract: The attenuation factor F responsible for the decay out of a superdeformed (SD) band is calculated with the help of a statistical model. This factor is given by F = (1 + Γ↓/ΓS)-1. Here, ΓS is the width for the collective E2 transition within the superdeformed band, and Γ↓ is the spreading width which describes the mixing between a state in the SD band and the normally deformed (ND) states of equal spin. The attenuation factor F is independent of the statistical E1 decay widths ΓN of the ND states provided that ΓN ≫ Γ↓, ΓS. This condition is generically met. Previously measured values of F are used to determine Γ↓.
• Navrátil, P., Barrett, B. R., & Ormand, W. E. (1997). Large-basis shell-model calculation of the ¹⁰C→¹⁰B Fermi matrix element. Physical Review C - Nuclear Physics, 56(5), 2542-2548.
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  Abstract: We use a 4ℏΩ shell-model calculation with a two-body effective interaction derived microscopically from the Reid93 potential to calculate the isospin-mixing correction for the 10C→10B superallowed Fermi transition. The effective interaction takes into account the Coulomb potential as well as the charge dependence of T = 1 partial waves. Our results suggest the isospin-mixing correction δC≈0.1%, which is compatible with previous calculations. The correction obtained in those calculations, performed in a 0ℏΩ space, was dominated by deviation from unity of the radial overlap between the converted proton and the corresponding neutron. In the present calculation this effect is accommodated by the large model space. The obtained δC correction is about a factor of 4 too small to obtain unitarity of the Cabibbo-Kobayashi-Maskawa matrix with the present experimental data.
• Navrátil, P., Thoresen, M., & Barrett, B. R. (1997). Microscopic origins of effective charges in the shell model. Physical Review C - Nuclear Physics, 55(2), R573-R576.
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  Abstract: We use a large-scale 6(Latin small letter h with stroke)Ω calculation for 6Li with microscopically derived two-body interaction to construct the 0(Latin small letter h with stroke)Ω 0p shell effective Hamiltonian, electric quadrupole, and magnetic dipole operators. While the E2 and M1 6(Latin small letter h with stroke)Ω operators are one-body operators with free nucleon charges, the effective operators are two-body operators with substantially different renormalization for the isoscalar and isovector matrix elements, especially for the E2 operator. We show that these operators can be very well approximated by one-body operators provided that effective proton and neutron charges are used. The obtained effective charges are compatible with those used in phenomenological shell-model studies. The two-body part of the effective operators is estimated.
• Davis, E. D., Diallo, A. F., & Barrett, B. R. (1996). g boson and systematics of the M1 scissors mode. Physical Review C - Nuclear Physics, 53(6), 2849-2854.
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  Abstract: We discuss systematics of the M1 scissors mode within the interacting boson model when the g-boson degree of freedom is included explicitly and microscopically motivated choices of model parameters are adopted. We try to relate the M1 centroid energy to the energetics of deformation. We conclude that, with the introduction of a hexadecapole-hexadecapole interaction and a g-boson admixture in the ground state of only a few percent, we can obtain reasonable estimates of the M1 centroid energy, without invoking a Majorana interaction. If one takes seriously variations in microscopic estimates of boson g factors, then the summed M1 strength near midshell can be interpreted in terms of boson occupation numbers which saturate.
• Navrátil, P., & Barrett, B. R. (1996). No-core shell-model calculations with starting-energy-independent multivalued effective interactions. Physical Review C - Nuclear Physics, 54(6), 2986-2995.
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  Abstract: Large-space no-core shell-model calculations have been performed for 3H, 4He, 5He, 6Li, and 6He, using a starting-energy-independent two-body effective interaction derived by application of the Lee-Suzuki similarity transformation. This transformation can be performed by direct calculation or by different iteration procedures, which are described. A possible way of reducing the auxiliary potential influence on the two-body effective interaction has also been introduced. The many-body effects have been partially taken into account by employing the recently introduced multivalued effective interaction approach. Dependence of the 5He energy levels on the harmonic-oscillator frequency as well as on the size of the model space has been studied. The Reid 93 nucleon-nucleon potential has been used in the study, but results have also been obtained using the Nijmegen II potential for comparison.
• Navrátil, P., & Barrett, B. R. (1996). Soluble model test of the multi-valued G-matrix effective interaction. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 369(3-4), 193-200.
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  Abstract: The recently proposed multi-valued G-matrix effective interaction is tested in a soluble multi-level monopole-pairing interaction model. To mimic the no-core shell model approach, different effective interactions including the multi-valued G-matrix are calculated in a two-particle space and subsequently applied for the many-particle calculation. The multi-valued G-matrix effective interaction, both starting energy dependent and starting energy independent, is shown to be superior to the single-valued G-matrix. The formalism is extended to effective operators, where a similar conclusion is found.
• Navrátil, P., Barrett, B. R., & Dobeš, J. (1996). M1 properties of tungsten isotopes in the interacting boson model-2. Physical Review C - Nuclear Physics, 53(6), 2794-2800.
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  Abstract: The M1 properties of even 182-186W isotopes are investigated in the interacting boson model-2 (IBM-2). The E2/M1 mixing ratios, g factors, and summed M1 strength are calculated. A least-squares fit of the excitation energies is used to fix the IBM-1 projected Hamiltonian parameters, while the F-spin-breaking terms are adjusted to reproduce the M1 properties of low-lying states. The influence of F-spin mixing on the summed M1 strength is studied using the coherent state technique in perturbation theory. When the standard boson g factors are used, the M1 properties of the low-lying states are described satisfactorily, but the summed M1 strengths are found to be larger than present experimental values. Possible g factor adjustment, which reconciles the calculated and experimental M1 strength, is discussed.
• Thoresen, M., Zheng, D. C., & Barrett, B. R. (1996). Test of shell-model interactions for nuclear structure calculations. Physical Review C - Nuclear Physics, 53(4), 1997-2000.
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  Abstract: The binding energy and excitation spectra of 6Li are calculated in a no-core shell-model space giving encouraging results. The results of this calculation are then treated as a theoretical experiment, against which different effective-interaction approximations are compared. In this way insight into the perturbation expansion for the effective interaction is obtained.
• Halse, P., Isacker, P. V., & Barrett, B. R. (1995). Sum rules for B(M1, 0₁⁺ → 1⁺) strength in IBM-3 and IBM-4. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 363(3), 145-150.
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  Abstract: Sum rules for B(M1, 01+ → 1i+) strength are derived for even-even nuclei in the isospin-invariant forms of the IBM, IBM-3 and IBM-4, in the cases where the respective natural internal symmetries, isospin U(3) and U(6) ⊃ SU(4), are conserved. Subsequently, the total strength is resolved into its component partial sums to the allowed isospins (and SU(4) representations in IBM-4). In cases where the usual IBM dynamical symmetries are also valid, a complete description of all B(M1, 01+ → 1i+) follows. In contrast to IBM-2, there is fragmentation of the strength even in the dynamical symmetry cases, for T ≢ 0, over two states in IBM-3, and over three states in IBM-4. An application to the first half of the sd-shell reveals differences in strength between IBM-4 and the shell model which may also indicate areas for further study in IBM-2 analyses of heavier nuclei.
• Zheng, D. C., Barrett, B. R., Vary, J. P., & Müther, H. (1995). Auxiliary potential in no-core shell-model calculations. Physical Review C, 51(5), 2471-2476.
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  Abstract: The Lee-Suzuki iteration method is used to include the folded diagrams in the calculation of the two-body effective interaction veff(2) between two nucleons in a no-core model space. This effective interaction still depends upon the choice of single-particle basis utilized in the shell-model calculation. Using a harmonic-oscillator single-particle basis and the Reid-soft-core NN potential, we find that veff(2) overbinds He4 in 0, 2, and 4Latin small letter h with strokeΩ model spaces. As the size of the model space increases, the amount of overbinding decreases significantly. This problem of overbinding in small model spaces is due to neglecting effective three- and four-body forces. Contributions of effective many-body forces are suppressed by using the Brueckner-Hartree-Fock single-particle Hamiltonian. © 1995 The American Physical Society.
• Zheng, D. C., Barrett, B. R., Vary, J. P., Haxton, W. C., & Song, C. -. (1995). Large-basis shell model studies of light nuclei with a multivalued G-matrix effective interaction. Physical Review C, 52(5), 2488-2498.
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  Abstract: Large-basis shell model studies of low-lying excitations in light nuclei from He4 to Li7 have been performed with a multivalued G-matrix effective interaction, as recently suggested by Haxton et al. Calculations were performed relative to the vacuum (no core) using very large, separable model spaces containing all excitations with unperturbed energies up to 8Latin small letter h with stroke. Using G matrices derived from a new Nijmegen potential, we achieve a very satisfactory description of these excitations. © 1995 The American Physical Society.
• Barrett, B. R., Davis, E. D., & Diallo, A. F. (1994). Can we do without the Majorana term in the effective nuclear interaction?. Physical Review C, 50(4), 1917-1923.
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  Abstract: We present phenomenological evidence that the strength of the Majorana term necessary to reproduce collective M 1-transition strength data could be significantly smaller than is conventionally assumed and therefore more in line with naive microscopic considerations. We also find that g-boson effects are important to the reproduction of the summed M1 strength. © 1994 The American Physical Society.
• Barrett, B. R., Halse, P., Jaqua, L. M., & Vary, J. P. (1994). Effective interaction calculations: Where do we go from here?. Physics Report, 242(1-3), 85-92.
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  Abstract: After a brief review of effective interaction theory and the problems related to its computation, we discuss some new approaches for calculating the effective shell-model interaction. The goal is to obtain a simple, but useful form for the effective interaction (a la Kuo and Brown).
• Barrett, B. R., Zheng, D. C., Jaqua, L., Vary, J. P., & McCarthy, R. J. (1994). Realistic microscopic calculations for the light nuclei A = 2 to 7. Nuclear Physics, Section A, 570(1-2), 23-30.
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  Abstract: The conventional theory of shell-model effective interactions encounters a divergence in its perturbation expansion owing to intruder states. By enlarging the model space to eliminate the core, and, hence, all core-polarization processes, we circumvent this problem. The perturbation expansion for the effective interaction can then be reasonably expressed in terms of only the Brueckner reaction matrix G in the no-core space plus all folded diagrams. The effective interaction for A = 2 is simply the Brueckner G-matrix. For A > 2 exact results for the eigenenergies are obtained, if the generalized, A-nucleon G matrix can be constructed. For A = 4 to 7, we approximate the A-nucleon G-matrix with the Brueckner G-matrix. Reasonable results can be obtained by treating the starting energy for the G matrix as a variable parameter to fix the binding energy. © 1994.
• Jaqua, L., Halse, P., Barrett, B. R., & Vary, J. P. (1994). Effective shell-model interaction for no-core model spaces. Nuclear Physics, Section A, 571(2), 242-252.
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  Abstract: We discuss the use of the no-core Pauli operator for calculating the effective shell-model interaction. The goal is to obtain a simple, but useful, form of the effective interaction for reproducing low-lying states, thereby reducing the effect of intruder states on these low-lying configurations. The techniques are applied to 4He as a test case. The method seems to converge well with increasing no-core space size. © 1994.
• Zheng, D. C., & Barrett, B. R. (1994). Nuclear shell-model calculations for Li6 and N14 with different NN potentials. Physical Review C, 49(6), 3342-3345.
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  Abstract: Two ''phase-shift equivalent'' local NN potentials with different parametrizations, Reid93 and NijmII, which were found to give nearly identical results for the triton by Friar et al., are shown to yield remarkably similar results for Li6 and N14 in a (0+2)Latin small letter h with strokeΩ no-core space shell-model calculation. The results are compared with those for the widely used Hamada-Johnson hard-core and the original Reid soft-core potentials, which have larger deuteron D-state percentages. The strong correlation between the tensor strength and the nuclear binding energy is confirmed. However, many nuclear structure properties seem to be rather insensitive to the details of the NN potential and, therefore, cannot be used to test various NN potentials. © 1994 The American Physical Society.
• Zheng, D. C., Barrett, B. R., Vary, J. P., & McCarthy, R. J. (1994). Simple approximation for the starting-energy-independent two-body effective interaction with applications to Li6. Physical Review C, 49(4), 1999-2004.
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  Abstract: We apply the Lee-Suzuki iteration method to calculate the linked-folded diagram series for a new Nijmegen local NN potential. We obtain an exact starting-energy-independent effective two-body interaction for a multishell, no-core, harmonic-oscillator model space. It is found that the resulting effective-interaction matrix elements can be well approximated by the Brueckner G-matrix elements evaluated at starting energies selected in a simply way. These starting energies are closely related to the energies of the initial two-particle states in the ladder diagrams. The ''exact'' and approximate effective interactions are used to calculate the energy spectrum of Li6 in order to test the utility of the approximate form. © 1994 The American Physical Society.
• Zheng, D. C., Vary, J. P., & Barrett, B. R. (1994). Large-space shell-model calculations for light nuclei. Physical Review C, 50(6), 2841-2849.
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  Abstract: An effective two-body interaction is constructed from a new Reid-like NN potential for a large no-core space consisting of six major shells and is used to generate the shell-model properties for light nuclei from A=2 to 6. For practical reasons, the model space is partially truncated for A=6. Binding energies and other physical observables are calculated and they compare favorably with experiment. © 1994 The American Physical Society.
• Barfield, A. F., & Barrett, B. R. (1993). High-spin states and superdeformation in the proton-neutron interacting boson model. Nuclear Physics, Section A, 557(C), 551-558.
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  Abstract: The superdeformed band in 192Hg has a similar structure to the ground-state bands in several actinide nuclei, particularly to the uranium isotopes, such as 232U. We report on neutron-proton Interacting Boson Model (IBM-2) calculations for the uranium isotopes and make a specific comparison of the superdeformed band in 192Hg with the ground-state band in 232U. Theoretically these two bands should have the same structure in the Interacting Boson Model, because they contain the same number of active proton bosons and neutron bosons, with the superdeformed band in 192Hg being treated as a 4p-6h excited state in terms of fermions. Results of a no new free parameter IBM-2 configuration mixing calculation for the (0p-2h), (2p-4h) and (4p-6h) configurations in 192Hg are presented. © 1993.
• Barrett, B. R., Zheng, D. C., McCarthy, R. J., & Vary, J. P. (1993). Minimizing effective many-body interactions. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 316(2-3), 219-225.
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  Abstract: A simple two-level model is developed and used to test the properties of effective interactions for performing nuclear structure calculations in truncated model spaces. It is shown that the effective many-body interactions sensitively depend on the choice of the single-particle basis and they appear to be minimized when a self-consistent Hartree-Fock basis is used.
• Diallo, A. F., Davis, E. D., & Barrett, B. R. (1993). An Improved Asymptotic Realization of the Projected Intrinsic State Approximation in IBM. Annals of Physics, 222(2), 159-186.
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  Abstract: We clarify the character of the semi-analytic 1/N-expansion method utilised in otherwise clumbersome studies with the sdg-variant of the interacting boson model. We draw attention to the dynamical foundations of the scheme. We argue that, by respecting the conditions under which use of the asymptotic expansions involved is legitimate, we can hope to learn whether the dynamical assumptions made are appropriate or not. To this end, we show that an ad hoc "gaussian" approximation of previous applications can be avoided without any sacrifice of simplicity. The new asymptotic expansion of the fundamental overlap integral differs in every order beyond leading-order. Nevertheless, we confirm that, to the order of practical interest, the all-important variational functional for the groundstate-band coincides with that employed previously; our demonstration makes explicit the cancellation mechanism. To illustrate the practical advantages of the new scheme, we derive an expression for the gyromagnetic factors of the groundstate-band; it is freed of the deficiencies of the former 1/N-expansion method result. In general, claims that strong variations in an observable unaccounted for by the leading term can be described by higher-order terms are necessarily suspect. © 1993 Academic Press. All rights reserved.
• Jaqua, L., Zheng, D. C., Barrett, B. R., & Vary, J. P. (1993). Effects of the single-particle potential insertions in the effective interaction. Physical Review C, 48(4), 1765-1769.
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  Abstract: We investigate the effects of the single-particle potential insertions in the effective interaction by comparing energy spectra obtained from different treatments of these insertions as a function of the size of the no-core model space. The Brueckner reaction matrix used in the first calculation includes the single-particle insertions in ladder diagrams to all orders, while the Brueckner reaction matrix used in the second calculation only keeps the single-particle potential term in the lowest-order ladder diagram. The two calculations yield almost identical ground-state energies and low-lying excitation spectra for He4 and Li6 for large enough no-core model spaces, indicating that the effects of the single-particle potential insertions in second- and higher-order ladder diagrams are small. We explain the reason for the diminishing role of these insertions with increasing size of the model space. We also show that, through a standard method of instilling a single center-of-mass wave function into all low-lying states, the spurious center-of-mass kinetic-energy term shifts the energies of all the low-lying states by nearly a constant and, therefore, has little effect on the excitation spectrum. © 1993 The American Physical Society.
• Zheng, D. C., Barrett, B. R., Jaqua, L., Vary, J. P., & McCarthy, R. J. (1993). Microscopic calculations of the spectra of light nuclei. Physical Review C, 48(3), 1083-1091.
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  Abstract: We perform large-space shell-model calculations for the low-lying energy spectra of a few light nuceli,4He, He5, Li6, and Li7, in a no-core model space with a realistic effective two-body interaction (Brueckner G matrix). Our G matrices are calculated for the Reid-soft-core potential in a harmonic-oscillator basis. Single-particle ''-U'' insertions are replaced by two-particle ''-U'' insertions and are included in the G-matrix calculations, which sum them to all orders. With the starting energy of the G matrix chosen to give approximately the experimental binding energy, we obtain nuclear energy spectra which are in reasonable agreement with experiment. We also investigate the dependence of our results on the size of the model space and on the harmonic-oscillator basis parameter (Latin small letter h with strokeΩ). © 1993 The American Physical Society.
• Zheng, D. C., Vary, J. P., & Barrett, B. R. (1993). Exact solutions of model hamiltonian problems with effective interactions. Nuclear Physics, Section A, 560(1), 211-222.
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  Abstract: We verify with soluble models that the effective-hamiltonian approach of Lee and Suzuki can be used to obtain all the exact eigenvalues of the full hamiltonian. We propose a new iteration scheme to obtain the effective hamiltonian and demonstrate its convergence properties. © 1993.
• Barrett, B. R., & Otsuka, T. (1992). E0 decays of vibrations in the O(6) limit of the neutron-proton interacting boson model. Physical Review C, 46(5), 1735-1740.
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  Abstract: Expressions are derived for the E0 transition strengths for the symmetric and antisymmetric -vibrational bandhead states to the ground state for O(6)-like nuclei. These E0 transitions are the only ones allowed to the ground state, and we predict them to be of similar magnitude. The isomer shifts for these -vibrational states are also discussed, as well as the isotope shifts for the ground states. We propose the Ba isotopes around A 132 as possible candidates for observing these E0 decays. © 1992 The American Physical Society.
• Barrett, B. R., Casten, R. F., Ginocchio, J. N., Seligman, T., & Weidenm̈ller, H. (1992). Is there incomplete mixing of states with different K quantum numbers in the neutron resonance region?. Physical Review C, 45(4), R1417-R1419.
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  Abstract: A recent publication claimed incomplete mixing of states with different K quantum numbers in the neutron resonance region. We discuss the theoretical implications of such a claim and show that it leads to serious discrepancies with the statistical model. We, therefore, reexamine the experimental data on which such a claim is based. The totality of the evidence invalidates the claim that K mixing in the resonance region is incomplete. © 1992 The American Physical Society.
• Barrett, B. R., Davis, E. D., & Diallo, A. F. (1992). g-boson panacea for magnetic properties of the nuclear groundstate band?. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 295(1-2), 5-10.
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  Abstract: The magnetic moments of excited members of the groundstate band of even-even medium-mass nuclei are considered within the framework of the sdg-version of IBM-2. A novel asymptotic realisation of the variation-after-(angular-momentum)-projection Hartree-Bose approximation is employed. The introduction of an explicit g-boson degree of freedom is found not to resolve the discrepancy between the values of the d-boson g-factors required phenomenologically and those expected microscopically. Further study of the microscopic underpinning of the g-boson and improved experimental data are required to clarify matters: a promising testing ground would appear to be the Hf-Pt nuclei. Neither the present asymptotic realisation nor its predecessor (the "1/N-scheme") are appropriate when strong variations of magnetic moments within a groundstate band are encountered.
• Jaqua, L., Hasan, M. A., Vary, J. P., & Barrett, B. R. (1992). Kinetic-energy operator in the effective shell-model interaction. Physical Review C, 46(6), 2333-2339.
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  Abstract: Differences in the Hartree-Fock and effective shell-model interaction arising from alternative treatments of the kinetic-energy operator in finite nuclear many-body problems are described. The Hartree-Fock single-particle energies and their relationship to experimental removal energies depend sensitively on whether or not the center-of-mass kinetic energy is retained in the nuclear Hamiltonian. Large effects in particle-hole energies are obtained which have important consequences for effective shell-model Hamiltonians. If the center-of-mass contribution of the kinetic-energy operator is removed from the Hamiltonian, substantial effects appear in a simple example of the shell-model spectra of O16 and O17 treated as four and five valence nucleons, respectively, outside a C12 core. The contributions to the energy coming from the valence, relative kinetic-energy operator push the energy spectra of both nuclei up by about 1 MeV relative to their ground states. © 1992 The American Physical Society.
• Barfield, A. F., & Barrett, B. R. (1991). Multiparticle-multihole configuration mixing within the neutron-proton interacting boson model. Physical Review C, 44(4), 1454-1459.
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  Abstract: The method of configuration mixing within the neutron-proton interacting boson model has been expanded to consider the simultaneous mixing of several multiparticle-multihole configurations, obtained by exciting pairs of protons and/or neutrons across major shell gaps. The determination of parameters to be employed for each configuration is discussed, along with methods for choosing the multiparticle-multihole excitation energies. As a test, the method is applied to the nucleus Hg192. © 1991 The American Physical Society.
• Barrett, B. R., Dracoulis, G. D., & Bark, R. A. (1991). Intruder bands as F-spin analog states. Physical Review C, 43(3), R926-R929.
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  Abstract: Data are presented which indicate the existence of F-spin multiplets for the shape-coexistent intruder states of sequences of nuclei differing by an ± particle. We argue that these intruder F-spin multiplets, or, equivalently, F-spin analog states, occur because of their larger and more nearly equal values of NN1/2. © 1991 The American Physical Society.
• Davis, E. D., Diallo, A. F., Barrett, B. R., & Balantekin, A. B. (1991). Particle-hole symmetry, F-spin, and r-process parameters. Physical Review C, 44(4), 1655-1660.
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  Abstract: We exploit approximate symmetry under particle-hole conjugation and the systematics associated with a classification scheme (inspired by the neutron-proton interacting boson model) to obtain estimates of binding energies and low-lying excitation energies for even-even r-process nuclei drawn from the major proton and neutron shells, 50
• Kuyucak, S., Lac, V. -., Morrison, I., & Barrett, B. R. (1991). γ-unstable nuclei in the sdg boson model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 263(3-4), 347-352.
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  Abstract: Following the recent Pt(p, p') experiments which indicated the need for g bosons to reproduce the E4 data, we have extended the O (6) limit of the sd boson model to include g bosons. It is shown that a γ-unstable hamiltonian in the sdg model consisting of a quadrupole interaction and a g boson energy leads to results that are very similar to the O (6) limit. Deviations from the empirical energy spectrum that stem from the γ-unstable nature of the hamiltonian can be improved by including a consistent hexadecapole interaction which induces triaxiality. The same hexadecapole operator can also account for the strong E4 transitions. Applications are made to the Xe and Pt isotopes.
• Barrett, B. R., & Otsuka, T. (1990). Structure and decay modes of antisymmetric vibrations in the O(6) limit of the neutron-proton interacting boson model. Physical Review C, 42(6), 2438-2441.
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  Abstract: We investigate the structure of the intrinsic states for the symmetric and antisymmetric vibrations in the O(6) limit of the neutron-proton interacting boson model and of the low-lying configurations projected from these intrinsic states. We study the decay modes of these low-lying states, particularly the antisymmetric 0+ state. This level appears to decay only to the 1+ and 2+ mixed-symmetry states. The signature for these decays is that the M1 and E2 strengths go to zero for N=N. © 1990 The American Physical Society.
• Kaup, U., & Barrett, B. R. (1990). Nuclear shape coexistence in a schematic model. Physical Review C, 42(3), 981-987.
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  Abstract: The phenomenon of shape coexistence, occurring frequently in the vicinity of nuclear subshell closures, is investigated within a schematic model with protons in two subshells and neutrons in a single shell. The results of this study shed some light on how one should model the phenomenon within the interacting-boson framework and relates to previous phenomenological studies. Our model employs an SO(8)SO(8)+SO(8)- dynamic symmetry to ensure exact decoupling of an S-D-pair space, thus providing a tight conceptual link with the interacting-boson model. The model has a critical point, namely, below a certain number of valence neutrons the deformed configuration ceases to coexist. This is intriguingly reminiscent of the data. © 1990 The American Physical Society.
• Halse, P., & Barrett, B. (1989). β-Decay and the structure of light nuclei. Annals of Physics, 192(1), 204-212.
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  Abstract: An analysis of Gamow-Teller β-decay data is used to derive information on the structure of J = 1 levels in sd-shell T = 0 odd-odd nuclei within the context of an extended Interacting Boson Model (IBM-4), in particular on the relation of their orbital wavefunctions to those of levels in the neighboring T = 1 systems. The data systematically indicate that the orbital wavefunctions of the even-even ground states are generally those of levels at high excitation in the odd-odd nuclei. Predictions are made for which even-even states do have similar orbital structure to the odd-odd ground states. © 1989.
• Halse, P., Jaqua, L., & Barrett, B. R. (1989). Pair truncation for rotational nuclei: J=(17/2 model. Physical Review C, 40(2), 968-973.
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  Abstract: The suitability of the pair condensate approach for rotational states is studied in a single j=(17/2 shell of identical nucleons interacting through a quadrupole-quadrupole Hamiltonian. The ground band and a K=2 excited band are both studied in detail. A direct comparison of the exact states with those constituting the SD and SDG subspaces is used to identify the important degrees of freedom for these levels. The range of pairs necessary for a good description is found to be highly state dependent; S and D pairs are the major constituents of the low-spin ground-band levels, while G pairs are needed for those in the band. Energy spectra are obtained for each truncated subspace. SDG pairs allow accurate reproduction of the binding energy and K=2 excitation energy, but still give a moment of inertia which is about 30% too small even for the lowest levels. © 1989 The American Physical Society.
• Schmitt, H. A., Halse, P., Balantekin, A. B., & Barrett, B. R. (1989). Noncompact orthosymplectic supersymmetry in Ni61 and Ni62. Physical Review C, 39(6), 2419-2425.
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  Abstract: Energy levels and transitions for the nuclei Ni61 and Ni62 are analyzed within the framework of the geometrical model. Features appropriate to the supersymmetry Osp(4/2,R)×SOBF(5), containing the noncompact orthosymplectic superalgebra Osp(4/2,R), are displayed. © 1989 The American Physical Society.
• Schmitt, H. A., Halse, P., Barrett, B. R., & Balantekin, A. B. (1989). Positive discrete series representations of the noncompact superalgebra Osp(4/2,R). Journal of Mathematical Physics, 30(11), 2714-2720.
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  Abstract: Some physically realizable positive discrete series representations of the noncompact orthosymplectic superalgebra Osp(4/2,R) are considered. The decomposition of these Osp(4/2,R) representations on reduction to Sp(2,R)XSO(4) is studied in detail, and the corresponding state vectors are explicitly constructed by acting with the generators on a general lowest weight state. Some examples are given to illustrate these results for particular single-particle spaces. © 1989 American Institute of Physics.
• Balantekin, A. B., Barrett, B. R., & Halse, P. (1988). Vibrations in the O(6) limit of the proton-neutron interacting boson model. Physical Review C, 38(3), 1392-1396.
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  Abstract: A study is made of vibrations in the O(6) limit of the proton-neutron interacting boson model. Using the procedure of Hatch and Levit, the dependence of the classical limit of an O(6) proton-neutron interacting boson model Hamiltonian is deduced, and the associated eigenvalues are found. The states corresponding to single -vibration quanta are pure in the O(6) classification, belonging to the second representations from both the [N,0] and [N-1,1] symmetries. This is in contrast to the U(5) limit, where the antisymmetric vibration corresponds to the lowest mixed-symmetry level. © 1988 The American Physical Society.
• Balantekin, A. B., Schmitt, H. A., & Barrett, B. R. (1988). Coherent states for the harmonic oscillator representations of the orthosymplectic supergroup Osp(1/2N,script R sign). Journal of Mathematical Physics, 29(7), 1634-1639.
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  Abstract: Coherent states for the harmonic oscillator representations of the noncompact supergroup Osp(1/2N,script R sign) are introduced and the invariant integration measure is calculated by studying transformation properties of supercoset variables. The generalized Bogoliubov transformation for mixed systems of bosons and fermions is also obtained. An example for the simple harmonic oscillator is given. © 1988 American Institute of Physics.
• Barfield, A., Barrett, B., Wood, J., & Scholten, O. (1988). An interacting boson model description of octupole states in nucleic. Annals of Physics, 182(2), 344-374.
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  Abstract: The IBM-1 + f-boson model is described and systematically applied to the nuclei 154Sm, 156Gd, 158Gd, 158Dy, 162Dy, 168Er, 172Yb, 178Hf, and 182W. Reasonable agreement with available energies and B(E3) transition rates is obtained in all cases except 162Dy, which has the anomalous octupole band order Kπ = 2-, 0-, 1-. This energy ordering of K- bands cannot be obtained within the present model. The parameter trends show considerable variation, indicating that the underlying fermionic subshell structure is very important in octupole states. © 1988.
• Schmitt, H. A., Balantekin, A. B., & Barrett, B. R. (1988). Comment on 'application of spinor symmetry to ^131,133Xe and ¹³⁵Ba'. Journal of Physics G: Nuclear Physics, 14(5), 657-659.
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  Abstract: It is argued that the spin (6) limit is inappropriate for representing the nuclei 131,133Xe and 135Ba. The importance of fitting transition rates as well as energy levels is stressed. This is a comment on a paper by Michailova (ibid., vol.13, p.L149, (1987)).
• Schmitt, H. A., Halse, P., Barrett, B. R., & Balantekin, A. B. (1988). Orthosymplectic supersymmetry complementary to combined Bose-Fermi seniority algebras. Physics Letters B, 210(1-2), 1-4.
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  Abstract: An orthosymplectic pairing supersymmetry is demonstrated for systems classified using combined Bose-Fermi seniority groups, such as SOB+F(5) and SOB+F(6) which can occur when coupling a fermion to the Bohr-Mottelson and interacting boson models. This supersymmetry is analogous to quasispin for bosons and fermions separately. By virtue of its association with a particular classification scheme, this supersymmetry can be subjected to a meaningful experimental verification. © 1988.
• Balantekin, A. B., & Barrett, B. R. (1987). Collective 2+ states in the U(5) classical limit of the proton-neutron interacting boson model. Physical Review C, 35(5), 1878-1882.
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  Abstract: The U(5) classical limit of the proton-neutron interacting boson model Hamiltonian, appropriate for the collective 2+ states, is investigated. The symmetric and mixed-symmetry 2+ states are identified as arising from the boson-number-weighted symmetric and antisymmetric vibrations in the beta degree of freedom, respectively. Also approximate formulas for the energies away from the U(5) limit and for the reduced matrix elements of the E2 and M1 transition operators are given. © 1987 The American Physical Society.
• Druce, C., Pittel, S., Barrett, B., & Duval, P. (1987). The interacting boson model: Microscopic calculations for the mercury isotopes. Annals of Physics, 176(1), 114-139.
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  Abstract: Microscopic calculations of the parameters of the proton-neutron interacting boson model (IBM-2) appropriate to the even Hg isotopes are reported. The calculations are based on the Otsuka-Armia-Iachello boson mapping procedure, which is briefly reviewed. Renormalization of the parameters due to exclusion of the l=4 g boson is treated perturbatively. The calculations employ a semi-realistic shell-model Hamiltonian with no adjustable parameters. The calculated parameters of the IBM-2 Hamiltonian are used to generate energy spectra and electromagnetic transition probabilities, which are compared with experimental data and with the result of phenomenological fits. The overall agreement is reasonable with some notable exceptions, which are discussed. Particular attention is focused on the parameters of the Majorana interaction and on the F-spin character of low-lying levels. © 1987.
• Semmes, P. B., Barfield, A. F., Barrett, B. R., & Wood, J. L. (1987). Testing interacting boson model cores through particle-core coupling: Negative parity states in the odd-mass Tl and Au isotopes. Physical Review C, 35(2), 844-847.
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  Abstract: Particle-core coupling calculations have been made for the h9/2 bands in the odd-Tl isotopes (A=191197) and the h11/2 bands in the odd-Au isotopes (A=189195). The even-mass Hg core descriptions were taken from previous proton-neutron interacting boson model calculations, and thus a comparison between the experimental and calculated level schemes for the Tl and Au isotopes can be interpreted as a test of the core description. A predicted transition from positive Q(2+) near A=195 to negative Q(2+) near A=191 is not borne out by the odd-A data. These results, combined with new proton-neutron interacting boson model calculations, indicate that the Hg isotopes are more U(5) than O(6) in character. © 1987 The American Physical Society.
• Balantekin, A. B., & Barrett, B. R. (1986). Erratum: Collective M states in the classical limit of the neutron-proton interacting boson model (Physical Review C (1985) 32 (288)). Physical Review C, 33(5), 1842-.
• Barfield, A. F., Wood, J. L., & Barrett, B. R. (1986). Interacting boson model calculation of octupole states in deformed nuclei. Physical Review C, 34(5), 2001-2004.
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  Abstract: An interacting boson model study of octupole states in deformed rare-earth nuclei is discussed. The parameters and octupole bandhead energies are given for Sm154, Gd158, Er168, Yb172, and Hf178. Detailed spectra and B(E3) transition rates are presented for Er168. Reasonable agreement with experiment is obtained for eight of the nine nuclei studied. © 1986 The American Physical Society.
• Daley, H. J., & Barrett, B. R. (1986). An interacting boson model of clustering in nuclei: α-like clustering in the heavy actinides. Nuclear Physics, Section A, 449(2), 256-300.
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  Abstract: An interacting boson model of α-like clustering in nuclei is utilized for the study of the systematic trends of the data available for actinide nuclei. Most of the results presented here are for the well-deformed heavy actinides; however, some trends in going to the spherical region are studied. Tests, based on experimental data, are presented to discriminate between this and other models. The limit of the cluster model presented here satisfies all of the experimental tests found. This phenomenological study indicates that α-like clustering effects are adequate to describe the structure and dynamics of heavy actinide nuclei. © 1986.
• Sala, P., Brentano, P. V., Harter, H., Barrett, B., & Casten, R. F. (1986). On the possibility of fitting a large set of rare earth nuclei with constant IBM-2 parameters. Nuclear Physics, Section A, 456(2), 269-278.
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  Abstract: A projection method from the IBM-2 on the IBM-1 space is used in order to carry out calculations for the rare-earth nuclei. The calculations make use of only five parameters which are constant for the whole range of nuclei considered. The agreement with the experimental data is satisfactory. © 1986.
• Balantekin, A. B., & Barrett, B. R. (1985). Collective M1 states in the classical limit of the neutron-proton interacting boson model. Physical Review C, 32(1), 288-292.
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  Abstract: Using the classical picture of the collective M1 mode in nuclei as an oscillation of the angle between the deformed valence protons and valence neutrons, we obtain an expression for the classical limit of the neutron-proton interacting boson model Hamiltonian. We use this result to contrast the excitation energy in the classical limit to the experimentally observed value for the 1sup+ state in sup156Gd. © 1985 The American Physical Society.
• Barrett, B. R., & Halse, P. (1985). M1 transition strength in the SU(3) limit of the generalized IBM-2. Physics Letters B, 155(3), 133-136.
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  Abstract: We generalize the SU(3) limit of the standard IBM-2 formalism of sd bosons to sdg...λ bosons, where λ denotes a boson of arbitrarily large, even angular momentum λ, and investigate the effect on the B(M1, 01+ → 1+) transition strength. In the SU(3) limit, all the M1 transition strength resides in a single 1+ state and is proportional to λ. © 1985.
• Druce, C. H., Pittel, S., Barrett, B. R., & Duval, P. D. (1985). Microscopic calculation of the Majorana parameters of the interacting boson model for the Hg isotopes. Physics Letters B, 157(2-3), 115-119.
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  Abstract: The parameters of the Majorana interaction of the neutron-proton interacting boson model are calculated for the Hg isotopes. The calculations utilize the Otsuka-Arima-Iachello mapping procedure and also lead to predictions for the other boson parameters. The resulting spectra are compared with experimental spectra and those obtained from phenomenological fits. © 1985.
• Barfield, A. F., & Barrett, B. R. (1984). The interacting boson model and the structure of ¹⁸²Hg. Physics Letters B, 149(4-5), 277-278.
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  Abstract: It is demonstrated that the interacting boson model is completely consistent with newly observed energy levels in 182Hg. This is accomplished by making a slight change in only one of the parameter values previously used. © 1984.
• Balantekin, A. B., Barrett, B. R., & Levit, S. (1983). Potential energy surfaces in the classical limit of the IBM-2. Physics Letters B, 129(3-4), 153-156.
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  Abstract: The classical limit of the Interacting Boson Model for both neutrons and protons (the IBM-2) is investigated. In particular, general expressions of the potential energy for the proton and neutron distributions aligned along the same axis are obtained and plotted for the even-even isotopes of tungsten. © 1983.
• Barfield, A. F., Barrett, B. R., Sage, K. A., & Duval, P. D. (1983). The interacting Boson Model applied to the mercury isotopes. Zeitschrift für Physik A Atoms and Nuclei, 311(3), 205-215.
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  Abstract: The even isotopes of mercury have been systematically studied using the Interacting Boson Model (IBM). In order to treat shape coexistence in the light isotopes, two separate IBM calculations were performed with different configurations, which were subsequently mixed. The four Hamiltonian parameters, which were allowed to vary freely from isotope to isotope, were found to be consistent with the corresponding IBM parameters used for platinum and osmium. Overall, the calculated energy spectra and electromagnetic properties are in reasonable agreement with experiment. © 1983 Springer-Verlag.
• Barrett, B. R., Duval, P. D., & Pittel, S. (1983). A microscopic determination of the interacting boson model parameters for nondegenerate orbits. Progress in Particle and Nuclear Physics, 9(C), 535-549.
• Barrett, B. R., Pittel, S., & Duval, P. D. (1983). Microscopic aspects of the IBA. Nuclear Physics, Section A, 396(C), 267-279.
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  Abstract: The current status of efforts to derive the Interacting Boson Model (IBM) from the microscopic Shell Model is described. Although several boson mapping procedures presently exist, only the procedure of Otsuka, Arima and Iachello (OAI) is discussed in detail. The IBM bosons are assumed to be correlated pairs of identical nucleons of definite generalized seniority and angular momentum. The steps, which must be implemented in the OAI procedure in order for it to be considered a truly microscopic theory of the IBM, are then described. Using this procedure, we present results of typical calculations for the IBM-2 parameter Xv, as an illustration. © 1983.
• Duval, P. D., Pittel, S., Barrett, B. R., & Druce, C. H. (1983). g-Boson renormalization effects in the interacting Boson model for nondegenerate orbits. Physics Letters B, 129(5), 289-293.
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  Abstract: A nonperturbative model-space truncation procedure is utilized to include the effects of a single g boson on the parameters of the neutron-proton Interacting Boson Model in the realistic case of nondegenerate single-particle orbits. Particular emphasis is given to the single-boson energies ε{lunate}dρ{variant} (ρ{variant} = v, π), with numerical results presented for the even isotopes of Hg. Only part of the observed renormalization is obtained. Possible sources of further renormalizations to ε{lunate}dρ{variant} are discussed. Results are also presented for the renormalizations of the boson quadrupole parameters κ and χρ{variant}. © 1983.
• Druce, C. H., McCullen, J. D., Duval, P. D., & Barrett, B. R. (1982). The even zinc isotopes in the interacting boson model. Journal of Physics G: Nuclear Physics, 8(11), 1565-1575.
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  Abstract: The interacting boson model of Arima, Iachello and co-workers is applied to the even zinc isotopes 62Zn-72Zn. Two boson configurations are used to account for the behaviour of excited 0+ states; one is the usual particle boson configuration and the other a configuration representing excitation from the 56Ni core. The parameter variation in the model is constrained as much as possible to agree with calculations from a non-degenerate multi-shell fermion basis for the bosons. Energy levels, quadrupole moments and B(E2) values are calculated. Values obtained compare favourably with experiment and with other calculations.
• Duval, P. D., & Barrett, B. R. (1982). Quantitative description of configuration mixing in the interacting boson model. Nuclear Physics, Section A, 376(2), 213-228.
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  Abstract: In many nuclei the coexistence of two quite different structures in the same energy region is manifest in the experimental data. Generally there is configuration mixing between these structures. We present a new, general technique for providing a quantitative description of configuration mixing in nuclei. The technique uses the interacting boson model for protons and neutrons to make separate descriptions of the different configurations, which are then mixed using an appropriate mixing hamiltonian. Examples are given using the mercury and molybdenum isotopes. © 1982.
• Pittel, S., Duval, P. D., & Barrett, B. R. (1982). Particle-hole ambiguity in the parameters of the microscopic interacting boson model. Physical Review C, 25(5), 2834-2836.
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  Abstract: The parameters of the microscopic interacting boson model that emerge from a multi-nondegenerate-orbit theory are shown to depend on whether they are generated in terms of correlated pairs of particles or correlated pairs of holes. It is suggested that the ambiguity results from the shell-model truncation inherent in the interacting boson model and that it can be alleviated by including renormalization effects from outside the interacting boson model subspace. NUCLEAR STRUCTURE Microscopic interacting boson model; particle-hole ambiguity in model parameters. © 1982 The American Physical Society.
• Pittel, S., Duval, P., & Barrett, B. (1982). The microscopic Interacting Boson Model for nondegenerate orbits. Annals of Physics, 144(1), 168-199.
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  Abstract: The microscopic Interacting Boson Model formalism is outlined and a general procedure is described for deriving the parameters of the model when the valence orbits are nondegenerate. This latter technique involves expanding pair creation operators for J = 0 (or J = 2) correlated pairs in terms of J = 0 (or J = 2) pair creation operators for individual orbits. This expansion enables us to relate matrix elements for the multi-orbit problem to matrix elements for individual orbits for which the well-known Racah-seniority reduction formulae apply. Our calculated results for the parameters of the boson-boson quadrupole-quadrupole interaction show a definite relationship to the underlying subshell structure of each major shell, in agreement with the phenomenological results. It is also discovered that the results obtained using particle states are not the same as those obtained using hole states, due to the truncation scheme used to extablish the correlated J = 0 and J = 2 pairs. © 1982.
• Sage, K. A., Goode, P. R., & Barrett, B. R. (1982). Microscopic calculation of the effects of the g boson on the interacting boson model Hamiltonian. Physical Review C, 26(2), 668-679.
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  Abstract: Second-order perturbation theory is used to examine the effect of excluding the g boson from the model space of the interacting boson model. Perturbative corrections are calculated in a paired fermion space (in a single j-shell approximation) and are mapped onto the interacting boson model Hamiltonian using the imaging techniques of Otsuka, Arima, and Iachello. The resulting renormalization of the boson parameters of the Hamiltonian to account for effects of the g boson depends strongly upon the numbers of valence protons and neutrons, and remains significant throughout the half shell. NUCLEAR STRUCTURE Interacting boson model, g boson, microscopic calculation using perturbation theory, renormalization of boson parameters. © 1982 The American Physical Society..
• Duval, P. D., & Barrett, B. R. (1981). Configuration mixing in the interacting boson model. Physics Letters B, 100(3), 223-227.
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  Abstract: We present a new, general technique for providing a quantitative description of configuration mixing in nuclei. The technique uses the Interacting Boson Model to make separate descriptions of the different configurations, which are then mixed using an appropriate mixing hamiltonian. An example is given using the mercury isotopes. © 1981.
• Duval, P. D., & Barrett, B. R. (1981). Interacting boson approximation model of the tungsten isotopes. Physical Review C, 23(1), 492-503.
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  Abstract: The interacting boson approximation model of Arima and Iachello and co-workers has been used to make a schematic study of the tungsten isotopes. For each isotope of tungsten we determine the values of the five parameters in the interacting boson approximation Hamiltonian which yield the best fit to the experimental energy spectrum. Based on these values, we can extrapolate to isotopes for which no experimental data exist and can make predictions for future experiments. Using the same values of these parameters for each isotope, we can also obtain the B(E2) transition rates, the (E0) values, the quadrupole moments of the first two excited 2+ states, the two-neutron separation energies, and the isomer and isotope shifts. Where data exist our results, in general, agree very well with experiment, although more experimental information is needed for the isomer and isotope shifts and the quadrupole moments of the excited 2+ states. The long range goal is to understand the origin of the model parameters in terms of a microscopic theory, such as the nuclear shell model. NUCLEAR STRUCTURE Interacting boson approximation model, investigation of the tungsten isotopes, energies, B(E2) transition rates, and other properties. Model parameters as a smooth function of neutron number. © 1981 The American Physical Society.
• Duval, P. D., & Barrett, B. R. (1981). Shell-model description of the interacting-boson-model parameters for two nondegenerate j shells. Physical Review Letters, 46(23), 1504-1507.
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  Abstract: The interacting-boson-model parameters are examined from a shell-model viewpoint with use of the generalized seniority scheme in two nondegenerate j shells. Predictions for the interacting-boson-model parameters are obtained by constructing the boson image of the corresponding fermion operator and are found to be in good overall agreement with the empirically determined values. © 1981 The American Physical Society.
• Duval, P. D., & Barrett, B. R. (1981). Shell-model determination of the interacting boson model parameters for two nondegenerate j shells. Physical Review C, 24(3), 1272-1282.
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  Abstract: The interacting boson model is examined from a microscopic viewpoint using the generalized seniority scheme. The present discussion focuses on regions of the periodic table in which the many nondegenerate nucleon orbits can be approximated in terms of two nondegenerate orbits, the sum of whose occupancies is chosen to be the same as the total occupancy of the major shell being studied. Predictions for the interacting boson model parameters are obtained by constructing the zeroth-order boson images of the corresponding fermion operators. Calculations are carried out for the tungsten isotopes, and the predicted interacting boson model parameters are found to be in good overall agreement with the empirically determined values for the tungsten isotopes. The calculations reproduce the observed SU(3) or rotational character of the low-lying energy states in the N = 96 to 114 mass region. NUCLEAR STRUCTURE Interacting boson model, microscopic determination of model parameters for two nondegenerate j shells. Use of theoretical parameters to predict experimental results for tungsten. © 1981 The American Physical Society.
• Sage, K. A., & Barrett, B. R. (1980). Influence of the g boson on the interacting boson approximation Hamiltonian. Physical Review C, 22(4), 1765-1771.
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  Abstract: The interacting boson approximation Hamiltonian for s and d bosons is renormalized in lowest order for the effects of the g boson using second-order perturbation theory in a single j shell approximation. In this paper only the correction term which renormalizes the single-boson energy is investigated in detail, with a specific application to the Ba isotopes. In the evaluation of this correction, the general form of the matrix elements of two-body quadrupole operators, taken between paired-fermion states, is obtained. Our numerical results for Ba indicate that the effects of the g boson on the single-boson energy are of the correct sign and magnitude and that a perturbative approach to including these effects appears to be appropriate. NUCLEAR STRUCTURE Interacting boson approximation, perturbation theory of g boson, calculated 2+ - 0+ splittings in Ba. © 1980 The American Physical Society.
• Barrett, B. R. (1979). Microscopic versus empirical effective interactions in a single j shell. Physical Review C, 20(5), 1926-1929.
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  Abstract: Effective-interaction matrix elements within a single j shell can be determined directly from experimental data. Such matrix elements have been found to be much different from those calculated microscopically within a complete major shell. The recent work of Moszkowski et al. showed that this difference is at least partially due to the severe truncation to a single j shell. We have constructed the microscopic effective interaction for a single j shell using two different methods: (1) simple perturbation theory and (2) explicit projection from the full major shell to a single j shell. We conclude that the empirical matrix elements and the full major-shell matrix elements should not agree, since the model spaces are different. On top of this the empirical values and the microscopic results for a single j shell would be expected to be similar only when the configurations |(j2)JT are very pure. NUCLEAR STRUCTURE Effective interactions, empirical and microscopic, in a single j shell; importance of model space size and of configuration purity. © 1979 The American Physical Society.
• Coon, S. A., Scadron, M. D., McNamee, P. C., Barrett, B. R., Blatt, D. W., & McKellar, B. H. (1979). The two-pion-exchange three-nucleon potential and nuclear matter. Nuclear Physics, Section A, 317(1), 242-278.
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  Abstract: We derive the complete three-nucleon potential of the two-pion-exchange type, suitable for nuclear structure calculations, by extending away from the forward direction the subthreshold off-pion-mass-shell πN scattering amplitude of Coon, Scadron and Barrett. The off-mass-shell extrapolation, subject to current algebra and PCAC constraints, yields approximately model independent amplitudes (in that they depend primarily on πN data) in the complete potential. The subtraction of the forward propagating nucleon term from the amplitudes is done in greater generality than before. The contribution of this three-nucleon potential to the binding energy of symmetric nuclear matter is estimated using the perturbative formalism of McKellar and Rajaraman. In our treatment of correlations in nuclear matter, the dominant three-nucleon potential has strong components from both s-wave and p-wave πN scattering. A three-body potential based on the p-wave Δ isobar can be considered a special case of the derived potential. Therefore, we are able to trace most of the discrepancies in previously reported binding energy contributions back to the assumed energy denominator in second order. We find the contribution of the three nucleon potential to the energy of symmetric nuclear matter to be - 1.90 ± 0.2 MeV. © 1979.
• Goode, P. R., Barrett, B. R., & Portilho, O. (1979). High-lying intermediate excitations in the nuclear effective interaction with a super-soft-core potential. Physical Review C, 19(2), 542-544.
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  Abstract: The earlier calculations of Goode and Barrett are repeated using the super-soft-core potential of Gogny, Pires, and de Tourreil. The particular third-order folded diagram which they calculated now converges in its intermediate-state energy summation, because of the suppression of the strong short-range repulsive effects present in earlier calculations. NUCLEAR STRUCTURE Theory, effective interaction in mass-18, convergence intermediate-state summation in third order to 26a.
• Shlomo, S., Barrett, B. R., & Weidenmüller, H. (1979). Microscopic calculation of the form factors for nucleon transfer in deeply inelastic collisions. Physical Review C, 20(1), 1-4.
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  Abstract: Previous calculations of form factors are extended to the case of inelastic nucleon transfer. The results generally agree well with those found earlier for inelastic scattering. The two main differences are (i) a systematic increase of the correlation length with distance, (ii) a significant contribution of angular momentum transfer of up to 7 or 8 units of to the transfer process. NUCLEAR REACTIONS Shell model used to calculate distribution of form factors. © 1979 The American Physical Society.
• Barrett, B. R., Shlomo, S., & Weidenmüller, H. (1978). Microscopic calculation of the form factors for deeply inelastic heavy-ion collisions within the statistical model. Physical Review C, 17(2), 544-554.
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  Abstract: Agassi, Ko, and Weidenmüller have recently developed a transport theory of deeply inelastic heavy-ion collisions based on a random-matrix model. In this work it was assumed that the reduced form factors, which couple the relative motion with the intrinsic excitation of either fragment, represent a Gaussian stochastic process with zero mean and a second moment characterized by a few parameters. In the present paper, we give a justification of the statistical assumptions of Agassi, Ko, and Weidenmüller and of the form of the second moment assumed in their work, and calculate the input parameters of their model for two cases: Ar40 on Pb208 and Ar40 on Sn120. We find values for the strength, correlation length, and angular momentum dependence of the second moment, which are consistent with those estimated by Agassi, Ko, and Weidenmüller. We consider only inelastic excitations (no nucleon transfer) caused by the penetration of the single-particle potential well of the light ion into the mass distribution of the heavy one. This is combined with a random-matrix model for the high-lying excited states of the heavy ion. As a result we find formulas which relate simply to those of Agassi, Ko, and Weidenmüller, and which can be evaluated numerically, yielding the results mentioned above. Our results also indicate for which distances of closest approach the Agassi-Ko-Weidenmüller theory breaks down. [NUCLEAR REACTIONS Random-matrix model and shell model used to calculate distribution of form factors.] © 1978 The American Physical Society.
• Goode, P. R., & Barrett, B. R. (1978). Importance of high-lying intermediate excitations on the nuclear effective interaction. Physical Review C, 17(5), 1848-1852.
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  Abstract: A particular third-order diagram which contributes to the effective two-body interaction in mass-18 nuclei is computed up to intermediate excitations of 26. We find that our results have not converged by 26 and that the slow decrease in the higher-lying contributions is mainly due to the strong short-range repulsion in the central components of the nucleon-nucleon force. NUCLEAR STRUCTURE Theory, effective interaction mass-18; convergence intermediate-state summation in third order to 26; effects of tensor and hard-core components of nuclear force. © 1978 The American Physical Society.
• Sandel, M. S., McCarthy, R. J., Barrett, B. R., & Vary, J. P. (1978). Convergence and the third-order effective shell-model interaction. Physical Review C, 17(2), 777-784.
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  Abstract: Several commonly made approximations in microscopic effective interaction calculations have been found to result in serious inaccuracies. Recent improved second-order calculations for A=18 nuclei suggested somewhat better order by order convergence in the reaction matrix G than indicated previously. A selected third-order term has been calculated to study further this possibility. The convergence of the intermediate-state summation was also investigated for this diagram. Our improved calculational technique results in a greater reduction of the third-order term than the reduction found earlier for the second-order term. The outlook for the (asymptotic) convergence of the expansion is much improved, but the prospects for a complete third-order calculation of the effective interaction are dim due to the difficulties of the calculation. [NUCLEAR STRUCTURE Effective interaction, theory; convergence of the intermediate-state sums; convergence of the diagram series through third-order in the nuclear reaction matrix; shell-model matrix elements in the sd shell.] © 1978 The American Physical Society.
• Goode, P., & Barrett, B. R. (1977). Average effective-interaction calculations in a simulated Hartree-Fock basis. Physics Letters B, 68(1), 47-50.
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  Abstract: The averaged effective interaction for mass-18 nuclei is computed through fourth-order perturbation theory in both a pure harmonic-oscillator basis and a simulated Hartree-Fock basis. Going to a Hartree-Fock basis does not eliminate the large fourth-order averages found earlier by Goode and Koltun using an harmonic-oscillator basis. © 1977.
• Sandel, M. S., McCarthy, R. J., & Barrett, B. R. (1977). Core polarization revisited. Zeitschrift für Physik A Atoms and Nuclei, 280(3), 259-266.
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  Abstract: The core-polarization process which has been so important in determining the twoparticle effective shell-model interaction is re-examined so as to include effects not present in previous calculations as well as to consolidate effects included in separate calculations. The effects considered here are (i) using reaction matrix elements G with the proper starting energy for their position in the diagram, (ii) summing to intermediate excitations of 10 h{combining short stroke overlay}Ω so as to saturate the effect due to the tensor force and (iii) treating the intermediate-state spectrum consistently in calculating both G and the core polarization. Our calculations are performed in a shifted harmonic oscillator basis, and we discuss the importance of the choice of the unperturbed Hamiltonian used in the calculations. Our results indicate that the core polarization is significantly changed from the lowest-order results when the correct starting energies and higher intermediate-state summations are included. We present our results as a function of the shift and find that agreement with experiment is better for a small shift. We conclude that at the very least one should always include the correct starting energy effect in computing the higherorder terms. © 1977 Springer-Verlag.
• Barrett, B. R., & McCarthy, R. J. (1976). Nuclear reaction matrix calculations with a shell-model Q. Zeitschrift für Physik A: Atoms and Nuclei, 279(3), 297-300.
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  Abstract: The Barrett-Hewitt-McCarthy (BHM) method for calculating the nuclear reaction matrix G is used to compute shell-model matrix elements for A=18 nuclei. The energy denominators in intermediate states containing one unoccupied single-particle (s.p.) state and one valence s.p. state are treated correctly, in contrast to previous calculations. These corrections are not important for valence-shell matrix elements but are found to lead to relatively large changes in cross-shell matrix elements involved in core-polarization diagrams. © 1976 Springer-Verlag.
• Barrett, B. R., & Kirson, M. W. (1975). Two-particle ladder diagrams and double-counting in effective interaction calculations. Physics Letters B, 55(2), 129-133.
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  Abstract: It is shown that including the two-particle ladder diagrams, computed with the Barrett, Hewitt, McCarthy G matrix elements at a starting energy of 47 MeV and for intermediate excitations of 2ℏΩ, in the perturbation expansion for the effective two-body interaction in mass-18 nuclei involves a double-counting of roughly 42%. It is argued by comparison that the double-counting should be roughly the same when the Kuo G matrix elements are used. © 1975.
• Barrett, B. R., Weng, W., Osnes, E., & Richert, J. (1975). Model calculations for ⁵⁰Ca and the convergence properties of the perturbation expansion for the effective interaction. Nuclear Physics, Section A, 248(3), 429-440.
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  Abstract: Using the results of the "exact" shell-model calculation of McGrory et al. for the Ca isotopes as "experimental data", we performed model calculations for 50Ca in order to test the convergence properties of different perturbation schemes for computing the effective interaction V. As such, our aim was not to describe the physical spectrum of 50Ca. Three different model spaces were investigated: (i) p 3 2 (ii) p 3 2 + p 1 2 and (iii) p 3 2 + p 1 2 + f 5 2. In the p 3 2 model space three different first-order interactions were used in computing the perturbation expansion for V through third order: (a) V ≡ {G + G}3p-1hKB, (b) a standard G-matrix computed from V in (a), and (c) a doubly partitioned G-matrix computed from V by excluding excitations into the p 1 2level. The results for the doubly partitioned G yielded the best convergence through third order and the best agreement with the J = 0, T = 1 ground state of 50Ca. The core polarization was found to be repulsive for a pure T = 1 system, so that certain third-order terms did not cancel against the large vertex renormalization terms in our special case. The [2, 1] padé approximant for each interaction appeared to indicate reasonable convergence in all three cases through third order. The results for the expanded (p 3 2 + p 1 2) and (p 3 2 + p 1 2 + f 5 2) model spaces were difficult to interpret in a meaningful way, because of small energy denominators. Our results would indicate that one should compute in a doubly partitioned space when there are single-particle levels lying close in energy to the model space levels. © 1975.
• Barrett, B., Halbert, E., & McGrory, J. (1975). Hidden configurations and effective interactions: A comparison of three different ways to construct renormalized hamiltonians for truncated shell-model calculations. Annals of Physics, 90(2), 321-390.
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  Abstract: We discuss in general some criteria and methods for constructing effective Hamiltonians. Then three different methods are compared for constructing an effective Hamiltonian to be used in nuclear shell-model calculations for A = 17-20, allowing (A-16) active nucleons in the d 5 2, s 1 2 vector space. For all three methods, the aim is to obtain a d 5 2, s 1 2 model which will simulate the results of a given full d 5 2, s 1 2, d 3 2 model. The three methods for finding the effective Hamiltonian are. 1. (a) conventional low-order perturbation theory; 2. (b) a projection technique, in which we construct a Hamiltonian whose eigenvalues excactly match a selected subset of d 5 2, s 1 2, d 3 2 eigenvalues, and whose eigenvectors excatly match the projections of d 5 2, s 1 2, d 3 2 eigenvectors on the d 5 2, s 1 2 space; and 3. (c) least-square fit to selected d 5 2, s 1 2, d 3 2 energies. For all three methods, we first restrict the effective Hamiltonian to a linear combination of 1-body and 2-body operators. Then for the perturbation and projection techniques, we also calculate the 3-body-operator terms in the effective Hamiltonian. When the effective Hamiltonians are limited to 1-body and 2-body terms, the leastsquare method yields the best overall fit to the low-lying spectrum of d 5 2, s 1 2, d 3 2. © 1975.
• Coon, S. A., Scadron, M. D., & Barrett, B. R. (1975). The three-body force, off-shell πN scattering and binding energies in nuclear matter. Nuclear Physics, Section A, 242(3), 467-480.
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  Abstract: We re-examine the off-shell πN amplitude occurring in the two-pion exchange three-body force, subject to all of the constraints of current algebra. This amplitude is not dominated by the Δ(1231) isobar; instead, if the σ-term is known, it can be determined from on-shell scattering. The resulting contribution to the binding energy of nuclear matter is small but attractive, varying from 0.2 MeV to 1.5 MeV, corresponding to πN σ-terms of 70 MeV to 40 MeV. © 1975.
• Barrett, B. R. (1974). Convergence properties of the perturbation expansion for the effective two-particle interaction in mass-18 nuclei in a doubly partitioned Hilbert space. Nuclear Physics, Section A, 221(2), 299-318.
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  Abstract: The theory for calculating the effective interaction ov for finite nuclei in a doubly partitioned Hubert space is discussed and then applied to the calculation of ov through third order in the nuclear reaction matrix G for the J = 0, T = 1 states in mass-18 nuclei. The G-matrix elements were computed using the technique of Barrett, Hewitt and McCarthy, which allowed an acccurate treatment of the Pauli projection operator. Calculations were first performed using the standard procedure for computing ov. These calculations were then repeated employing the double-partition procedure, and its results were compared with those from the standard procedure. The convergence of the perturbation expansion for ov through third order in G was improved in the double-partition approach but was not conclusive. However, the double-partition procedure allows the possibility of performing much more sophisticated and accurate calculations of ov than the standard procedure. All calculations were performed as a function of the starting energy ω of G, which is related to constant shifts between the energy levels of the occupied and unoccupied single-particle states. For all calculations a value of ω was found at which the 0+ ground state agreed with experiment. A procedure is proposed for determining in advance the value of ω at which G and ov should be computed. © 1974.
• Barrett, B. R. (1972). The contribution of two-particle ladder and RPA terms to the effective interaction in A = 18 nuclei. Physics Letters B, 38(6), 371-375.
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  Abstract: Two-particle ladder and RPA terms are included in the perturbation expansion for the effective interaction θ in A = 18 nuclei through third order in the reaction matrix. Although the possibility of convergence is improved, this improvement is questionable, because of double counting. Ways for improving the calculation of θ are discussed. © 1972.
• Barrett, B. R., Hewitt, R. G., & McCarthy, R. J. (1972). Binding-energy calculations for ¹⁶O and their dependence on the treatment of the Pauli operator in the G-matrix. Nuclear Physics, Section A, 184(1), 13-22.
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  Abstract: The binding energy per particle and the single-particle energies and occupation probabilities for 16O are calculated using G-matrix elements computed with an exact Pauli operator Q and with various shifts in the energies of the intermediate state spectrum with respect to the energies of the occupied states. These calculations are than repeated with G-matrix elements computed with several commonly used approximations for Q, namely the Eden-Emery Q and the angle-averaged Q of Wong. The results of these latter calculations are compared with the results obtained with the exact treatment of Q and are found to be very similar. It is concluded that in binding-energy calculations, but not necessarily in more sophisticated calculations, the approximate treatments of Q discussed in this paper can be used to obtain reasonable results. © 1972.
• Barrett, B. R., Hewitt, R. G., & McCarthy, R. J. (1971). Simple and exact method for calculating the nuclear reaction matrix. Physical Review C, 3(3), 1137-1145.
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  Abstract: A new, simple, and exact method is given for calculating the reaction matrix G in a two-particle harmonic-oscillator basis. The method makes use of an expansion of the Bethe-Goldstone wave function in terms of solutions of the Schrödinger equation for two interacting particles in a harmonic-oscillator well. Since a two-particle basis is used, the Pauli operator Q is diagonal and can be treated exactly. Reaction matrix elements based on the Hamada-Johnston potential are used in a shell-model calculation of A=18 nuclei. The results are compared with those of earlier calculations using approximate Pauli operators. The dependence of the reaction matrix on the starting energy is studied, and the relationship of this energy to the intermediate-state spectrum and to the Pauli operator Q is discussed. In this same context the difference between using a Brueckner Q and a shell-model Q is also discussed. © 1971 The American Physical Society.
• Barrett, B. R., & Kirson, M. W. (1970). Higher-order terms and the apparent non-convergence of the perturbation expansion for the effective interaction in finite nuclei. Nuclear Physics, Section A, 148(1), 145-180.
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  Abstract: We have calculated all significant terms through third order in the reaction matrix G which contribute to the perturbation series for the J = 0, T = 1 effective interaction between two valence nucleons in the mass-18 nuclei and also a few selected fourth-order terms. We have shown that the perturbation series does not converge order-by-order to third order in G and that certain large third-order terms tend to cancel the second-order contribution. An intuitive physical picture of the process giving rise to this effect and to analogous effects in related calculations of the effective charge is given. This picture suggests a rearrangement of the perturbation series into physically significant groups of diagrams, so that each group converges order-by-order in G. However, one must then find some way to sum all these groups of diagrams. We conclude that simple perturbation theory is not a reliable method for calculating the effective two-nucleon interaction in mass-18 nuclei, when currently standard calculational techniques are used, and that the success of first- plus second-order perturbation theory in fitting experimental spectra for these nuclei is unexplained. © 1970.
• Barrett, B. R., Hewitt, R. G., & McCarthy, R. J. (1970). Discussion of a new technique for solving the Bethe-Goldstone equation. Physical Review C, 2(4), 1199-1204.
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  Abstract: The new method of Truelove and Nicholls for obtaining reaction matrix elements for nuclear-structure calculations is discussed. In this method, the Bethe-Goldstone wave function is expanded in terms of eigenfunctions of two interacting nucleons bound in a common potential well. The Bethe-Goldstone equation, which is written in terms of an expansion over noninteracting two-particle states, is then solved iteratively. In practice, the method is most easily applied when a harmonic-oscillator basis is used; the Pauli operator Q can then be treated exactly. The convergence of the Truelove-Nicholls iteration scheme and of the above two expansions is investigated. It is shown that the original method is incorrect for nucleon-nucleon potentials with an infinite hard core. A simple way of correcting the method is presented. © 1970 The American Physical Society.
• Barrett, B. R., & Kirson, M. W. (1969). Number-conserving sets and third-order renormalization contributions to the effective nuclear interaction. Physics Letters B, 30(1), 8-10.
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  Abstract: The simplest third-order number-conserving set of diagrams, which represents the renormalization of the bare reaction matrix G, is computed for A=18 nuclei using the Kuo G matrices. As predicted by Brandow, the sum of terms within this set is found to be small, being 10% of G or less. © 1969.
• Barrett, B. R. (1968). Higher-order corrections to collective particle-hole excitations using green function techniques. Nuclear Physics, Section A, 109(1), 129-145.
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  Abstract: Using Green function techniques, we determine higher-order corrections to the Tamm-Dancoff and Random Phase Approximation equations. In particular, we find that the second-order corrections to the Tamm-Dancoff equations consist of a t-matrix term and a core-polarization term. If we truncate our configuration space, we obtain an additional second-order correction from the particle-hole ladder term. We carry out numerical calculations of these second-order corrections for the negative-parity excited states of 4He using the Tabakin separable potential. © 1968.
• Barrett, B. R., & Kirson, M. W. (1968). Higher-order core polarization contributions to effective interactions. Physics Letters B, 27(9), 544-548.
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  Abstract: The perturbation theory calculation of the core-polarization contribution to effective interactions in mass 18 nuclei is carried to higher order, and it is shown that the perturbation series appears to diverge. It is argued, by analogy with nuclear matter results, that all three-body contributions to the core polarization must be treated together. © 1968.
• Barrett, B. R. (1967). Particle-hole states in the alpha particle with realistic forces. Physical Review, 154(4), 955-970.
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  Abstract: We solve the Tamm-Dancoff equations, using the realistic separable potential of Tabakin, for the odd-parity excited states of He4. A comparison is made with results obtained using the hard-core potentials of Brueckner, Gammel, and Thaler and of Hamada. The calculated spectrum is found to be strongly influenced by the p-state contributions, particularly by the effect of the tensor interaction. We predict that the 0-, T=0 state lies close to the 2-, T=0 state. The spin-orbit splitting between the p12 and p32 single-particle states is calculated and found in first order to depend only on the relative two-body spin-orbit interaction. Our estimate for the ratio of the probability of an E1 transition from the upper 1-, T=1 state to the ground state to that of an E1 transition from the lower 1-, T=1 state is calculated to be 1.6, compared with the experimental ratio which is . We also calculate the squared matrix elements and the total capture rate for muon capture in He4. The squared matrix elements are found to be equal within 10 percent, but the calculated total capture rate is smaller than the experimental rate. Our theoretical results tend to justify the use of the supermultiplet theory for the excited states of the particle. We find that our seven equations for the energy splittings depend upon only four quantities. Consequently, we are able to obtain three relations, which give the two unobserved energy splittings and the ratio of the E1 transition probabilities in terms of the four observed energy splittings. The two empirical results which can be compared with experiment are in excellent agreement. © 1967 The American Physical Society.
• Barrett, B. R. (1967). Properties of the [15]-dimensional SU(4) supermultiplets of negative-parity excitations of O16 using realistic nuclear forces. Physical Review, 159(4), 816-829.
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  Abstract: Using particle-hole theory in the Tamm-Dancoff approximation and Wigner's SU(4) supermultiplet theory, we determine the negative-parity excited states of O16 in terms of [15]-dimensional supermultiplets. Only the supermultiplets with total L=1 are studied in detail, since they are the ones of importance with regard to the giant dipole resonance and to muon capture and electron scattering. Working in terms of nonmixing supermultiplets, we find that each supermultiplet can be theoretically explained in terms of five parameters, while there are eight pieces of experimental data regarding each supermultiplet. Thus, our theory is overdetermined, and we can eliminate the parameters to obtain empirical sum rules, which can then be used to predict unobserved levels or to check the consistency of our calculation, independent of the radial dependence of the nuclear force. Since there are two L=1 supermultiplets, we also determine the mixing between them. Even after mixing, we obtain a sum rule for the T=0 states. We then use the realistic nuclear potentials of Tabakin and Brueckner, Gammel and Thaler to calculate the L=1 spectrum, so that we can compare it with the experimental spectrum and our sum-rule predictions. Theoretically, we find that some of the parameters are small enough to be neglected with respect to the other parameters and that there is very little mixing between the two L=1 supermultiplets. Both of these results allow us to obtain approximate sum rules. We get a total of five sum rules, of which four can be used for making empirical predictions of so-far unobserved experimental quantities. We also calculate the squared matrix elements for muon capture to our theoretically determined T=1 levels and obtain results similar to previous calculations. © 1967 The American Physical Society.
• Barrett, B. R., Walecka, J. D., & Meyerhof, W. E. (1966). Some observations concerning the supermultiplet of negative-parity excited states in the α particle. Physics Letters, 22(4), 450-454.
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  Abstract: Seven theoretical equations for the supermultiplet of negative-parity excited states of 4He can be expressed in terms of four parameters. Using four empirically determined energy splitting the following quantities can be predicted: the 0- and 1-, T = 0 states lie near 22 and 28 MeV excitation energy respectively; the ratio of gamma-decay widths of the 1-, T = 1 states at 30 and 26 MeV is approximately 0.4. These predictions are compared with experimental evidence. © 1966.

Proceedings Publications

• Barrett, B. (2013, May/Summer). Conference Summary. In International Conference ``Nuclear Theory in the Supercomputing Era'' (NTSE-2013), Proceedings International Conference: Nuclear Theory in the Supercomputing Era-2013, 383-387.
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  Dates: May 13-17, 2013
• Papadimitriou, G., Barrett, B., Rotureau, J., Michel, N., & Ploszajczak, M. (2013, June/Summer). The No Core Gamow Shell Model for ab initio Nuclear Structure Calculations. In International Nuclear Physics Conference, EPJ Web of Conferences 66, 1-4.
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  Dates of the conference June 2-7, 2013
• Barrett, B. (2013, October). Microscopic Calculations of Nuclear Structure Beyond the 0p-Shell. In ENSFN2012 Conference, 012002.
• Barrett, B. (2012, June). Beyond Light Nuclei within the No Core Shell Model. In HITES International Conference, 012013.
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  Dates: June 4-7, 2012
• Barrett, B. (2012, September). Extending the No Core Shell Model to heavier mass nuclei. In International School of Nuclear Physics, 33rd Course, From Quarks and Gluons to Hadrons and Nuclei, 521.
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  Dates: September 16-24, 2011

Presentations

• Barrett, B. R. (2015, August/Fall). Deriving the Nuclear Shell Model Microscopically. IMP-CUSTIPEN Workshop: Properties of exotic nuclei and asymmetric nuclear matter. Institute for Modern Physics, Lanzhou, China: IMP-CUSTIPEN.
• Barrett, B. R. (2015, August/Fall). The NCSM as an Effective Field Theory. PKU-CUSTIPEN Workshop: Advances in computations of nuclear structure and nuclear forces. Peking University, Beijing, China: PKU-CUSTIPEN.
• Barrett, B. R. (2015, August/Fall). The No-Core Shell Model: Its Formulation and Applications. Nuclear Theory Seminar. Institute for Theoretical Physics, Beijing, China: Institute for Theoretical Physics/Chinese Academy of Science.
• Barrett, B. R. (2015, February/Spring). Ab initio effective interactions for sd-shell valence nucleons. TRIUMF Nuclear Theory Workshop: Progress in Ab Initio Techniques in Nuclear Physics. TRIUMF, University of British Columbia, Vancouver, B.C., Canada: TRIUIMF.
• Barrett, B. R. (2015, June/Summer). Deriving the Nuclear Shell Model Microscopically. INT Program on Neutrino Astrophyiscs and Fundamental Properties. University of Washington, Seattle, WA: National Institute for Nuclear Theory, University of Washington.
• Barrett, B. R. (2015, March/Spring). Ab initio effective interactions for sd-shell valence nucleons. GANIL Topical Meeting: New Directions for Nuclear Structure and Reaction Theories. GANIL, Caen, France: GANIL/FUSTIPEN.
• Barrett, B. R. (2015, May/Summer). Ab initio effective interactions for sd-shell valence nucleons. Workshop on Theory for open-shell nuclei near the limits of stability. Michigan State University, East Lansing, MI: NSCL/FRIB at MSU.
• Barrett, B. R. (2015, October/Winter). A-dependence of the Spectra of the F Isotopes frm ab initio Calculations. Annual Fall Meeting of the Division of Nuclear Physics. Santa Fe, NM: Division of Nuclear Physics of the American Physical Society.
• Barrett, B. R. (2014, April 18). Understanding the Structure of Atomic Nuclei from First Principles. University of Arizona Physics Department Colloquium. University of Arizona: Department of Physics.
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  Physics Department weekly colloquium on the present status for calculating the structure of atomic nuclei from first principles.
• Barrett, B. R. (2014, February 18-26). Investigations of the A-dependence of the Core Energies and Other Terms in the Ab Initio Shell Model Formalism. TRIUMF Nuclear Theory Workshop: Nuclear Structure & Reactions:Experimental and Ab Initio Theoretical Perspectives. Vancouver, BC, Canada: TRIUMF.
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  The talk presents the results of calculations using the Ab Initio No Core Shell Model to determine the input for Standard Shell Model calculations for sd-shell nuclei. The workshop had no proceedings but the slides of the presentations were posted on the workshop webpage.
• Barrett, B. R. (2014, March 17-21). Ab initio shell model with a core. FUSTIPEN Topical Workshop: "Understanding Nuclear Structure and Reactions Microscopically, including the continuum. Caen, France: GANIL.
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  The presentation explain how the Ab initio No Core Shell Model can be used to calculate microscopically the input for standard shell model calculations in the sd-shell.
• Barrett, B. R. (2014, May 12-16). Deriving the nuclear shell model from first principles. 11th International Spring Seminar on Nuclear Physics: Shell Model and Nuclear Structure: achievements of the past two decades. Ischia, Italy: University of Naples, Italy.
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  The successes of the Ab Initio No Core Shell Model approach can be used to calculate microscopically the input for standard shell model calculations for sd-shell nuclei.
• Barrett, B. R. (2014, Ocotber 7-11). Deriving the nuclear shell model from first principles. HAW 2014 Annual Meeting of the Division of Nuclear Physics of the APS. The Big Island, Hawaii: Division of Nuclear Physics (APS) and the JSPS.
• Barrett, B. (2013, April). Recent developments on the Gamow NCSM. INT Program INT-13-1a, on Computational and Theoretical Advances for Exotic Isotopes in the Medium Mass Region.
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  Other Information: no proceedings
• Barrett, B. (2013, August). The No Core Shell Model in an Effective Field Theory Framework. Nuclear Structure 2012. IL: ANL.
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  Date: 08/13; Other Information: no formal proceedings, presentations posted online
• Barrett, B. (2013, December). The No Core Gamow Shell Model: The NCSM including the Continuum. JUSTIPEN/JUSEIPEN Workshop. Wakoshi, Japan: RIKEN.
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  Date: 12/10; Other Information: no proceedings
• Barrett, B. (2013, February). The No Core Shell Model for bound, resonant and scattering states. TRIUMF workshop on Progress in Ab Initio Techniques in Nuclear Physics. Vancouver, B.C., Canada.
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  Date: 02/23; Other information: no proceedings, but talks are posted on the meeting website
• Barrett, B. (2013, March). Spin Density Matrices for Nuclear Density Functionals with Parity Violations. GANIL/ FUSTIPEN Topical Meeting on The Microscopic Description of Light Nuclei. Caen, France.
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  Other Information: no proceedings
• Barrett, B. (2013, March). Workshop Summary and Discussion Group Leader. GANIL/ FUSTIPEN Topical Meeting on The Microscopic Description of Light Nuclei. Caen, France.
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  Date: 03/12; Other Information: no proceedings
• Barrett, B. R. (2013, February). Update on the No Core Shell Model. Nuclear Physics Seminar. Oak Ridge, TN.
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  Date: 02/07
• Barrett, B. R. (2013, November). Extending the NCSM to Heavier Mass Nuclei. Nuclear Theory Seminar. Daejeon, South Korea: RISP.
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  Date: 11/13
• Barrett, B. R. (2013, November). The No Core Shell Model within an Effective Field Theory Framework. Nuclear Theory SeminarUniversity of Tokyo.
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  Date: 11/27
• Dikmen, E., Lisetskiy, A., Barrett, B., & Vary, J. (2013, October). Effective interactions in sd-shell from ab initio shell model with a core. APS DNP meeting. Newport News, VA.
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  Journal: Bull. Am. Phys. Soc; Volume 58; Number: 9; Pages: 127
• Barrett, B. (2012, April). Effective Interactions for Nuclear Structure Calculations: The NCSM and Beyond. Workshop on Ab Initio Density Functional Theory. Saclay, France: CEA.
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  Other Information: no proceedings
• Barrett, B. (2012, February). Closing Remarks: Workshop Summary and Outlook. TRIUMF workshop on Perspectives of the Ab Initio No Core Shell Model. Vancouver, B.C., Canada.
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  Date: 02/25; Other Information: no proceedings, but talks are posted on the meeting website
• Barrett, B. (2012, February). The NCSM in an Effective Field Theory Framework. TRIUMF workshop on Perspectives of the Ab Initio No Core Shell Model. Vancouver, B.C., Canada.
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  Other Information: no proceedings, but talks are posted on the meeting website; Exact Presentation Date: 02/25/2012
• Barrett, B. (2012, March). Beyond the No Core Shell Model: Extensions to Heavier Mass Nuclei. GANIL/ FUSTIPEN workshop. Caen, France.
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  Date: 03/21; Other Information: no proceedings
• Barrett, B. (2012, March). Workshop Summary and Discussion Group Leader. GANIL/ FUSTIPEN workshop. Caen, France.
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  Date: 03/21; Other Information: no proceedings
• Barrett, B. (2012, May). Lectures on Theoretical Nuclear Physics: A Short Course of Seven Lectures. Australian National University. Canberra, Australia.
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  Other Information: no proceedings
• Barrett, B. (2012, September). Update on the No Core Shell Model. NT program.
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  Date: 09/14; Other Information: no proceedings
• Barrett, B. R. (2012, March). Beyond the No Core Shell Model: Extending the NCSM to Heavier Nuclei. Nuclear Theory Seminar. Orsay, France.
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  Date: 03/28
• Barrett, B. R. (2012, March). Using Concavity of Thermodynamical Functions to Predict Nuclear Binding Energies. GANIL. Caen, France.
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  Date: 08/22
• Kruse, M., Jorgenson, E., Navratil, P., Barrett, B., & Ormand, E. (2012, October). Uncertainty quantification in the Importance-truncated No-core Shell Model. APS DNP meeting.
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  Journal: Bull. Am. Phys. Soc; Volume 57; Number: 9; Pages: 30
• Papadimitriou, G., Barrett, B., Rotureau, J., & Ploszajczak, M. (2012, October). The Gamow Shell Model as a tool for ab-initio nuclear structure calculations. APS DNP meeting.
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  Journal: Bull. Am. Phys. Soc; Volume 57; Number: 9; Pages: 29

Poster Presentations

• Barrett, B. R. (2014, July). Deriving the nuclear shell model from first principles. Nuclear Structure 2014 Conference. University of British Columbia, Vancouver, BC, Canada: TRIUMF.

Reviews

• Barrett, B., Navratil, P., & Vary, J. (2013. Ab initio no core shell model(p. 131). Prog. Part. Nucl. Phys..
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  Volume: 69; doi:10.1016/j.ppnp.2012.10.003