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B. R. Barrett

Publications and source records attributed to B. R. Barrett.

52 records · Page 3Linked to original sources
arXiv1998

Spreading Width for Decay out of a Superdeformed Band

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 1/F = (1 + Gamma(down) / Gamma(S)). Here, Gamma(S) is the width for the collective E2 transition within the superdeformed band, and Gamma(down) 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 Gamma(N) of the ND states provided that the Gamma(N) are much larger than both Gamma(down) and Gamma(S). This condition is generically met. Previously measured values of F are used to determine Gamma(down).

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arXiv1998

Comparison of techniques for computing shell-model effective operators

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 $^6$Li. The convergence trends and dependence of the effective operators on differing excitation spaces and Pauli Q-operators is 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.

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arXiv1998

Large-basis shell-model calculations for p-shell nuclei

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 $6\hbarΩ$ model space was used, while for the rest of the studied nuclides, the calculations were performed in a $4\hbarΩ$ 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.

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arXiv1997

Shell-model calculations for the three-nucleon system

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 $32 \hbarΩ$ 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.

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arXiv1997

Large-basis shell-model calculation of 10C->10B Fermi matrix element

We use a $4\hbarΩ$ 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 $δ_{C}\approx 0.1 %$, which is compatible with previous calculations. The correction obtained in those calculations, performed in a $0\hbarΩ$ 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 $δ_{C}$ correction is about a factor of four too small to obtain unitarity of the Cabibbo-Kobayashi-Maskawa matrix with the present experimental data.

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arXiv1996

Microscopic origins of effective charges in the shell model

We use a large-scale 6 hbar Omega calculation for Li6 with microscopically derived two-body interaction to construct the 0 hbar Omega 0p-shell effective hamiltonian, electric quadrupole, and magnetic dipole operators. While the E2 and M1 6 hbar Omega 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.

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arXiv1996

No-core shell-model calculations with starting- energy-independent multi-valued effective interactions

Large-space no-core shell model calculations have been performed for A=3-6 nuclei, 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 multi-valued effective interaction approach. Dependence of the He5 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.

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arXiv1995

Sum Rules for B(M1,0+ -> 1+) Strength in IBM-3 and IBM-4

Sum rules for $B(M1,0^+_1\rightarrow1^+_i)$ 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 $U(6)\supset SU$(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 $B(M1,0^+_1\rightarrow1^+_i)$ is given. In contrast to IBM-2, there is fragmentation of the strength even in the dynamical symmetry cases, for $T\neq 0$, over two states in IBM-3, and over three states in IBM-4. The presence of $pn$ bosons in the ground state of the extended versions reduces the expected strength from that for IBM-2, allowing in principle the possibility of using $B(M1)$ data for a given nucleus to infer which version is the most appropriate.

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arXiv1995

Large-basis shell model studies of light nuclei with a multi-valued G-matrix effective interaction

Large-basis shell model studies of low-lying excitations in light nuclei from 4He to 7Li have been performed with a multi-valued 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 8\hbarΩ. Using G matrices derived from a new Nijmegen potential, we achieve a very satisfactory description of these excitations.

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arXiv1994

Auxiliary potential in no-core shell-model calculations

The Lee-Suzuki iteration method is used to include the folded diagrams in the calculation of the two-body effective interaction $v^{(2)}_{\rm eff}$ 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 {\it NN} potential, we find that $v^{(2)}_{\rm eff}$ overbinds $^4\mbox{He}$ in 0, 2, and $4\hbarΩ$ 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.

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arXiv1994

Large-space shell-model calculations for light nuclei

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 compare favorably with experiment.

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arXiv1993

Simple approximation for the starting-energy-independent two-body effective interaction with applications to 6Li

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 multi-shell, 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 simple 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 6Li in order to test the utility of the approximate form.

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arXiv1993

Nuclear shell-model calculations for 6Li and 14N with different NN potentials

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 6Li and 14N in a (0+2)hw 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. (Submitted to Phys. Rev. C on Nov. 9, 1993 as a Brief Report.)

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arXiv1993

Minimizing Effective Many-Body Interactions

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.

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arXiv1993

Microscopic Calculations of the Spectra of Light Nuclei

We perform large-space shell-model calculations for the low-lying energy spectra of a few light nuclei, $^4\mbox{He}$, $^5\mbox{He}$, $^6\mbox{Li}$ and $^7\mbox{Li}$, 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 ($\hbarΩ$).

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