B. H. Wildenthal

Empirical strengths of spin operators in nuclei

Abstract New shell-model wave functions, derived from a single parametrization of the effective Hamiltonian, have been calculated for all sd-shell nuclei. The energies and matrix elements for single-nucleon transfer and electric-multipole operators predicted from these calculations are briefly surveyed in comparison with experimental values. The matrix elements predicted from these wave functions for Gamow-Teller, magnetic-dipole and other related spin-type operators are then compared in detail with the magnitudes of the corresponding experimentally determined matrix elements from A = 17–39 nuclei. From these comparisons, the empirical corrections to the free-nucleon normalizations of these spin operators are extracted. These empirical values of the corrections are compared with theoretical estimates of the effects of many-ω-configuration mixing and of mesonic-exchange currents and isobar excitations. Finally, the predicted distributions of matrix-element magnitudes with excitation energy are studied and compared with experiment, the difference between Gamow-Teller and M1 probes examined and the predicted momentum-transfer-dependence of the matrix elements compared with the results of electron scattering experiments.

Experimental and theoretical Gamow-Teller beta-decay observables for the sd-shell nuclei

Abstract A comprehensive comparison of experimentally observed Gamow-Teller beta decay with theory is presented for the sd-shell (A = 17–39) nuclei. Relevant experimental data on half-lives, Q values, and branching ratios are tabulated and used to deduce experimental log(ft) values and Gamow-Teller matrix elements. These are compared with theoretical values based on complete (0d 5 2 , 1s 1 2 , 0d 3 2 )- space shell-model wave functions. These wave functions are obtained from diagonalizations of a model Hamiltonian formulation which reproduces observed energy-level structures throughout the sd shell. The calculations are carried out both with the “free-nucleon” normalization for the Gamow-Teller single-particle matrix elements and with effective values for these matrix elements obtained from analyses of experimental Gamow-Teller magnitudes with the shell-model wave functions.

TWO-BODY MATRIX ELEMENTS FROM A MODIFIED SURFACE DELTA INTERACTION.

The addition of a T-dependent but J-independent term to the surface delta interaction greatly improves the agreement between the values of the two-body matrix elements calculated from this interaction and the corresponding values obtained both from emperical fits to level energies and from a realistic (Hamada-Johnston) interaction. This is shown for 1d-2s and 1f-2p configurations. The use of this modified surface delta interaction as a shell-model residual interaction produces good agreement between the calculated and experimental energies ofmany-nucleon configurations. In particular, total binding energies and the energy spacings between levels of different isospin are fitted much better than is possible without the use of the extra T-dependent term.

Semi-empirical effective interactions for the 1s-Od shell

Abstract Ground-state binding energies and excited-state energies of nuclei in the 1s-Od shell are analyzed in terms of a variety of two-body interactions. In addition to simple interactions such as the delta and surface-delta, we consider potentials of the finite-range, one-boson-exchange type for the central, tensor, and spin-orbit components of the interaction, with multipole terms added to the central part. The relative importance of these components, together with that of the antisymmetric spin-orbit component, is considered. The antisymmetric spin-orbit component is found to be the least important. Both density-dependent and density-indpendent interactions are considered. Our results favor a density-dependent form for the central and spin-orbit components. We develop a semi-empirical “best-fit” interaction based on a 14-parameter density-dependent two-body potential which reproduces 447 sd-shell binding-energy data to within an rms deviation between experiment and theory of 260 keV. This semiempirical interaction is compared to typical G-matrix interactions as well as to the purely empirical interactions obtained by using two-body matrix elements or Talmi integrals as parameters of the fit.

Empirically optimum M1 operator for sd-shell nuclei

Abstract M1 matrix elements deduced from experimental data on M1 transitions and magnetic moments in the sd-shell nuclei are analysed with calculations based on the full-basis sd-shell wave functions of Wildenthal to extract the parameters for an effective M1 operator. These empirical parameters are analogous to the predicted corrections for the free-nucleon M1 operator which arise from the effects of higher-order configuration mixing and mesonic-exchange currents. From the differences between the effective operators associated with isoscalar M1 matrix elements, isovector M1 matrix elements, and Gamow-Teller (GT) matrix elements (as deduced previously from GT beta decay data) we are able to evaluate the relative importance of higher-order configuration mixing, mesonic exchange currents involving the Δ-isobar, and other mesonic exchange currents.

A comparison of the effective two-nucleon interaction in 2s121d32-shell nuclei with a surface delta interaction☆

Abstract It is shown that the effective two-nucleon interaction in 2s 1 2 -1d 3 2 -shell nuclei can be well approximated by a delta function which acts only at the nuclear surface.

SHELL-MODEL CALCULATION FOR NUCLEI OF MASSES 30 THROUGH 33.

Abstract Level energies and spectroscopic factors for isotopes of P, Si, and S are calculated with a shell model which includes active particles in the 1d 5 2 , 2s 1 2 and 1d 3 2 shells.

Electric quadrupole and hexadecupole nuclear excitations from the perspectives of electron scattering and modern shell-model theory

Abstract Shell-model wave functions obtained from a complete, unified treatment of the structure of the positive parity states in nuclei between 16 O and 40 Ca are used to calculate the features of inelastic electron scattering to 2+ and 4+ states in this region. These predictions of E2 and E4 form factors, and the corresponding elastic scattering predictions, are compared with the collected experimental data which are available on this topic. The dependence of the calculated results upon alternate models for single-nucleon wave functions and core-polarization transition densities is investigated, as is the consistency between the (e,e′) measurements and the analogous B (E2) measurements.

Shell-model calculation of M1 scattering strengths in 42,44,48Ca

Abstract Calculation in the complete f 7 2 f 5 2 p 3 2 p 1 2 model space are presented for the M1 excitation of the ground states of 42,44,48 Ca.

Shell-model calculations for the zinc isotopes

Shell-model calculations for the zinc isotopes have been carried out with active particles distributed in the 1p32, 0f52 and 1p12 orbits outside a closed “56Ni” core. The effective Hamiltonian used was one obtained by Koops and Glaudemans from a fit to Ni and Cu level energies. An average absolute deviation of 0.19 MeV between the calculated and experimental ground-state binding energies is obtained for the A = 62−68 Zn isotopes. Good agreement is also found between most calculated and experimental excitation energies and spectroscopic factors for single-nucleon transfer for the low-lying levels in these nuclei. Experimentally known B(E2) values are generally well reproduced by the present model with effective charges of 1.0 ± 0.1 and 1.6 ± 0.2 for the neutron and proton, respectively. Magnetic dipole as well as Gamow-Teller transitions are not well accounted for by these calculations and seem to be sensitive to excitations of the 56Ni core.