Shell Model of the Nickel Isotopes

Abstract

The isotopes of nickel are described by a shell model within the identical-nucleon configurations (2pz/2,lfb/2,2pi/2) n . A least-squares fit to observed level energies yields an effective interaction which satisfactorily reproduces the level structure of the Ni isotopes from Ni 58 to Ni 65 . This best-fit interaction is shown to indicate repulsive interactions between identical-nucleon shells and to conserve seniority to a useful degree of approximation. The interaction matrix elements are in fair agreement with those of an approximate reaction matrix computed by Kuo from Hamada and Johnston's free-nucleon interaction, this agreement being obtained only when core polarization is taken into account. Moments and transitions also show the strong influence of core excitation. Observed quadrupole moments and E2 transition rates are adequately reproduced with an effective neutron charge of between 1.5e and 2e; in particular, the observed inhibition of the crossover ground-state decay of the second 2 + (2 2 + ) states of Ni 60 and Ni 62 is reproduced with 2 2 + wave functions for which a two-phonon vibrational description is clearly incorrect. It is shown that the original model cannot account for the large deviations of observed magnetic moments from the Schmidt values, nor for the observed spreading of stripping strength into a given orbit over several states of the residual nucleus. To account for these, it is necessary to introduce effective transition operators, strongly modified by the influence of neglected configurations.

Shell-model calculations on the nickel isotopes

“…10 agree excellently with experiment. The discrepancy found in the dipole moment of the first excited 57Nj Ex(MeV ) jn ~m(fS) 1 …”

Status of vibrational structure inNi62

“…The closure of both the 1f 7/2 proton and neutron shells in 56 28 Ni 28 leads to a simple shell-model description of the low-lying levels in the nickel isotopes with the proton shells completely inert and the valence neutrons in the 2p 3/2 , 1f 5/2 , and 2p 1/2 orbitals. Shell model calculations with this simple configuration space reproduce the energy spectra of the nickel isotopes up to ∼ 3 MeV [1][2][3]; however, calculations of electromagnetic transition rates do not reproduce the experimental values. This failure indicates the necessity for excitations of the 56 Ni core.…”

Shell-model calculations on Ni and Cu isotopes

“…So far only the Ni isotopes have been studied somewhat more extensively. Shell-model calculations on energies, spectroscopic factors and some electromagnetic transition strengths, with active neutrons in the 2p3/2, lf5/2 and 2pl/z orbits, have been performed [1,2] using empirical two-body matrix elements. Effective one-and two-body matrix elements have been used in a detailed shell-model study [3] involving energy spectra and electromagnetic properties.…”