Shell Model of the Nickel Isotopes

The isotopes of nickel are described by a shell model within the identical-nucleon configurations ${(2\mathrm{}{p}_{\frac{3}{2}}, 1f_{\frac{5}{2}}, 2p_{\frac{1}{2}})}^n$. A least-squares fit to observed level energies yields an effective interaction which satisfactorily reproduces the level structure of the Ni isotopes from ${\mathrm{Ni}}^{58}$ to ${\mathrm{Ni}}^{65}$. 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 $E2\mathrm{}$ 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 ${\mathrm{Ni}}^{60}$ and ${\mathrm{Ni}}^{62}$ 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.