STATE-DEPENDENT EFFECTIVE CHARGE IN 2P-1F SHELL

Motivated by a desire to understand the electric quadrupole transition rates in Ni58, calculations of the effective charge for both neutrons and protons were carried out, first with Ca40 as a core and then with Ni56. The calculation was done in perturbation theory using the Kallio-Kolltveit interaction. Concerning state dependence, it was first observed and then proved that in the limit in which energy differences in the 2p-1f shell were small compared with 2 excitations, the effective charge depended on the initial and final orbital angular momentum of a given transition, but when these l's were specified, it was independent of the initial and final j values. The effective-charge correction was much bigger for a neutron than for a proton. This may have the effect of reducing the isovector part of the quadrupole operator and hence causing T=1 transitions to be inhibited. The effective charge is substantially larger with Ni56 as a core than with Ca40 as a core, but is somewhat too small to explain the E2 transition from the first excited 21+ stage to ground. The effect of state dependence in the examples considered was to change certain E2 rates by a factor of 1.5 to 2. In N158, the E2 ratio 22+01+/22+21+, if calculated with shell-model wave functions, is extremely sensitive to the two-body interaction that is used. For example, it is about sixty times smaller (and closer to experiment) if Kuo's matrix elements, which are derived from a realistic interaction, are used rather than matrix elements chosen to give a least-squares fit to the energy levels of the nickel isotopes. If only one of the matrix elements obtained from the energy fit is changed by 0.3 MeV, the ratio becomes forty-two times smaller, also closer to the experimental value. The possibility that a lowlying 2+ state was basically a 3p-1h state was examined. The lowest two such states had very weak E2 transitions to ground and therefore did not at all resemble the one-phonon state or the electric quadrupole state. By themselves, these states fail as candidates, not only for the 21+ state but also the 22+ state because they radiate more to the ground than to the 21+ state. © 1969 The American Physical Society.