Charge-dependent two-body interactions deduced from displacement energies in the [formula omitted] shell

Abstract

The f 7 2 shell model is used to relate displacement energies in the region A = 41–55 to a single-particle displacement energy and the differences between the proton-proton, proton-neutron, and neutron-neutron two-body matrix elements for J = 0, 2, 4 and 6. We find that the displacement energies for essentially all measured states (about 60) can be calculated to within an rms deviation of 12 keV by using a fixed set of these parameters. A few discrepancies such as for the 0 + and 2 + states in A = 42 can be due to large admixtures outside f 7 2 configurations. The deduced two-body matrix elements are compared with previous results for the d 5 2 s 1 2 and d 3 2 shells. The empirical results are compared with calculations of the Coulomb two-body matrix elements assuming j 2 configurations. The empirical pp-nn matrix elements are anomalous relative to these simple calculations. The size of the anomaly for the 2 J + 1 weighted average of the pp-nn interactions in the 1 f 7 2 shell is about the same as that deduced from the single-particle nuclei by Nolen and Schiffer; the J-dependence of the anomaly is very irregular. The empirical pn-nn matrix elements are consistent with zero except in the case of J = 0. The anomalies in both the pp-nn and pn-nn interactions may be due to configuration mixing and/or a charge dependence in the nucleon-nucleon interaction. The importance of the mass dependence in ħω for rms radii and Coulomb shifts is discussed. The displacement energies for proton rich f 7 2 nuclei are predicted and isospin-mixing matrix elements are calculated. Relations between the exact calculation and the generalized-seniority approximation are discussed.