Charge-dependent and A-dependent effects in isotope shifts of Coulomb displacement energies

Coulomb displacement energies in a series of isotopes generally decrease with A. This decrease can arise from an increase with A of the average distance of interaction between pairs of protons. In the shell model a decrease can also result from charge-independence-breaking effects if the neutron-proton interaction for the valence nucleons is more attractive than the neutron-neutron interaction. Using the model recently proposed by Sherr and Talmi for the 1d/sub 3/2/ shell, existing data for this shell and also the 1d/sub 5/2/ and 1f/sub 7/2/ shells were analyzed allowing all matrix elements to vary as A/sup -lambda/3/. Least squares calculations of the rms deviation sigma were carried out for varying values of lambda from -2 to +2. It was found that although there was a minimum in sigma vs lambda it was too shallow to exclude any lambda for -1 to +1 in the 1d/sub 3/2/ and 1f/sub 7/2/ shells or 0 to +1 in the 1d/sub 5/2/ shell. It is therefore not possible to distinguish between A dependence and charge dependence in this model. The magnitude of the latter as expressed in terms of (np-nn) matrix elements depends strongly on the former. As lambda increases from -1 to +1, these (np-nn) matrix elements decrease roughly linearly in absolute magnitude and eventually change sign. For lambda = 0 they have appreciable and reasonable magnitudes for the 1d/sub 3/2/ and 1f/sub 7/2/ shells but for the 1d/sub 5/2/ shell the values are too small to be considered significant