Neutron-proton matrix element ratios of 21+ states in 58,60,62,64 Ni

The neutron-proton matrix element ratios (η) for 21+ states of even Ni isotopes are investigated within the framework of the shell model quasi-particle random-phase approximation. Special attention is devoted to the dependence of η ratios on the radial neutron and proton ground-state density distribution differences (Δnp). This dependence is found to be about 0.5Δnp. The theoretical η ratios are (14-23)% greater than the hydrodynamical limit. The knowledge of the Δnp dependence of η ratios enable us to understand the empirical η ratio results