Energy dependence of neutron-proton matrix element ratios derived from 25<i>–</i>800 MeV energy proton scattering

Abstract

New data are presented on elastic and inelastic proton scattering by $^{58}\mathrm{Ni}$ at 333 and 498 MeV and $^{208}\mathrm{Pb}$ at 318 MeV. We have analyzed these data using phenomenological distorting potentials and potentials generated by folding neutron and proton densities with a free nucleon-nucleon t matrix or with a medium modified nucleon-nucleon interaction. Making use of electromagnetic matrix elements, or charge transition densities, we have calculated neutron-proton transition matrix element ratios in the vibrating potential--vibrating density model (``collective form factors''), or with a scaling model in which the neutron transition densities are taken as proportional to the proton densities. In addition, we have calculated, neutron-proton matrix element ratios from earlier (p,p') results at 25--800 MeV for $^{40}\mathrm{Ca}$, $^{58}\mathrm{Ni}$, and $^{208}\mathrm{Pb}$. We conclude that, although there are some irregularities, the derived neutron/proton matrix element ratios for natural parity states show a tendency to decrease in magnitude with decreasing proton energy in the range 500--100 MeV. A quantitatively similar effect is seen in the ratio of experimental to theoretical cross sections, where the latter are calculated using transition densities adjusted to fit electron or 800 MeV proton scattering. We attribute these results to a failure of the impulse approximation and the vibrating potential model in this energy region.