Neutron-proton decomposition of transition matrix elements from a comparison of 800 MeV proton scattering with electromagnetic methods

Differential cross sections for inelastic proton scattering at 800 MeV have been measured for a number of low-lying states in ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{144}{}_{}{}^{}\mathrm{Sm}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. The data from this and earlier experiments on ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ were analyzed with a collective vibrational model to obtain separate neutron and proton deformation lengths, making use of electromagnetic measurements. Ratios of neutron to proton transition matrix elements are calculated. These ratios are generally less than $\frac{N}{Z}$ for the open proton shell nuclei and greater for the open neutron shell nuclei.