Neutron and proton transition matrix elements forZr90from a microscopic analysis of 0.8 GeV proton inelastic scattering

Abstract

We have analyzed recent 0.8 GeV proton inelastic scattering cross sections for eight low-lying states in $^{90}\mathrm{Zr}$ using the distorted wave impulse approximation and transition densities from a large basis shell model calculation. The shell model basis consists of the configurations of 12 valence protons in the $2{p}_{\frac{1}{2}}$, $2{p}_{\frac{3}{2}}$, $1{f}_{\frac{5}{2}}$, and $1{g}_{\frac{9}{2}}$ orbits. In general the shapes of the cross sections are well reproduced, but the calculated transition amplitudes must be multiplied by factors of 2.2 to 4.6 to fit the magnitudes. These enhancement factors are larger than those required for the $B(E\ensuremath{\lambda})$ values derived from electron scattering, indicating large neutron components in these states. We argue that transitions to the ${3}_{1}^{\ensuremath{-}}$ and ${2}_{3}^{+}$ states cannot be described adequately in the chosen shell model basis. From the proton and electromagnetic enhancement factors we are able to obtain estimates of the missing neutron and proton matrix elements.NUCLEAR REACTIONS $^{90}\mathrm{Zr}$(p,p\ensuremath{'}) at 0.8 GeV, analyzed with DWIA and shell model theory. $B(E\ensuremath{\lambda})$ values calculated. Neutron and proton core matrix elements deduced.