(d,He3) Reactions on the Even Zirconium Isotopes

Abstract

An investigation of the proton ground-state configurations in the even zirconium isotopes ($A=90, 92, 94, 96$) was undertaken using the ($d$,${}_{}{}^3{}_{}{}^{}\mathrm{He}$) reaction at a deuteron energy of 34.4 MeV. The experimental angular distributions were compared with distorted-wave calculations in the finite-range approximation which include nonlocality in the distorted waves. The residual yttrium isotopes ($A=89, 91, 93, 95$) have ${\mathrm{½}}^{-}$ ground states, and the observed spectra can be interpreted in terms of a simple shell-model picture which considers hole and particle configurations in the $1g_{\frac{9}{2}}$, $2p_{\frac{1}{2}}$, $2p_{\frac{3}{2}}$, and $1f_{\frac{5}{2}}$ proton shells and allowed couplings in the $2d_{\frac{5}{2}}$ neutron shell. It was found that the filling of the $2d_{\frac{5}{2}}$ neutron shell apparently has a measurable effect on the relative amounts of the ${\left(2\mathrm{}{p}_{\frac{1}{2}}\right)}^2$ and ${\left(1\mathrm{}{g}_{\frac{9}{2}}\right)}^2$ proton admixtures in the zirconium ground states. The strength of the ${\left(2\mathrm{}{p}_{\frac{1}{2}}\right)}^2$ term in the ground-state wave functions was determined to be: 64% for ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, 55% for ${}_{}{}^{92}{}_{}{}^{}\mathrm{Zr}$, 66% for ${}_{}{}^{94}{}_{}{}^{}\mathrm{Zr}$, and 86% for ${}_{}{}^{96}{}_{}{}^{}\mathrm{Zr}$.