(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 ${\mathrm{\textonehalf{}}}^{\ensuremath{-}}$ 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 $1{g}_{\frac{9}{2}}$, $2{p}_{\frac{1}{2}}$, $2{p}_{\frac{3}{2}}$, and $1{f}_{\frac{5}{2}}$ proton shells and allowed couplings in the $2{d}_{\frac{5}{2}}$ neutron shell. It was found that the filling of the $2{d}_{\frac{5}{2}}$ neutron shell apparently has a measurable effect on the relative amounts of the ${(2{p}_{\frac{1}{2}})}^{2}$ and ${(1{g}_{\frac{9}{2}})}^{2}$ proton admixtures in the zirconium ground states. The strength of the ${(2{p}_{\frac{1}{2}})}^{2}$ 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 $^{96}\mathrm{Zr}$.