Nuclear Structure Studies in the Zirconium Isotopes with (d, p) and (d, t) Reactions

Angular distributions from ($d, p$) reactions in the zirconium isotopes are found to agree exceedingly well with distorted-wave Born approximation calculations; this agreement includes the absolute cross sections. These reactions are used to assign all levels excited by ($d, p$) reactions is ${\mathrm{Zr}}^{90}$, ${\mathrm{Zr}}^{91}$, ${\mathrm{Zr}}^{92}$, ${\mathrm{Zr}}^{94}$, and ${\mathrm{Zr}}^{96}$ to single-particle (S.P.) states. The summed cross sections for each S.P. state in each isotope are close to expectations. The "centers of gravity" of each S.P. state are located; all of these including the nonpaired levels from the ($d, p$) reaction on ${\mathrm{Zr}}^{91}$, behave very smoothly as a function of $A$. The summed cross sections for states of $I=0, 2, \mathrm{and} 4$ from ${\mathrm{Zr}}^{91}(d, p)$ each also agree with theory. The ground state of ${\mathrm{Zr}}^{92}$ is found to be 78% ${\left(d_{\frac{5}{2}}\right)}^2$. Results from ($d, t$) reactions on the even isotopes leading to states other than $d_{\frac{5}{2}}$ behave very anomalously. Attempts to explain them are discussed but more data are needed. The ${\mathrm{Zr}}^{91}(d, t)$ reaction is used to obtain information on the ground state of ${\mathrm{Zr}}^{91}$, and on the 3— state of ${\mathrm{Zr}}^{90}$.