Study of the Level Structure ofN=82Nuclei via Proton-Transfer Reactions

Measurements of the angular distributions of the (${}_{}{}^3{}_{}{}^{}\mathrm{He},d$) and ($d,{}_{}{}^3{}_{}{}^{}\mathrm{He}$) reactions on the stable, even-mass $N=82\mathrm{}$ isotones are presented and discussed. In each of the residual nuclei formed in these reactions, ${}_{}{}^{135}{}_{}{}^{}\mathrm{I}$, ${}_{}{}^{137}{}_{}{}^{}\mathrm{Cs}$, ${}_{}{}^{139}{}_{}{}^{}\mathrm{La}$, ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pr}$, ${}_{}{}^{143}{}_{}{}^{}\mathrm{Pm}$, and ${}_{}{}^{145}{}_{}{}^{}\mathrm{Eu}$, the lowest two levels are populated with significant strength, one by $l_p=4\mathrm{}$ transfer and one by $l_p=2\mathrm{}$ transfer. Analysis indicates that these states result from coupling a $1g_{\frac{7}{2}}$ or $2d_{\frac{5}{2}}$ proton (or proton hole) to the respective $J^{\pi }=0^{+}$ target ground states. The relative energies of these states change as a function of mass, the ${\frac{5}{2}}^{+}$ state lying 590 keV above the ${\frac{7}{2}}^{+}$ state in ${}_{}{}^{135}{}_{}{}^{}\mathrm{I}$, and 330 keV below the ${\frac{7}{2}}^{+}$ state in ${}_{}{}^{145}{}_{}{}^{}\mathrm{Eu}$. Spectroscopic factors extracted from the data with distorted-wave Born-approximation analysis indicate that the active particles in the target ground states predominantly occupy the $1g_{\frac{7}{2}}$ and $2d_{\frac{5}{2}}$ orbits, with the ratio of $1g_{\frac{7}{2}}$ protons to $2d_{\frac{5}{2}}$ protons varying from 3.5/0.5 for