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

Many new energy levels up to ∼2-MeV excitation are located in the odd-$A$ cadmium isotopes. Spins, parities, as well as spectroscopic factors, are determined with the aid of distorted-wave Born approximation (DWBA) calculations. The distinction between the $d_{\frac{5}{2}}$ and $d_{\frac{3}{2}}$ levels was made according to the pickup-to-stripping cross-section ratios. The systematic behavior of the first excited state for the various spin values enables us to conclude that the first excited states in ${\mathrm{Cd}}^{115}$ and ${\mathrm{Cd}}^{117}$ are $d_{\frac{3}{2}}$ states and the 300-keV state in ${\mathrm{Cd}}^{113}$ is an unresolved $d_{\frac{3}{2}}-d_{\frac{5}{2}}$ doublet. The ($d, p$) spectra for reactions leading to odd cadmium isotopes which differ from each other by as much as four neutron pairs, and to Cd-Pd isotones which differ by one proton pair, are compared. The changes in the observed spectra, as well as in the location of the neutron single-particle states, are rather small in both cases. The various approximations for the evaluation of the pairing-theory parameters, such as the occupation numbers and the single-quasiparticle energies, from the experimental data are discussed. The need for good DWBA calculations for the ($d, t$) reactions in order to avoid the necessity of renormalizations, and for cross checking of the results, is stressed. The effect of the quadrupole interaction on the single quasiparticles is clearly seen in cadmium from the fact that the $s_{\frac{1}{2}}$ state becomes the ground state in ${\mathrm{Cd}}^{111}$ even though its occupation number is as low as ${V_{\frac{1}{2}}}^2=0.1\mathrm{}$.