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

Many new energy levels are located in the odd-$A$ palladium isotopes and the spin and parity values assigned. The parameters of the pairing theory, such as the single quasiparticle energies, the occupation numbers, the strength of the pairing interaction, etc., are evaluated. By means of them, the single-particle energies are obtained and compared with other nuclei of the same neutron shell. While the orbits $2d_{\frac{5}{2}}$, $3s_{\frac{1}{2}}$, and $2d_{\frac{3}{2}}$ do not change their relative locations significantly, the $1g_{\frac{7}{2}}$ orbit shows drastic changes. In the palladium isotopes the $1g_{\frac{7}{2}}$ orbit is found to be below the $2d_{\frac{5}{2}}$ orbit, while in zirconium it is as high as the $2d_{\frac{3}{2}}$ orbit, and in tin somewhat above the $2d_{\frac{5}{2}}$ orbit. This indicates that the interaction between the $1g_{\frac{7}{2}}$ neutrons and the $1g_{\frac{9}{2}}$ protons, which causes the shifts of the $1g_{\frac{7}{2}}$ orbit, is most effective in palladium isotopes, i.e., where the $1g_{\frac{9}{2}}$ proton orbit is about half-full. The strength of the pairing interaction is evaluated to be $GA=29.2\mathrm{}\pm 0.9$ MeV.