Theoretical Predictions for the Spectra of the Odd-Mass Xenon and Tellurium Isotopes

The spectra of the isotopes ${\mathrm{Te}}^{123,125}$, ${\mathrm{Xe}}^{127,129}$ are calculated by assuming that the odd neutron, having available the $3s_{\frac{1}{2}}$ and $2d_{\frac{3}{2}}$ states, is coupled to collective surface vibrations of the core. Good agreement is obtained with the known levels in these nuclei using a reasonable value for the coupling parameter. To obtain the agreement, the $d_{\frac{3}{2}}-s_{\frac{1}{2}}$ splitting, $\epsilon$, must be regarded as a function of neutron number. The manner in which $\epsilon$ varies, as found in the intermediate coupling calculation is compared with the predictions of the pairing correlation theory originally introduced in connection with superconductivity. Agreement as to the general trend is found. This may be regarded to some extent as an indication of the applicability of the pairing correlation theory to nuclear structure calculations.