Splitting of One-Phonon Coupling States in the Weakly Coupling Model

The splitting of one-phonon coupling states in the weakly coupling model for odd-A nuclei is studied. Matrix elements are given explicitly, and an analytical expression for the energy levels is given in a perturbation approach. An application is given to ⁹³Nb and ⁵¹V. A comparison between the weakly coupling model and the shell model treatment for ⁵¹V is discussed.