The particle-vibration coupling model is treated in a perturbation approach in order to
1. (i) obtain simple expressions for the reduced E2 transition probabilities and thus derive approximate selection rules and
2. (ii) study the convergence properties of the perturbation series (up to sixth-order) by comparing with the exact diagonalization procedure. The results are in both cases compared with diagonalization results and the experimental data available on 121Sb and 123Sb.
The perturbation expansion, treated to higher order, can be performed easily in terms of a diagrammatic method based on Goldstone and Jutsis-Bandzaitis-Vizbaraite formalisms.
It is shown that the perturbation method gives reliable results if “physical” single-particle energies are used instead of “bare” single-particle energies with the neglect of all self-energy corrections and a renormalized particle-vibration coupling strength.
This higher order perturbation expansion is applied to the case of 119Sb and 123Sb.