Diagrammatic method of the particle-vibration coupling model: (II). Application to convergence and self-energy problems in 201Tl

Abstract

Diagrams describing a system of a single-particle (hole) coupled to a quadrupole vibrator are systematically treated. Comparison between the results of a diagonalization and perturbation approach is made on the example of 201Tl, with special emphasis on the self-energy problem. It is seen that the self-energy diagrams represent the main “diverging” contributions, but their effect can be incorporated in the renormalization of the coupling strength. In the latter case, single-particle energies should be taken directly from experiment. The expressions for reduced matrix elements of the E2 operator from diagrams up to the third order simply give the behaviour of quadrupole moments and B(E2) values in terms of the phonon energy and the single-particle configurations involved.