Importance of higher order corrections to the effective charge

Abstract

Rayleigh-Schrödinger perturbation theory through second order is applied to the problem of electromagnetic transitions in closed-shell-plus-one-nucleon nuclei. The concept of effective charge is introduced and its usefulness as a physical parameter is discussed. Effective charges relevant to quadrupole moments and E2 transitions in 17O and 17F are calculated in first and second order. The semi-realistic Kallio-Kolltveit interaction is used to evaluate two-body matrix elements. The Tamm-Dancoff and random phase approximations are also discussed, and results of effective charge calculations made in these approximations are presented. In a set of appendices, explicit formulas for the second-order corrections to the reduced matrix element which describes electromagnetic transitions between single-particle states are given (appendices 1 and 2). Also included in these appendices is a discussion of state dependent separation distances in the Kallio-Kolltveit interaction (appendix 3). In appendix 4, results of effective charge calculations carried out with Kuo-Brown two-body matrix elements are presented. Finally, in appendix 5, E2 effective charges relevant to the closed-shell-minus-one-nucleon nuclei 15O, 15N, 39Ca and 39K are given.