Core polarization effects on first-forbidden β-transitions and the analogous E1 γ-transitions

Abstract

Effective coupling constants g eff for the first-forbidden β-transitions with operators r and σ× r in medium and heavy nuclei were obtained by comparing experimental matrix elements with pairing model calculations. The matrix elements 〈 r〉 were taken from the E1 γ-ray matrix elements for the isobaric analogue states of the parent nuclei. The values g eff/ g are 0.2–0.3 for semi-magic nuclei and 0.4–0.5 for double-magic nuclei. They are analyzed in terms of isospin (spin) core polarizations. A simple expression for g eff is given in a schematic model. The core polarizations explain well the obtained values of g eff. Spin-flip matrix elements 〈↓∥ tir Y 1∥↑〉 were also analyzed. Detailed discussions are given on the possible giant resonances associated with the first-forbidden β-transitions.