The effect of pairing correlations on nuclear transition rates

An attempt is made to study the influence of pairing correlations in some γ and β decay processes, using “projected” wave functions that are eigenfunctions of the number operator, and that have extremely large overlaps with the exact solutions of the pairing Hamiltonian. It is not much more difficult to obtain accurate numerical results with the new wave functions than it is with the usual Bardeen-Copper-Schrieffer wave functions. The results show some appreciable differences between the two types of wave functions, which in some β-decay cases studied can be as much as 10% to 25% when the same single particle level structure and pairing force parameters are used. Also the β-decay results are compared with those calculated by Soloviev in order to illustrate the sensitivity to the single-particle spectrum assumed. The ratio of M4 transitions in Pb and Sn isotopes are found to be insensitive to the use of projected wave functions, but the rates in the N = 50 isotopes are appreciably altered. In general, the projected wave functions indicate that pairing correlations can account for only part of the configuration mixing required to explain the large deviations from single particle values that are experimentally observed.