Solution of Angular Parts of the Forbidden Beta Moment Matrix Elements for Rank 0, 1 and 2

In astrophysical environments, allowed Gamow-Teller (GT) transitions are important, particularly for β -decay rates in presupernova evolution of massive stars, since they contribute to the fine-tuning of the lepton-to baryon content of the stellar matter prior to and during the collapse of a heavy star. In environments where GT transitions are unfavored, first-forbidden transitions become important especially in medium heavy and heavy nuclei. Particularly in case of neutron-rich nuclei, first-forbidden transitions are favored primarily due to the phase-space amplification for these transitions. In this study, the angular part of the beta (β) moment matrix elements of the ,  and  first forbidden beta decay transition have been solved directly without any assumption. In the calculation of the nuclear matrix elements have been considered the contribution coming from the spin-orbit term in the shell model potential.