Review of Gamow-Teller and Fermi transition strength functions

Abstract

We studied the temperature effect in isospin-singlet pairings in Gamow-Teller excitations.
We use theories of a hole-particle in the mean-field shell model to study decay transition
using the one-particle-one-hole model for the $\beta$-decay of odd-even isotopes and the
two-particle-hole models for the $\beta$-decay of even-even and/or odd-odd isotopes.
Our reference isotopes for the one-particle-one-hole model are \ce{^{15}O}, \ce{^{15}N}, \ce{^{17}F}, and \ce{^{41}Sc},
whereas for the two-particle-hole model we use \ce{^{16}N} (for $\beta^-$-decay)
and \ce{^{56}Ni} and \ce{^{40}Sc} (for $\beta^+$/EC).

The calculations involve evaluating the matrix elements of Gamow-Teller and Fermi transitions,
then calculating the reduced transition probabilities of Gamow-Teller and Fermi, from which we evaluate
the half-lives and the strength function $ft$. The results are compared with the available experimental data.
For the one-particle-one-hole model, we found there is a deviation from experimental values which indicates that the
model is not valid for beta decay for the even-even nuclei in the ground state due to the residual nucleon-nucleon
interaction. As for a two-particle-hole model, we calculated the transition amplitude, from which we calculated
the strength of the transition $\log ft$ values. We found an excellent agreement between experimental and theoretical results.

By drawing the relationship between temperature versus $\log ft$ values, we found the general trend is that the strength function values slowly
decrease as temperatures increase. There are fluctuations $\log ft$ due to the strongly dependent of $\log ft$ on the shell configuration of the valence nucleons.