A modified Brink-Axel hypothesis for astrophysical Gamow-Teller transitions

TL;DR

This paper introduces a modified local Brink-Axel hypothesis for Gamow-Teller transitions in medium-mass nuclei, enabling more accurate calculations of weak transition rates crucial for astrophysical modeling of stellar cores.

Contribution

It presents numerical evidence that strength functions from nearby initial states are similar, allowing improved computation of weak transition rates at various excitation energies.

Findings

Strength functions from nearby states are similar within statistical fluctuations.

The modified hypothesis enables calculations at previously inaccessible energies.

Provides a method for accurate thermal weak transition rates in stellar environments.

Abstract

Weak interaction charged current transition strengths from highly excited nuclear states are fundamental ingredients for accurate modeling of compact object composition and dynamics, but are difficult to obtain either from experiment or theory. For lack of alternatives, calculations have often fallen back upon a generalized Brink-Axel hypothesis, that is, assuming the strength function (transition probability) is independent of the initial nuclear state but depends only upon the transition energy and the weak interaction properties of the parent nucleus ground state. Here we present numerical evidence for a modified `local' Brink-Axel hypothesis for Gamow-Teller transitions for $pf$-shell nuclei relevant to astrophysical applications. Specifically, while the original Brink-Axel hypothesis does not hold globally, strength functions from initial states nearby in energy are similar within statistical fluctuations. This agrees with previous work on strength function moments. Using this modified hypothesis, we can tackle strength functions at previously intractable initial energies, using semi-converged initial states at arbitrary excitation energy. Our work provides a well-founded method for computing accurate thermal weak transition rates for medium-mass nuclei at temperatures occurring in stellar cores near collapse. We finish by comparing to previous calculations of astrophysical rates.