Validity of Brink-Axel Hypothesis for calculations of allowed stellar weak rates of heavy nuclei

Abstract

The knowledge of beta-decay transitional probabilities and Gamow-Teller (GT) strength functions from highly excited states of nuclides is of particular importance for applications to astrophysical network calculations of nucleosynthesis in explosive stellar events. These quantities are challenging to achieve from the experimental measurements or computations using various nuclear models. Due to unavailability of feasible alternatives, many theoretical studies often rely on the Brink-Axel (BA) hypothesis, that is, the response of strength functions depends merely on the transition energy of the parent nuclear ground state and is independent of the underlying details of the parent state, for the calculation of stellar rates. BA hypothesis has been used in many applications from nuclear structure determination to nucleosynthesis yield in the astrophysical matter. We explore here the the validity of BA hypothesis in the calculation of stellar beta-decay (BD) and electron-capture (EC) weak rates of fp- and fpg-shell nuclides for GT transitions. Strength functions have been computed in a microscopic way by employing fully microscopic proton-neutron QRPA (quasi-particle random-phase approximation) within a broad density, ρYe = (10 - 1011) [g cm-3], and temperature, T = (1−30) [GK], grids relevant to the pre-collapse astrophysical environment. Our work provides evidence that the use of the approximation based on the BA hypothesis does not lead to reliable calculations of excited states strength functions under extreme temperature-density conditions characteristic of presupernova and supernova evolution of massive stars. Weak rates obtained by incorporating the BA hypothesis in the calculation of strength functions substantially deviate from the rates based on the state-by-state microscopically calculated strength functions. Deviation in the two calculations becomes significant as early as neon burning phases of massive stars. The deviation in the calculation of BD rates is even more pronounced, reaching up to three orders of magnitude.

Impact of the Brink-Axel hypothesis on unique first-forbidden β-transitions for r-process nuclei*

“…The majority of the previously calculated set of weak rate calculations [24,[30][31][32][33] used an approximate method invoking the socalled Brink-Axel (BA) hypothesis [34,35]. Several studies have investigated the accuracy of the BA hypothesis [36][37][38][39][40][41][42][43][44][45][46][47]. Most of these works have shown that the BA hypothesis is a poor approximation for usage in calculations related to stellar weak rates.…”