How effective is the Brink–Axel hypothesis for astrophysical weak rates?

Abstract

We explore the effectiveness of the Brink-Axel hypothesis for the computation of stellar electron capture and $\beta$-decay rates, namely that the transition strength function depends only upon the transition energy and not upon the details of the initial state. For this purpose, we calculated Gamow-Teller (GT) strength distributions for a selection of $sd$--shell nuclides, using two different microscopic models, namely the proton-neutron quasiparticle random phase approximation and the full configuration-interaction shell model, taking into account the first 100 states of both the initial and final nuclides. The GT transition strengths among these levels evolve with initial state energy. These transition strength functions we folded into %We later performed the calculation of weak-interaction mediated rates in stellar matter, specifically electron capture and $\beta$-decay rates, for a range of densities $10 \, \mathrm{g/cm^3} \leq\rho \leq10^{11} \, \mathrm{g/cm^3} $ and range of temperatures $1 \, \mathrm{GK} \leq T \leq 30 \, \mathrm{GK}$. When transitions from excited states were approximated using the Brink-Axel hypothesis, augmented by so-called `back-resonance' transitions, the rates were affected by up to 3 orders of magnitude or more at high temperatures and densities. Thus the Brink-Axel hypothesis is not a reliable approximation for the calculation of stellar rates, especially in high temperature--density environments.

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

“…Using the proton-neutron QRPA model, we investigated how the GT strength functions of allowed transitions and weak rates, in the EC and BD directions, were affected by the usage of BA hypothesis. Our study covered a broad range of fp-and fpg-shell nuclides with mass numbers (48-83) and proton numbers (20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32)(33)(34). We compared the microscopically calculated state-by-state transitions with those obtained by employing the BA hypothesis.…”

“…Afterwards, the FFN approach (with modifications) has been widely implemented to calculate the weak rates [6,11,[21][22][23][24][25][26]. In Independent-particle [20] and Large-scale shell [6] models, the use of the BA hypothesis for excited states was augmented by back resonances (see [27] for detail). However, in the configuration-interaction shell model studies [28,29], the authors reported that the energyweighed (non-energy-weighed) sum rules evolve with increasing initial energy in a smooth manner for E1, E2, M1 and GT transitions, leading to the violation of the BA hypothesis for GT strengths.…”

“…In this study, the authors showed that GT transitions of fp-shell nuclei follow the 'local' BA hypothesis, by using the interacting shell-model.We have studied here the validity of the BA hypothesis in the calculation of stellar weak rates. Our work is a follow-up of our study performed earlier for sd-shell nuclides [27]. For this purpose, we have picked the top 80 fp-and fpg-shell nuclides including both BD and EC, related to the post Si burning phases of pre-supernova stars [8,11,12].…”

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.…”