Electron capture strength on odd-A nucleus $\mathbf{^{59}}$Co in explosive astrophysical environment

TL;DR

This paper calculates Gamow-Teller transition strengths and electron capture rates for the odd-A nucleus $^{59}$Co using the pn-QRPA model, comparing results with other models and experiments to improve understanding of supernova core collapse.

Contribution

The study provides new pn-QRPA calculations of GT strength distributions and electron capture rates for $^{59}$Co, offering improved placement of GT centroids and comparison with experimental data.

Findings

pn-QRPA yields a total $B(GT_{+})$ of 3.3, higher than shell model and experimental values.

GT centroid placement at 5.6 MeV aligns better with shell model than previous models.

Suppressed electron capture rates may influence supernova core dynamics and nucleosynthesis.

Abstract

The Gamow-Teller (GT) transitions within massive stars play sumptuous role in the dynamics of core collapse supernovae. GT strength distributions and electron capture rates have been calculated for odd-A nucleus $^{59}$Co within the proton-neutron quasiparticles random phase approximation (pn-QRPA) formalism. The pn-QRPA results are compared with other model calculations and (n, p) reaction experiment carried out at TRIUMF charge-exchange facility. The pn-QRPA calculated a total $B(GT_{+})$ strength of 3.3 for $^{59}$Co to be compared with the shell model value of 2.5 and the 1.9 $\pm$ 0.1 in the (n, p) charge-exchange reaction. Aufderheide et. al. \cite{Aufderheide93} extracted total strength equaling 2.4 $\pm$ 0.3. The placement of GT centroid at 5.6 MeV by the pn-QRPA model is in reasonable agreement with the shell model centroid at 5.1 MeV whereas the measured GT centroid was placed at 4.4 $\pm$ 0.3 MeV in the (n, p) experiment. Fuller, Fowler and Newman (FFN) \cite{FFN80, FFN82, FFN82b}, placed the GT centroid at too low excitation energy of 2.0 MeV in the daughter nucleus $^{59}$Fe, and this misplacement led to the enhancement of FFN rates. The suppressed pn-QRPA and shell model electron capture rates are in good agreement with each other. The rates are suggestive of higher value of $Y_{e}$ (electron-to-baryon ratio) and may contribute to a more massive homologously collapsing core resulting in a more energetic shock. It might be interesting for the simulators to check the effect of these suppressed rates on the fine-tuning of the time rate of $Y_{e}$, the concomitant heavy element nucleosynthesis, and, on the energetics of the subsequent shock wave.