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

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.