Gamow-Teller strength distribution in proton-rich nucleus $^{57}$Zn and its implications in astrophysics

Gamow-Teller (GT) transitions play a preeminent role in the collapse of stellar core in the stages leading to a Type-II supernova. The B(GT) strength distributions for ground and excited states of $^{57}$Zn are calculated in the domain of proton-neutron Quasiparticle Random Phase Approximation (pn-QRPA) theory. No experimental insertions were made (as usually made in other pn-QRPA calculations of B(GT) strength function) to check the performance of the model for proton-rich nuclei. The calculated ground-state B(GT) strength distribution is in good agreement with measurements and shows differences with the earlier reported shell model calculation. The pn-QRPA model reproduced the measured low-lying strength for $^{57}$Zn better in comparison to the KB3G interaction used in the large-scale shell model calculation. The stellar weak rates are sensitive to the location and structure of these low-lying states in daughter $^{57}$Cu. The primary mechanism for producing such nuclei is the rp-process and is believed to be important in the dynamics of the collapsing supermassive stars. Small changes in the binding and excitation energies can lead to significant modifications of the predictions for the synthesis of proton rich isotopes. The $\beta^{+}$-decay and electron capture (EC) rates on $^{57}$Zn are compared to the seminal work of Fuller, Fowler and Newman (FFN). The pn-QRPA calculated $\beta^{+}$-decay rates are generally in good agreement with the FFN calculation. However at high stellar temperatures the calculated $\beta^{+}$-decay rates are almost half of FFN rates. On the other hand, for rp-process conditions, the calculated electron capture ($\beta^{+}$-decay) rates are bigger than FFN rates by more than a factor 2 (1.5) and may have interesting astrophysical consequences.