Allowed and forbidden $\beta$-decay log ft values of neutron-rich Pb and Bi isotopes

Abstract

The $\beta$-decay log ft values for $^{210-215}$Pb $\rightarrow$ $^{210-215}$Bi and $^{210-215}$Bi $\rightarrow$ $^{210-215}$Po transitions in the north-east region of $^{208}$Pb nuclei are estimated using the proton-neutron quasiparticle random phase approximation (pn-QRPA) model. The pn-QRPA equations were solved using the schematic model approach. The Woods–Saxon (WS) potential was inserted as a mean-field basis and nuclei were treated as spherical. Allowed Gamow–Teller (GT) and first-forbidden (FF) transitions were investigated in the particle-hole (ph) channel. The calculated log ft values of the allowed GT and FF transitions using the pn-QRPA model with WS potential were found closer to the experimental values. Later we performed calculation of $\beta$-decay rates in stellar environment. Here we solved the random phase approximation (RPA) equations in deformed Nilsson basis, both in the particle-particle (pp) and particle-hole (ph) channels. Allowed $\beta$-decay and unique first-forbidden (U1F) rates were calculated in stellar matter. For certain cases, the calculated U1F contribution was much more than the allowed $\beta$-decay rates under prevailing stellar conditions, in line with previous findings. Increasing temperature of the stellar core affected the allowed GT rates more than the U1F rates.