Unique first-forbidden $\beta$-decay rates for neutron-rich nickel isotopes in stellar environment

In astrophysical environments, allowed Gamow-Teller (GT) transitions are important, particularly for $\beta$-decay rates in presupernova evolution of massive stars, since they contribute to the fine-tuning of the lepton-to-baryon content of the stellar matter prior to and during the collapse of a heavy star. In environments where GT transitions are unfavored, first-forbidden transitions become important especially in medium heavy and heavy nuclei. Particularly in case of neutron-rich nuclei, first-forbidden transitions are favored primarily due to the phase-space amplification for these transitions. In this work the total $\beta$-decay half-lives and the unique first-forbidden(U1F) $\beta$-decay rates for a number of neutron-rich nickel isotopes, $^{72-78}$Ni, are calculated using the proton-neutron quasi-particle random phase approximation (pn-QRPA) theory in stellar environment for the first time. For the calculation of the $\beta$-decay half-lives both allowed and unique first-forbidden transitions were considered. Comparison of the total half-lives is made with measurements and other theoretical calculations where it was found that the pn-QRPA results are in better agreement with experiments and at the same time are suggestive of inclusion of rank 0 and rank 1 operators in first-forbidden rates for still better results.