  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.
