  First-forbidden (FF) charge-changing transitions become relatively important
for nuclei as their proton number increases. This is because the strength of
allowed Gamow-Teller (GT) transitions decreases with increasing Z. The FF
transitions play an important role in reducing the half-lives as against those
calculated from taking the GT transitions alone into account. In this paper we
calculate allowed GT as well as $0^{+} \rightarrow 0^{-}$ and $0^{+}
\rightarrow 2^{-}$ transitions for neutron-rich Zn and Ge isotopes. Two
different pn-QRPA models were used with a schematic separable interaction to
calculate GT and FF transitions. Half-lives calculated after inclusion of FF
transitions were in excellent agreement with the experimental data. Our
calculations were also compared to previous QRPA calculations and were found to
be in better agreement with measured data. Stellar $\beta$-decay rates were
calculated for these nuclei including allowed GT and unique FF transitions for
astrophysical applications. $^{86,88}$Ge has a sizeable contribution to the
total stellar rate from unique FF transitions.
