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

First-forbidden transitions and stellar $\beta$-decay rates of Zn and Ge isotopes