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First-forbidden $\mathbfβ$-decay rates, energy rates of $β$-delayed neutrons and probability of $β$-delayed neutron emissions for neutron-rich nickel isotopes

First-forbidden (FF) transitions can play an important role in decreasing the calculated half-lives specially in environments where allowed Gamow-Teller (GT) transitions are unfavored. Of special mention is the case of neutron-rich nuclei where, due to phase-space amplification, FF transitions are much favored. We calculate the allowed GT transitions in various pn-QRPA models for even-even neutron-rich isotopes of nickel. Here we also study the effect of deformation on the calculated GT strengths. The FF transitions for even-even neutron-rich isotopes of nickel are calculated assuming the nuclei to be spherical. Later we take into account deformation of nuclei and calculate GT + unique FF transitions, stellar $β$-decay rates, energy rate of $β$-delayed neutrons and probability of $β$-delayed neutron emissions. The calculated half-lives are in excellent agreement with measured ones and might contribute in speeding-up of the $r$-matter flow.