We study charged-current neutrino cross sections on neutronrich nuclei in the mass $Asim60$ region. Special attention is paid to environmental effects, i.e. finite temperature and density, on the cross sections. As these effects are largest for small neutrino energies, it is sufficient to study only the Gamow-Teller (GT) contributions to the cross sections. The relevant GT strength distributions are derived from large-scale shell model calculations. We find that the low-energy cross sections are enhanced at finite temperatures. However, for $( u_e,e^-)$ reactions Pauli blocking of the electrons in the final state makes the cross sections for low-energy neutrinos much smaller than for the competing inelastic scattering on electrons at moderate and large densities. Absorption cross sections for low-energy antineutrinos are strongly enhanced at finite temperatures.
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