Temperature dependence of the nucleon effective mass and the physics of stellar collapse

The temperature dependence of the nucleon effective mass is calculated for the $^{98}\mathrm{Mo}$, $^{64}\mathrm{Zn}$, and $^{64}\mathrm{Ni}$. In all three cases, the effective mass is found to decrease appreciably in the temperature interval 0--1 MeV. Such a dependence has consequences, among other things, on the level-density parameter and on the symmetry energy. In particular, the effect of the increased symmetry energy on the neutronization processes in collapsing stars is estimated. We find indication that the larger initial lepton fraction thus obtained may significantly help the subsequent supernova explosion.