Neutrino deuteron reaction in the heating mechanism of core-collapse supernovae

We examine a potential role of the neutrino deuteron reactions in the mechanism of supernova explosion by evaluating the energy transfer cross section for the neutrino heating. We calculate the energy loss rate due to the neutrino absorptions through the charged-current process as well as the neutrino scattering through the neutral-current process. In so doing, we adopt a detailed evaluation of cross sections for the neutrino deuteron reactions with the phenomenological Lagrangian approach. We find the energy transfer cross section for the deuteron is larger than those for $^{3}$H, $^{3}$He and $^{4}$He for neutrino temperatures (T$_\nu$ $\sim 4$ MeV) relevant to supernova core. Because of the low energy threshold for the deuteron breakup, the energy transfer rate rapidly increases from low temperature, T$_\nu$ $\sim 1$ MeV. This suggests that the neutrino deuteron reactions may contribute effectively to the heating mechanism during the dissociation of irons into light elements and nucleons in the shocked material of supernova core.