Neutrino-nucleus reactions based on new shell model Hamiltonians

A new shell model Hamiltonian for $p$-shell nuclei which properly takes into account important roles of spin-isospin interactions is used to obtain cross sections of neutrino-$^{12}\mathrm{C}$ reactions induced by decay-at-rest neutrinos as well as supernova neutrinos. Branching ratios to various decay channels are calculated by the Hauser-Feshbach theory. Neutrino-$^{4}\mathrm{He}$ reactions are also investigated by using recent shell model Hamiltonians. The reaction cross sections are found to be enhanced for both $^{12}\mathrm{C}$ and $^{4}\mathrm{He}$ compared with previous calculations. As an interesting consequence of this, a possible enhancement of the production yields of light elements, $^{7}\mathrm{Li}$ and $^{11}\mathrm{B}$, during supernova explosions is pointed out.