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.

• Received 29 May 2006

DOI:https://doi.org/10.1103/PhysRevC.74.034307