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A short review of the Rein-Sehgal and isobar models is presented. The attention is focused on the nucleon-{Delta}(1232) weak transition form-factors. The results of the recent re-analyses of the ANL and BNL bubble chamber neutrino-deuteron scattering data are discussed.
We describe recent progress of the EOS tables for numerical simulations of core-collapse supernovae and related astrophysical phenomena. Based on the Shen EOS table, which has been widely used in supernova simulations, there is systematic progress by extending the degrees of freedom such as hyperons and quarks. These extended EOS tables have been used, for example, to study the neutrino bursts from the gravitational collapse of massive stars leading to the black hole formation. Observations of such neutrinos from galactic events in future will provide us with the information on the EOS. Recently, studies of the supernova EOS with the multi-composition of nuclei under the nuclear statistical equilibrium have been made beyond the single nucleus approximation as used in the Shen EOS. It has been found that light elements including deuterons are abundant in wide regions of the supernova cores. We discuss that neutrino-deuteron reactions may have a possible influence on the explosion mechanism through modifications of neutrino heating rates.