Superscaling properties of ${}^{12}\mathrm{C}$, ${}^{16}\mathrm{O}$, and ${}^{40}\mathrm{Ca}$ nuclear responses, induced by electron and neutrino scattering, are studied for momentum transfer values between 300 and 700 MeV/$c$. We have defined two indexes to have quantitative estimates of the scaling quality. We have analyzed experimental responses to get the empirical values of the two indexes. We have then investigated the effects of finite dimensions, collective excitations, meson exchange currents, short-range correlations, and final state interactions. These effects strongly modify the relativistic Fermi gas scaling functions, but they conserve the scaling properties. We used the scaling functions to predict electron and neutrino cross sections and we tested their validity by comparing them with the cross sections obtained with a full calculation. For electron scattering we also made a comparison with data. We have calculated the total charge-exchange neutrino cross sections for neutrino energies up to 300 MeV.

• Received 28 November 2006

DOI:https://doi.org/10.1103/PhysRevC.75.034604