Neutrino-nucleus interactions at low energies within Fermi-liquid theory

Cross sections are calculated for neutrino scattering off heavy nuclei at energies below 50 MeV. The theory of Fermi liquid is applied to estimate the rate of neutrino-nucleon elastic and inelastic scattering in a nuclear medium in terms of dynamic form factors. The cross sections, obtained here in a rather simple way, are in agreement with the results of the other much more sophisticated nuclear models. A background rate from the solar neutrino interactions within a large Ga detector is estimated in the above-mentioned approach. The knowledge of the rate is in particular rather important for new-generation large-scale neutrino experiments.

Figure 1

The total $\nu {‐}^{71}$Ga cross section as a function of the neutrino energy $E_{\nu }$. The solid line corresponds to the Fermi-gas approximation (FG), the long-dashed curve is the calculation within the Fermi liquid theory (FLT), the short-dashed line is the calculation within the shell model including the short-range part of the $NN$ interaction which is due to the π- and ρ-meson exchange [2], whereas the dotted line is the results of [2] without these isobaric effects.

Figure 2

The total absorption $\nu {‐}^{40}$Ar cross section as a function of the neutrino energy $E_{\nu }$.The solid line is the FG approximation, the long-dashed curve is the FLT calculation, the crosses correspond to the calculation of [10] within the RPA.

Figure 3

The illustration of the energy dependence of the solar neutrino flux continuum from Ref. [33]

Figure 4

The total number of neutrino interactions per month and per MeV produced from the ${}^8\mathrm{B}$-ν flux interacting with 1-kg ${}^{71}\mathrm{Ga}$ detector as a function of the neutrino energy $E_{\nu }$. Notation is the same as in Fig. 1