Neutrino Cross Sections: Low Energy

Low-energy neutrino interactions with isolated nucleons are accurately described by the effective theory based on Fermi's groundbreaking description of neutron $\beta$-decay. On the other hand, the extension of this scheme to the case of neutrino interactions with nuclear matter -- the understanding of which is critical for the description of a variety of astrophysical processes -- involves non trivial difficulties, originating from the complexity of nuclear structure and dynamics. This chapter provides a concise introduction to the formalism of nuclear many-body theory, suitable to perform theoretical calculations of the nuclear matter response to neutrino interactions, as well as a detailed analysis of the relevant reaction mechanisms. The neutrino mean free path in nuclear matter and its implications for the description of astrophysical processes are also discussed.