*2.2. Neutrino–Nucleus Scattering*

At sufficiently high densities (*<sup>ρ</sup>* > <sup>4</sup> × <sup>10</sup><sup>11</sup> g cm−3), neutrinos become trapped and thermalized in the collapsing core by coherent scattering on nuclei and inelastic scattering on electrons. It had been suggested that de-excitation of thermally excited nuclei by neutrino pair emission [60] and inelastic neutrino–nucleus scattering [61] might be other modes contributing to neutrino thermalization. Although both processes have been found as rather unimportant cooling mechanisms [47,62], they have interesting impacts elsewhere. Neutrino pair emission has been identified as the major source of neutrino types other than electron neutrinos (produced overwhelmingly by electron capture) [47]. As the consequences of inelastic neutrino scattering are based on shell model calculations, the latter are briefly summarized. The formalism for the calculation of neutrino-nucleus reactions has been introduced in Ref. [63].

Supernova neutrinos have rather low energies (of order 10 MeV). Therefore, inelastic neutrino scattering of such neutrinos is dominated by allowed GT0 transitions. Unfortunately, no data about inelastic neutrino scattering on nuclei exist at such energies. Due to its success in describing GT<sup>+</sup> (and GT−) distributions, one can expect that the shell model will also reproduce the GT0 component quite well. Nevertheless, a validation of the shell model approach to inelastic neutrino-nucleus scattering is desired. This can be achieved by

exploiting the fact that the GT0 strength is, in a rather good approximation, proportional to the M1 strength of spherical nuclei [64]. In fact, precision M1 data, obtained by inelastic electron scattering for such nuclei, are well reproduced by shell model calculations [64,65]. The same approaches can also be used to derive GT0 distributions for excited nuclear states, which can be thermally populated at finite supernova conditions [64,66]. At higher neutrino energies, forbidden transitions also contribute to the inelastic scattering cross section, which has been derived by RPA calculations. Supernova simulations that incorporate inelastic neutrino–nucleus scattering indicate that this mode has a noticeable effect on the early neutrino spectra emitted from supernova [62]. Here, nuclei act as obstacles for high-energy neutrinos which are down scattered in energy. This reduces significantly the tail of the neutrino spectra and, hence, also the predicted event rates for the observation of supernova neutrinos by earthbound detectors [62].

Charged-current and neutral-current neutrino–nucleus reactions are key to a specific nucleosynthesis process (called neutrino nucleosynthesis [67]), which are initiated by neutrinos emitted after core bounce in the supernova. Upon passing through the outer layers of the star, these neutrinos excite nuclei above particle thresholds so that the subsequent decay is by particle emission (mainly of protons or neutrons). Neutrino nucleosynthesis has been identified as the main or a strong source for the production of selected isotopes, 11B and 19F, from charged- and neutral-current reactions on the abundant isotopes 12C and 20Ne; 138La and 180Ta mainly by charged-current reactions on Ba and Ta isotopes, which had been previously been produced by the slow neutron-capture process (s-process) [67–71]. The partial neutrino–nucleus cross sections have been obtained by combining shell-model or RPA excitation functions with statistical model decay probabilities [72–74]. A particular interest in neutrino nucleosynthesis arises from the fact that the abundances of the produced nuclides depend on the spectra of those neutrino types (*νμ*, *ντ* and their antiparticles and *νe*), which have likely not been observed from supernova 1987A.

In principle, neutrino–nucleus reactions also play a role in the *νp* process that operates in the neutrino-driven wind during cooling of the newborn proton–neutron star [75–77]. Simulations, however, show that the main neutrino reaction is the absorption of *ν*¯*<sup>e</sup>* on protons that produce a continuous source of free neutrons, which drives the process and allows mass flow through long-lived waiting points such as 64Ge. The *νp* process is discussed as a potential source of isotopes such as 92Nb and 94,96Ru.
