Influence of supernova-neutrino spectra on the neutrino signal in a terrestrial detector

Neutrino interactions on a ²⁰⁸Pb target nucleus are widely regarded as an excellent tool for the study of a galactic supernova explosion in a terrestrial detector. To serve this goal an accurate knowledge of the neutrino cross section on ²⁰⁸Pb is needed. We examine the influence of the supernova-neutrino energy spectrum on the response in a detector. In view of the results of recent calculations for supernova-neutrino spectra, we discuss the importance of the distribution’s average energy and width and comment on the influence of uncertainties in the parametrization of the spectrum. We show that changes in the energy distributions parameters can have a disproportionately large influence on the folded cross section. Our calculations point out that implementing the new supernova-neutrino spectra causes a reduction of the folded supernova-neutrino cross sections. We note a remarkably large sensitivity of the folded cross sections to the high-energy tail of the spectrum. The discussion focuses on neutral-current reactions in a terrestrial detector considering one- and two-neutron knockout.