Cross sections for coherent elastic and inelastic neutrino-nucleus scattering

The prospects of extracting new physics signals in coherent elastic neutrino--nucleus scattering (CE$\nu$NS) processes are limited by the precision with which the underlying nuclear structure physics, embedded in the weak nuclear form factor, is known. We present calculations of charge and weak nuclear form factors and CE$\nu$NS cross sections on $^{12}$C, $^{16}$O, $^{40}$Ar, $^{56}$Fe and $^{208}$Pb nuclei. We obtain the proton and neutron densities, and charge and weak form factors by solving Hartree--Fock (HF) equations with a Skyrme (SkE2) nuclear potential. We validate our approach by comparing $^{208}$Pb and $^{40}$Ar charge form factor predictions with available elastic electron scattering data. Since CE$\nu$NS experiments at stopped--pion sources are also well suited to measure inelastic charged--current and neutral--current neutrino--nucleus cross sections, we also present calculations for these processes, incorporating a continuum Random Phase Approximation (CRPA) description on top of the HF-SkE2 picture of the nucleus. Providing both coherent as well as inelastic cross sections in a consistent framework, we aim at obtaining a reliable and detailed comparison of the strength of these processes in the energy region below ~100 MeV. Furthermore, we attempt to gauge the level of theoretical uncertainty pertaining to the description of the $^{40}$Ar form factor and CE$\nu$NS cross sections by comparing relative differences between recent microscopic nuclear theory and widely--used phenomenological form factor predictions. Future precision measurements of CE$\nu$NS will potentially help in constraining these nuclear structure details that will in turn improve prospects of extracting new physics.