  Studies of neutrino mixing and oscillations, solar neutrinos as background in
dark matter searches involving electron detection, detection of sterile
neutrino warm dark matter, and of possible electromagnetic properties of
neutrinos, have generated interest in the low energy O(10 keV) scattering of
electron neutrinos and antineutrinos by atomic electrons where the binding of
the atomic electron cannot be ignored. Of particular interest is the ionization
of atoms by neutrinos and antineutrinos. Most existing calculations are based
on modifications of the free electron differential cross section, which destroy
the relationship between the neutrino helicities and the orbital and spin
angular momenta of the atomic electrons. The present calculations maintain the
full collision dynamics by formulating the scattering in configuration space
using the Bound Interaction Picture, rather than the usual formulation in the
Interaction Picture in momentum space as appropriate to scattering by free
electrons. Energy spectra of ionization electrons produced by scattering of
neutrinos and antineutrinos with energies of 5, 10, 20, and 30 keV by hydrogen,
helium and neon have been calculated using Dirac central field eigenfunctions
and are presented as ratios to the spectra for scattering by free electrons.
Binding effects increase strongly with atomic number, are largest for low
neutrino energy and, for each neutrino energy, greatest at the high electron
energy end of the spectrum. The most extreme effects of binding are for 5 keV
scattering by Ne where the ratios are less than 0.1. The energy spectra are
calculated for both a Coulombic final electron state and a free final electron
state. The results indicate that the binding effects from the continuum state
of the final electron are significant and can be comparable to those arising
from the bound initial electron state.
