  We show that the nonzero electron mass plays a critical role in determining
the magnetic properties of neutron stars, making it impossible to generate the
chiral charge density needed to trigger a strong chiral magnetic instability
during the core collapse of supernovae. This instability has been proposed as a
plausible mechanism for generating extremely large helical magnetic fields in
neutron stars at their birth; the mechanism relies on the generation of a large
non-equilibrium chiral charge density via electron capture reactions that
selectively deplete left-handed electrons during core-collapse and the early
evolution of the protoneutron star. Our calculation shows that the electron
chirality violation rate induced by Rutherford scattering, despite being
suppressed by the smallness of the electron mass relative to the electron
chemical potential, is still fast compared to the weak interaction electron
capture rate. The resulting asymmetry between right and left-handed electron
densities is therefore never able to attain an astrophysically relevant
magnitude.
