  We consider the degree of conservation of nuclear spin polarization in the
process of optical pumping under typical spin-exchange optical pumping
conditions. Previous analyses have assumed that negligible nuclear spin
precession occurs in the brief periods of time the alkali-metal atoms are in
the excited state after absorbing photons and before undergoing quenching
collisions with nitrogen molecules. We include excited-state hyperfine
interactions, electronic spin relaxation in collisions with He and N_2,
spontaneous emission, quenching collisions, and a simplified treatment of
radiation trapping.
