  We derive the semiclassical evolution equations for a system consisting of
helium-3 atoms in the $2^3S$ metastable state interacting with a light field
far-detuned from the $2^3S-2^3P$ transition, in the presence of metastability
exchange collisions with ground state helium atoms and a static magnetic field.
For two configurations, each corresponding to a particular choice of atom-light
detuning in which the contribution of either the metastable level $F=1/2$ or
$F=3/2$ is dominant, we derive a simple model of three coupled collective spins
from which we can analytically extract an effective coupling constant between
the collective nuclear spin and light. In these two configurations, we compare
the predictions of our simplified model with the full model.
