  The nonlinear Schr\"odinger-Newton equation, a prospective semiclassical
alternative to a quantized theory of gravity, predicts a gravitational
self-force between the two trajectories corresponding to the two z-spin
eigenvalues for a particle in a Stern-Gerlach interferometer. To leading order,
this force results in a relative phase between the trajectories. For the
experimentally relevant case of a spherical particle with localized wave
function, we present a re-derivation of that phase which is both rigorous in
its approximations and concise, allowing for simple but accurate experimental
predictions.
