A second order, O(αs2), calculation in perturbative quantum
chromodynamics is presented of the longitudinal spin dependence of the cross
section for the two particle inclusive reaction p+p→γ+c+X for
large values of the transverse momentum of the prompt photon and charm quark.
Differential distributions are provided for the spin-averaged cross section and
for the two-spin longitudinal polarization asymmetry ALL at the energy of
the Brookhaven Relativistic Heavy Ion Collider. An assessment is given of the
prospects for determination of the spin dependence of the charm quark density.Comment: 27 pages, RevTex, and 10 figure