  The two particle inclusive cross section for the reaction $p
+\bar{p}\rightarrow \gamma + c + X$ is studied in perturbative quantum
chromodynamics at order $O(\alpha ^2_s)$, for large values of the transverse
momentum of the prompt photon and charm quark. Two different techniques are
used in performing the phase-space integrals; the first is purely analytical,
and the second is a combination of analytic and Monte Carlo integration
methods. The second, more versatile technique facilitates imposition of photon
isolation restrictions and other selections of relevance in experiments.
Differential distributions are provided for various observables, and a
comparison is made with preliminary data from the CDF collaboration.
