Conatraints on $\Delta G$ from Prompt Photon plus Jet Production at HERA-$\vec{N}$

The utility of prompt photon plus associated jet production for constraining the size and shape of the polarized gluon density of the proton $\Delta G$ is examined at $\sqrt{S}=40$ GeV, appropriate for the proposed HERA-$\vec{N}$ polarized $\vec{p}\vec{p}$ collider experiment. The calculation is performed at next-to-leading order (O($\alpha\alpha_s^2$)) in QCD. The reliability of the predictions are examined in some detail.