Monte Carlo Simulations for RHIC Spin Physics

Direct photon production in longitudinally polarised proton-proton collisions offers the most direct and unproblematic possibility to determine the polarised gluon distribution of a proton. This information could play a major role for improving our understanding of the nucleon structure and QCD in general. It is hoped that such experiments will be done at RHIC. We present results of detailed Monte Carlo simulations using a code called {\sc SPHINX}. We find that for RHIC energies and large gluon polarisation the Compton graph dominates allowing for a direct test of $\Delta g$. Triggering on away-side jets with the envisaged jet-criteria should allow to obtain more detailed information on $\Delta g(x)$. The photon asymmetry resulting from the asymmetry of produced $\pi^0$'s provides an additional signal, which is complementary to the other two. For small gluon polarisation, i.e. $\Delta g \le 0.5$ or very soft polarised gluon-distributions the envisaged experiments will require a highly sophisticated simulation and large statistics to extract more than upper bounds for $|\Delta g(x)|$.}