Evaluation of Phase-Space Integrals

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Abstract
The relativistic phase‐space integral over the submanifold defined by total momentum zero and fixed total energy is reduced to a single contour integration. The number of particles involved and their masses are arbitrary. It is shown that the contour integration may be readily approximated by the saddle‐point technique and yields a result which is easily handled by a computer. In the nonrelativistic and extreme relativistic limits, this method leads to expressions for the phase space which may be obtained from the exact results for these cases by replacing Γ‐function factors by the Stirling approximation.

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