Numerical results on the integral expression for the semiclassical S matrix are compared with exact quantum results for a multidimensional problem. The collision of a rigid rotor with an atom is treated. The integral method proves to be easy to apply. Within its range of maximum validity (no sign changes in the prehyphen;exponential factor of the semiclassical wavefunction) the agreement was typically within 20percnt;. When sign changes occurred, the agreement was about a factor of 2 or better. Conditions affecting sign changes are described.
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