Abstract
The differential geometry of admissible wavefronts of N-body scattering is investigated for each term of the multiple scattering series and within angular sectors of uniform asymptotic behaviour. The differential equations are dimension independent in form and thus investigated in Rn. A general theorem is proved stating that, if not spherical, the wavefront must be a (ruled) K=0 surface tangent to a sphere around the origin. For n=3 a rather simple geometrical description is given of the most general structure.
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