Sommerfeld factor for arbitrary partial wave processes

Abstract

The Sommerfeld factor for arbitrary partial wave processes is derived in the non-relativistic limit. The s-wave and p-wave numerical results are presented for the case of Yukawa interactions. An approximate analytic expression is also found for the Sommerfeld factor of Yukawa interactions with arbitrary partial waves, which is exact in the Coulomb limit. It is demonstrated that this result is accurate to within 10% for some common scenarios. The non s-wave Sommerfeld effect is determined to be significant, and can allow higher partial waves to dominate cross sections.

20 pages, 6 figures

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• A Theory of Dark Matter
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