Sommerfeld factor for arbitrary partial wave processes

TL;DR

This paper derives a general expression for the Sommerfeld factor in non-relativistic partial wave processes, providing numerical results and an accurate analytic approximation for Yukawa interactions, highlighting the importance of higher partial waves.

Contribution

It introduces a new analytic approximation for the Sommerfeld factor applicable to arbitrary partial waves in Yukawa interactions, accurate within 10%.

Findings

Non s-wave Sommerfeld effects are significant.

Higher partial waves can dominate cross sections.

The analytic approximation is exact in the Coulomb limit.

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.