Uniform analytic approximation of Wigner rotation matrices

TL;DR

This paper derives a uniform asymptotic approximation for Wigner rotation matrix elements at low angles, expressed via Bessel functions, with potential applications in wavepacket scattering analysis.

Contribution

It introduces a novel uniform asymptotic approximation for Wigner rotation matrices, useful for low-angle scenarios and applicable in wavepacket scattering.

Findings

Approximation expressed in terms of Bessel functions

Numerical analysis shows the approximation's accuracy over a range of angles

Potential applications in partial wave analysis of scattering

Abstract

We derive the leading asymptotic approximation, for low angle {\theta}, of the Wigner rotation matrix elements $d^j_{m_1m_2}(\theta)$, uniform in $j,m_1$ and $m_2$. The result is in terms of a Bessel function of integer order. We numerically investigate the error for a variety of cases and find that the approximation can be useful over a significant range of angles. This approximation has application in the partial wave analysis of wavepacket scattering.