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arXiv · 1710.11282

Uniform analytic approximation of Wigner rotation matrices

Scott E. Hoffmann
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Abstract

We derive the leading asymptotic approximation, for low angle θ, of the Wigner rotation matrix elements $d^j_{m_1m_2}(θ)$, 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.

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Scott E. Hoffmann. 2017-10-31. Uniform analytic approximation of Wigner rotation matrices. https://doi.org/10.1063/1.5012583

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