Uniform analytic approximation of Wigner rotation matrices
Abstract
We derive the leading asymptotic approximation, for low angle θ, of the Wigner rotation matrix elements djm1m2(θ), uniform in j,m1 and m2. 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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