Uniform analytic approximation of Wigner rotation matrices

Abstract

We derive the leading asymptotic approximation, for low angle θ, of the Wigner rotation matrix elements $d_{m_1{m}_2}^j(\theta )$, 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.

8 pages, 5 figures

References in corpus (3)

• High-precision evaluation of Wigner's d-matrix by exact diagonalization
• Analytical formula for numerical evaluations of the Wigner rotation matrices at high spins
• Prediction of deviations from the Rutherford formula for low-energy Coulomb scattering of wavepackets

Cited by in corpus (1)

• Measurability of Coulomb wavepacket scattering effects