An effective and efficient algorithm for the Wigner rotation matrix at high angular momenta

Abstract

The Wigner rotation matrix ($d$-function), which appears as a part of the angular-momentum-projection operator, plays a crucial role in modern nuclear-structure models. However, it is a long-standing problem that its numerical evaluation suffers from serious errors and instability, which hinders precise calculations for nuclear high-spin states. Recently, Tajima [Phys. Rev. C 91, 014320 (2015)] has made a significant step toward solving the problem by suggesting the high-precision Fourier method, which however relies on formula-manipulation softwares. In this paper we propose an effective and efficient algorithm for the Wigner $d$ function based on the Jacobi polynomials. We compare our method with the conventional Wigner method and the Tajima Fourier method through some testing calculations, and demonstrate that our algorithm can always give stable results with similar high-precision as the Fourier method, and in some cases (for special sets of $j,m,k$ and $\theta$) ours are even more accurate. Moreover, our method is self-contained and less memory consuming. A related testing code and subroutines are provided as Supplemental Material in the present paper.

References in corpus (13)

• Energy density functional study of nuclear matrix elements for neutrinoless $\beta \beta$ decay
• Mach-Zehnder Interferometry at the Heisenberg Limit with coherent and squeezed-vacuum light
• Beyond the relativistic mean-field approximation (III): collective Hamiltonian in five dimensions
• Systematic study of nuclear matrix elements in neutrinoless double-beta decay with a beyond mean-field covariant density functional theory
• Phase detection at the quantum limit with multi-photon Mach-Zehnder interferometry
• Wigner formula of rotation matrices and quantum walks
• Toward extremes of angular momentum: Application of the Pfaffian algorithm in realistic calculations
• Configuration interaction in symmetry-conserving covariant density functional theory
• Analytical formula for numerical evaluations of the Wigner rotation matrices at high spins
• Shell model method for Gamow-Teller Transitions in heavy, deformed nuclei
• Projection of angular momentum via linear algebra
• Systematic study of near yrast band structures in odd-mass ${}^{125-137}$Pr and ${}^{127-139}$Pm isotopes
• Franck-Condon Effect in Central Spin System