Pfaffian formulation for matrix elements of three-body operators in multiple quasiparticle configurations

Chen, Zirui; Wang, Long-Jun

doi:10.1103/physrevc.105.034342

Cited by 7 publications

(1 citation statement)

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“…Therefore, the Wigner D-function is indispensable in the study of modern physics, for example in nuclear physics [5], quantum metrology [6,7] and many other fields [8,9]. Especially in theoretical calculations with the nuclear beyond-mean-field methods [10][11][12][13][14][15][16], where angular-momentum projection serves as an important ingredient, the Wigner D-function is the cerntral part of the angular-momentum projector [10,[17][18][19][20][21][22][23][24][25][26][27]. Angular-momentum projected wave functions obtained in modern nuclear theories are applied to the study of β-decay [28,29], neutrinoless double-β decay [30][31][32], astrophysical weak process [33][34][35], nuclear fission [36][37][38][39][40], and many others.…”

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confidence: 99%

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

Gao¹,

Wang²,

Sun³

2022

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The Wigner rotation matrix (d-function), which appears as a part of the angular-momentumprojection operator, plays a crucial role in modern nuclear-structure models. However, it is a longstanding 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 θ) 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.

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