$SO(3)$ quadratures in angular-momentum projection

TL;DR

This paper evaluates different quadrature methods for angular-momentum projection in nuclear physics, demonstrating that Lebedev quadrature offers a significant efficiency improvement over traditional methods, reducing computational cost.

Contribution

It introduces the use of Lebedev quadrature and spherical t-design for angular-momentum projection, clarifying their exactness conditions and efficiency advantages.

Findings

Lebedev quadrature is the most efficient among tested methods.

The number of sampling points is reduced by 1.5 times compared to conventional methods.

Accuracy of quadratures is compared and validated against traditional approaches.

Abstract

While the angular-momentum projection is a common tool for theoretical nuclear structure studies, a large amount of computations are required particularly for triaxially deformed states. In the present work, we clarify the conditions of the exactness of quadratures in the projection method. For efficient computation, the Lebedev quadrature and spherical $t$-design are introduced to the angular-momentum projection. The accuracy of the quadratures is discussed in comparison with the conventional Gauss-Legendre and trapezoidal quadratures. We found that the Lebedev quadrature is the most efficient among them and the necessary number of sampling points for the quadrature, which is often proportional to the computation time, is reduced by a factor 3/2 in comparison with the conventional method.