Alignment of wave functions for angular momentum projection

TL;DR

This paper introduces an alignment method based on variance minimization of a7J_z to improve the concentration of K-distribution in wave functions, enhancing angular momentum projection accuracy in nuclear physics.

Contribution

The paper proposes a novel alignment technique using variance minimization of a7J_z to achieve concentrated K-distribution in wave functions for better angular momentum projection.

Findings

The alignment method effectively concentrates K-distribution across various wave functions.

Benchmark calculations demonstrate the method's usefulness in nuclear structure models.

The approach improves the accuracy of multi-configuration mixing calculations.

Abstract

Angular momentum projection is used to obtain eigen states of angular momentum from general wave functions. Multi-configuration mixing calculation with angular momentum projection is an important microscopic method in nuclear physics. For accurate multi-configuration mixing calculation with angular momentum projection, concentrated distribution of $z$ components $K$ of angular momentum in the body-fixed frame ($K$-distribution) is favored. Orientation of wave functions strongly affects $K$-distribution. Minimization of variance of $\hat{J}_z$ is proposed as an alignment method to obtain wave functions that have concentrated $K$-distribution. Benchmark calculations are performed for $\alpha$-$^{24}$Mg cluster structure, triaxially superdeformed states in $^{40}$Ar, and Hartree-Fock states of some nuclei. The proposed alignment method is useful and works well for various wave functions to obtain concentrated $K$-distribution.