Intrinsic Density Matrices of the Nuclear Shell Model

TL;DR

This paper introduces a novel method for calculating intrinsic density matrices in the nuclear shell model, emphasizing antisymmetry, translation invariance, and computational efficiency without group-theoretical classification.

Contribution

It presents a new approach to compute intrinsic density matrices that are antisymmetric and translation-invariant, avoiding numerical diagonalization and orthogonalization.

Findings

The method produces fully antisymmetric, translation-invariant density matrices.

It enables exact density matrix expansion within the reduced Hamiltonian framework.

The computational procedures are implemented in a new computer code.

Abstract

A new method for calculation of shell model intrinsic density matrices, defined as two-particle density matrices integrated over the centre-of-mass position vector of two last particles and complemented with isospin variables, has been developed. The intrinsic density matrices obtained are completely antisymmetric, translation-invariant, and do not employ a group-theoretical classification of antisymmetric states. They are used for exact realistic density matrix expansion within the framework of the reduced Hamiltonian method. The procedures based on precise arithmetic for calculation of the intrinsic density matrices that involve no numerical diagonalization or orthogonalization have been developed and implemented in the computer code.