Restoring Broken Symmetries for Nuclei and Reaction Fragments

TL;DR

This paper introduces a new formalism for simultaneously restoring multiple symmetries in microscopic nuclear models, improving the accuracy of quantum number definitions and energy calculations for nuclei and reaction fragments.

Contribution

It presents a novel, singularity-free formalism for symmetry restoration of particle numbers and spins in nuclear systems with pairing correlations.

Findings

Formalism effectively restores multiple symmetries simultaneously.

New formulas are free of singularities unlike previous methods.

Enhances the accuracy of symmetry-restored densities and energies.

Abstract

In typical microscopic approaches, particularly when pairing correlations are present, nuclei and nuclear fragments do not have well defined quantum numbers and symmetries should be restored. I present here a formalism for the simultaneous projection of total particle numbers of a nucleus, particle number of reaction fragments, and of the reaction fragment intrinsic spins and of their correlation, and also for their symmetry restored densities and total energies. These new formulas for the symmetry restored quantities, are free of any singularities, unlike those in the previously introduced prescriptions.