Revisiting the variational two-particle reduced density matrix for nuclear systems

TL;DR

This paper explores the application of the variational two-particle reduced density matrix method to nuclear systems, introducing new constraints to improve accuracy, especially for systems with only valence neutrons, while addressing challenges with proton-neutron systems.

Contribution

It introduces new constraints to the variational two-particle reduced density matrix method for nuclear systems, improving its accuracy for valence neutron systems.

Findings

Method provides proper description for valence neutron systems.

Overbinding persists in systems with both neutrons and protons.

Discrepancies and potential solutions are discussed.

Abstract

In most nuclear many-body methods, observables are calculated using many-body wave functions explicitly. The variational two-particle reduced density matrix method is one of the few exceptions to the rule. Ground-state energies of both closed-shell and open-shell nuclear systems can indeed be evaluated by minimizing a constrained linear functional of the two-particle reduced density matrix. However, it has virtually never been used in nuclear theory, because nuclear ground states were found to be well overbound, contrary to those of atoms and molecules. Consequently, we introduced new constraints in the nuclear variational two-particle reduced density matrix method, developed recently for atomic and molecular systems. Our calculations then show that this approach can provide a proper description of nuclear systems where only valence neutrons are included. For the nuclear systems where both neutrons and protons are active, however, the energies obtained with the variational two-particle reduced density matrix method are still overbound. The possible reasons for the noticed discrepancies and solutions to this problem will be discussed.