Long Range Tensor Correlations in Charge and Parity Projected Fermionic Molecular Dynamics

TL;DR

This paper introduces a method within Fermionic Molecular Dynamics to incorporate long-range tensor correlations in nuclei, improving energy calculations and visualizing extended correlations over the entire nucleus.

Contribution

It develops a novel approach combining charge and parity projection with energy minimization to better account for long-range tensor correlations in nuclear systems.

Findings

Systematically lower energies than Hartree-Fock results.

Accounts for about 20% of the long-range correlation energy in helium-4.

Visualizes the extended correlations via isospin and spin-isospin densities.

Abstract

Within the framework of Fermionic Molecular Dynamics a method is developed to better account for long range tensor correlations in nuclei when working with a single Slater determinant. Single-particle states with mixed isospin and broken parity build up an intrinsic Slater determinant which is then charge and parity projected. By minimizing the energy of this many-body state with respect to the parameters of the single-particle states and projecting afterwards on angular momentum ground state energies are obtained that are systematically lower than corresponding Hartree-Fock results. The realistic Argonne V18 potential is used and short range correlations are treated with the Unitary Correlation Operator Method. Comparison with exact few-body calculations shows that in $^4$He about one fifth of the correlation energy due to long-range correlations are accounted for. These correlations which extend over the whole nucleus are visualized with the isospin and spin-isospin density of the intrinsic state. The divergence of the spin-isospin density, the source for pion fields, turns out to be of dipole nature.