# Correlation Energy of Proton-Neutron Subsystem in Valence Orbit

## TL;DR

This study evaluates the proton-neutron correlation energy in specific nuclei using a three-body model, revealing environment-dependent differences in deuteron-like binding in $^6$Li and $^{18}$F.

## Contribution

It introduces a simple three-body model to compare proton-neutron correlations in different nuclear environments using two interaction potentials.

## Key findings

- Proton-neutron binding is stronger in $^6$Li than in vacuum deuteron.
- In $^{18}$F, the correlation is weak and does not favor a deuteron-like state.
- Deuteron correlation depends significantly on the nuclear environment and valence orbit.

## Abstract

Deuteron correlation energy (DCE) of the valence proton-neutron subsystem is evaluated by utilizing a simple three-body model. We focus on the $^6$Li and $^{18}$F nuclei assuming the doubly-closed core and the valence proton and neutron. Two interaction models, schematic density-dependent contact (SDDC) and Minnesota potentials, are utilized to describe the proton-neutron interaction. Evaluating DCE, we conclude that the proton-neutron binding in $^6$Li can be stronger than its counterpart of a deuteron in vacuum. On the other hand, in $^{18}$F, the energetic correlation is remarkably weak, and does not favor the bound, deuteron-like configuration. This significant difference between two systems can be understood from a competition between the proton-neutron kinetic and pairing energies, which are sensitive to the spatial extension of the wave function. This result indicates a remarkable dependence of the deuteron correlation to its environment and the valence orbits.