# Neutron-proton pairing in Nuclear Matter

## TL;DR

This paper investigates the effects of self-energy and three-body forces on neutron-proton pairing gaps in nuclear matter using advanced many-body theoretical approaches, providing insights relevant for finite nuclei.

## Contribution

It combines extended Bruecker-Hartree-Fock and BCS theories to analyze self-energy effects on np pairing gaps, including the impact of three-body forces and establishing an effective pairing force.

## Key findings

- Second-order self-energy reduces the pairing gap significantly.
- Renormalization enhances the pairing gap.
- Three-body force has negligible effect on the pairing gap.

## Abstract

The self-energy effect on the neutron-proton (np) pairing gap is investigated up to the third order within the framework of the extend Bruecker-Hartree-Fock (BHF) approach combined with the BCS theory. The self-energy up to the second-order contribution turns out to reduce strongly the effective energy gap, while the \emph{renormalization} term enhances it significantly. In addition, the effect of the three-body force on the np pairing gap is shown to be negligible. To connect the present results with the np pairing in finite nuclei, an effective density-dependent zero-range pairing force is established with the parameters calibrated to the microscopically calculated energy gap.