# In-medium bound states and pairing gap

## TL;DR

This paper investigates in-medium two-nucleon bound states using a non-Hermitian RPA Hamiltonian, linking complex eigenvalues to BCS pairing gaps, and compares different pairing channels in nuclear matter.

## Contribution

It introduces a novel approach to analyze in-medium bound states via a non-Hermitian RPA Hamiltonian, connecting complex eigenvalues with BCS pairing gaps in nuclear matter.

## Key findings

- Complex conjugate eigenvalues indicate in-medium bound states.
- Calculated pairing gaps match conventional BCS solutions.
- Differences observed in the $^3SD_1$ channel at low densities.

## Abstract

The propagator of two nucleons in infinite nuclear matter is evaluated by a diagonalization of the $pphh$ RPA Hamiltonian. This effective Hamiltonian is non-Hermitian and, for specific density domains and partial waves, yields pairs of complex conjugated eigenvalues representing in-medium bound states of two nucleons. The occurrence of these complex poles in the two-particle Greens function is tightly related to the well known BCS pairing approach. It is demonstrated that these complex eigenvalues and the corresponding bound state wavefunctions contain all information about the BCS gap function. This is illustrated by calculations for $^1S_0$ and $^3PF_2$ pairing gaps in neutron matter which essentially coincide with the corresponding gap functions extracted from conventional solutions of the gap equation. Differences between the bound states in the conventional BCS approach and the $pphh$ RPA are arising in the case of $^3SD_1$ channel in symmetric nuclear matter at low densities. These differences are discussed in the context of transition from BEC for quasi-deuterons to the formation of BCS pairing.