Relativistic description of BCS-BEC crossover in nuclear matter

TL;DR

This paper provides a relativistic theoretical analysis of the BCS-BEC crossover in nuclear matter, examining how neutron pairing evolves from superfluidity to Bose-Einstein condensation across different densities.

Contribution

It introduces a microscopic relativistic framework to study the continuous evolution of neutron pairing from BCS to BEC regimes in nuclear matter, using realistic interactions.

Findings

Neutron Cooper pair wave function evolves continuously from BCS to BEC with decreasing density.

No true BEC state of neutron pairs is observed at any density.

Features of the BCS-BEC crossover are identified in specific density regions for nuclear and neutron matter.

Abstract

We study theoretically the di-neutron spatial correlations and the crossover from superfluidity of neutron Cooper pairs in the $^1S_0$ pairing channel to Bose-Einstein condensation (BEC) of di-neutron pairs for both symmetric and neutron matter in the microscopic relativistic pairing theory. We take the bare nucleon-nucleon interaction Bonn-B in the particle-particle channel and the effective interaction PK1 of the relativistic mean-field approach in the particle-hole channel. It is found that the spatial structure of neutron Cooper pair wave function evolves continuously from BCS-type to BEC-type as density decreases. We see a strong concentration of the probability density revealed for the neutron pairs in the fairly small relative distance around $1.5 {\rm fm}$ and the neutron Fermi momentum $k_{Fn}\in[0.6,1.0] {\rm fm^{-1}}$. However, from the effective chemical potential and the quasiparticle excitation spectrum, there is no evidence for the appearance of a true BEC state of neutron pairs at any density. The most BEC-like state may appear at $k_{Fn}\thicksim0.2 {\rm fm^{-1}}$ by examining the density correlation function. From the coherence length and the probability distribution of neutron Cooper pairs as well as the ratio between the neutron pairing gap and the kinetic energy at the Fermi surface, some features of the BCS-BEC crossover are seen in the density regions, $0.05 {\rm fm^{-1}}<k_{Fn}<0.7 (0.75) {\rm fm^{-1}}$, for the symmetric nuclear (pure neutron) matter.