Correlation functions for a di-neutron condensate in asymmetric nuclear matter

TL;DR

This paper investigates the BCS-BEC crossover in asymmetric nuclear matter by analyzing density and spin correlation functions, identifying signatures of the transition and its limitations at high isospin asymmetry.

Contribution

It provides a detailed analysis of correlation functions in asymmetric nuclear matter, extending previous work to include effects of isospin asymmetry on the BCS-BEC crossover signatures.

Findings

Density correlation function changes sign at low momentum transfer in symmetric matter.

Signatures of the BCS-BEC transition are less reliable at high isospin asymmetry.

Spin correlation function satisfies the sum rule at zero temperature.

Abstract

Recent calculations with an effective isospin dependent contact interaction show the possibility of the crossover from superfluidity of neutron Cooper pairs in $^1S_0$ pairing channel to Bose-Einstein condensation (BEC) of di-neutron bound states in dilute nuclear matter. The density and spin correlation functions are calculated for a di-neutron condensate in asymmetric nuclear matter with the aim to find the possible features of the BCS-BEC crossover. It is shown that the zero-momentum transfer spin correlation function satisfies the sum rule at zero temperature. In symmetric nuclear matter, the density correlation function changes sign at low momentum transfer across the BCS-BEC transition and this feature can be considered as a signature of the crossover. At finite isospin asymmetry, this criterion gives too large value for the critical asymmetry $\alpha_c^d\sim0.9$, at which the BEC state is quenched. Therefore, it can be trusted for the description of the density-driven BCS-BEC crossover of neutron pairs only at small isospin asymmetry. This result generalizes the conclusion of the study in Phys. Rev. Lett. {\bf 95}, 090402 (2005), where the change of sign of the density correlation function at low momentum transfer in two-component quantum fermionic atomic gas with the balanced populations of fermions of different species was considered as an unambiguous signature of the BCS-BEC transition.