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arXiv:1208.0123 · Physical Review C

Phase diagram of dilute nuclear matter: Unconventional pairing and the BCS-BEC crossover

Matthias Oliver Stein, Xu-Guang Huang, Armen Sedrakian, J. W. Clark

Published Dec 6, 2012• 25 citations
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Abstract

We report on a comprehensive study of the phase structure of cold, dilute nuclear matter featuring a ${}^{3}\phantom{\rule{-0.16em}{0ex}}{S}_{1}$-${}^{3}\phantom{\rule{-0.16em}{0ex}}{D}_{1}$ condensate at nonzero isospin asymmetry, within wide ranges of temperatures and densities. We find a rich phase diagram comprising three superfluid phases, namely, a Larkin-Ovchinnikov-Fulde-Ferrell phase, the ordinary BCS phase, and a heterogeneous, phase-separated BCS phase, with associated crossovers from the latter two phases to a homogeneous or phase-separated Bose-Einstein condensate of deuterons. The phase diagram contains two tricritical points (one a Lifshitz point), which may degenerate into a single tetracritical point for some degree of isospin asymmetry.

DOI
10.1103/physrevc.86.062801

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Recent calculations with an effective isospin-dependent contact interaction show the possibility of the crossover from superfluidity of neutron Cooper pairs in the 1S0{^{1}\mathrm{S}}_{0}1S0​ 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 of finding 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 a value for the critical asymmetry ${\ensuremath{\alpha}}_{c}^{d}~0.9$, 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. 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.
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