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arXiv:1401.4651 · Journal of Physics Conference Series

Inhomogeneous condensates in dilute nuclear matter and BCS-BEC crossovers

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

Published Mar 25, 2014• 7 citations
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Abstract

We report on recent progress in understanding pairing phenomena in low-density nuclear matter at small and moderate isospin asymmetry. A rich phase diagram has been found comprising various superfluid phases that include a homogeneous and phase-separated BEC phase of deuterons at low density and a homogeneous BCS phase, an inhomogeneous LOFF phase, and a phase-separated BCS phase at higher densities. The transition from the BEC phases to the BCS phases is characterized in terms of the evolution, from strong to weak coupling, of the condensate wavefunction and the second moment of its density distribution in r-space. We briefly discuss approaches to higher-order clustering in low-density nuclear matter.

DOI
10.1088/1742-6596/496/1/012008

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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.
The density, spin, and isospin correlation functions in nuclear matter with a neutron-proton condensate are calculated to study the possible signatures of the BEC-BCS crossover in the low-density region. It is shown that the criterion of the crossover (Phys. Rev. Lett. 95 , 090402 (2005)), consisting in the change of the sign of the density correlation function at low momentum transfer, fails to describe correctly the density-driven BEC-BCS transition at finite isospin asymmetry or finite temperature. The presence (BCS regime) or absence (BEC regime) of the singularity in the momentum distribution of the quasiparticle density of states can be used as an unambiguous signature of the BEC-BCS transition.
Finding the distinct features of the crossover from the regime of large overlapping Cooper pairs to the limit of non-overlapping pairs of fermions (Shafroth pairs) in multicomponent Fermi systems remains one of the actual problems in a quantum many-body theory. Here this transition is studied by calculating the two-body density, spin and isospin correlation functions in dilute asymmetric nuclear matter. It is shown that criterion of the crossover (Phys. Rev. Lett. 95 , 090402 (2005)), consisting in the change of the sign of the density correlation function at low momentum transfer, fails to describe correctly the density-driven BEC-BCS transition at finite isospin asymmetry or finite temperature. As an unambiguous signature of the BEC-BCS transition, there can be used the presence (BCS regime) or absence (BEC regime) of the singularity in the momentum distribution of the quasiparticle density of states.
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