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arXiv:0902.3717 · Physical Review C

Dineutron correlations in quasi-two-dimensional systems in a simplified model, and possible relation to neutron-rich nuclei

Yoshiko Kanada-En’yo, Nobuo Hinohara, Tadahiro Suhara, Peter Schuck

Published May 6, 2009• 16 citations
arXivHTMLPDF

Abstract

Two-neutron correlation in the ${}^{1}S$ channel in quasi-two-dimensional (2D) neutron systems at zero temperature is studied by means of the BCS theory with finite-range effective nuclear forces. The dineutron correlation in low density neutron systems confined in an infinite slab is investigated in a simplified model that neutron motion of one direction is frozen. When the slab is thin enough, two neutrons form a tightly bound dineutron with a small size in the quasi-2D system, and a Bose dineutron gas is found in low density limit. With increase of Fermi momentum, the neutron system changes from the Bose-gas phase to the superfluid Cooper pair phase. The density dependence of the neutron pairing shows the BCS-BEC crossover phenomena at finite low-density region. In the transition region, the size shrinking of neutron pair and enhancement of pairing gap are found. The relation to dineutron correlation at surface of neutron-rich nuclei is also discussed.

DOI
10.1103/physrevc.79.054305

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Two-neutron correlation in the 1S{}^{1}S1S channel in quasi-two-dimensional (2D) neutron systems at zero temperature is studied by means of the BCS theory with finite-range effective nuclear forces. The dineutron correlation in low density neutron systems confined in an infinite slab is investigated in a simplified model that neutron motion of one direction is frozen. When the slab is thin enough, two neutrons form a tightly bound dineutron with a small size in the quasi-2D system, and a Bose dineutron gas is found in low density limit. With increase of Fermi momentum, the neutron system changes from the Bose-gas phase to the superfluid Cooper pair phase. The density dependence of the neutron pairing shows the BCS-BEC crossover phenomena at finite low-density region. In the transition region, the size shrinking of neutron pair and enhancement of pairing gap are found. The relation to dineutron correlation at surface of neutron-rich nuclei is also discussed.
Based on the relativistic Hartree-Bogoliubov theory, the influence of the pairing interaction strength on the dineutron correlations and the crossover from superfluidity of neutron Cooper pairs in the 1S0{}^{1\phantom{\rule{-0.16em}{0ex}}}{S}_{0}1S0​ channel to Bose-Einstein condensation of dineutron pairs is systematically investigated in the nuclear matter. The bare nucleon-nucleon interaction Bonn-B is taken in the particle-particle channel with an effective factor to simulate the medium effects and take into account the possible ambiguity of pairing force, and the effective interaction PK1 is used in the particle-hole channel. If the effective factor is larger than 1.101.101.10, a dineutron Bose-Einstein condensation (BEC) state appears in the low-density limit, and if it is smaller than 0.850.850.85, the neutron Cooper pairs are found totally in the weak coupling Bardeen-Cooper-Schrieffer (BCS) region. The reference values of several characteristic quantities which characterize the BCS-BEC crossover are obtained, respectively, from the dimensionless parameter 1/(kFna)1/({k}_{\mathrm{Fn}}a)1/(kFn​a) with aaa the scattering length and kFn{k}_{\mathrm{Fn}}kFn​ the neutron Fermi momentum, the zero-momentum transfer density correlation function D(0)D(0)D(0), and the effective chemical potential ${\ensuremath{\nu}}_{\mathrm{n}}$.
Due to the large neutron–neutron scattering length, dilute neutron matter resembles the unitary Fermi gas, which lies half-way in the crossover from the BCS phase of weakly coupled Cooper pairs to the Bose–Einstein condensate of dimers. We discuss crossover effects in analogy with the T-matrix theory used in the physics of ultracold atoms, which we generalize to the case of a non-separable finite-range interaction. A problem of the standard Nozières–Schmitt-Rink approach and different ways to solve it are discussed. It is shown that in the strong-coupling regime, the spectral function exhibits a pseudo-gap at temperatures above the critical temperature Tc. The effect of the correlated density on the density dependence of Tc is found to be rather weak, but a possibly important effect due to the reduced quasiparticle weight is identified.
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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The condensation of fermion pairs lies at the heart of superfluidity. However, for strongly correlated systems with reduced dimensionality the mechanisms of pairing and condensation are still not fully understood. In our experiment we use ultracold atoms as a generic model system to study the phase transition from a normal to a condensed phase in a strongly interacting quasi-two-dimensional Fermi gas. Using a novel method, we obtain the in situ pair momentum distribution of the strongly interacting system and observe the emergence of a low-momentum condensate at low temperatures. By tuning temperature and interaction strength, we map out the phase diagram of the quasi-2D BEC-BCS crossover.
Abstract We theoretically investigate the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) crossover in a two-dimensional Fermi gas with the finite-range interaction by using the Hartree–Fock–Bogoliubov theory. Expanding the scattering phase shift in terms of the scattering length and effective range, we discuss the effect of the finite-range interaction on the pairing and thermodynamic properties. By solving the gap equation and the number equation self-consistently, we numerically calculate the effective-range dependence of the pairing gap, chemical potential, and pair size throughout the BCS–BEC crossover. Our results would be useful for further understanding of low-dimensional many-body problems.