Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1206.3407 · Physical Review C

BCS-BEC crossover in nuclear matter with the relativistic Hartree-Bogoliubov theory

T. Sun, Bao Yuan Sun, Jie Meng

Published Jul 3, 2012• 23 citations
arXivHTMLPDF

Abstract

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 ${}^{1\phantom{\rule{-0.16em}{0ex}}}{S}_{0}$ 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 $1.10$, a dineutron Bose-Einstein condensation (BEC) state appears in the low-density limit, and if it is smaller than $0.85$, 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 $1/({k}_{\mathrm{Fn}}a)$ with $a$ the scattering length and ${k}_{\mathrm{Fn}}$ the neutron Fermi momentum, the zero-momentum transfer density correlation function $D(0)$, and the effective chemical potential ${\ensuremath{\nu}}_{\mathrm{n}}$.

DOI
10.1103/physrevc.86.014305

Related papers

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

A. A. Isayev

Recent calculations with an effective isospin-dependent contact interaction show the possibility of the crossover from superfluidity of neutron Cooper pairs in the ${^{1}\mathrm{S}}_{0}$ 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 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.

arXiv:0803.3362•Physical Review C•Jul 9, 2008•15 citations

Relativistic BCS-BEC crossover in a boson-fermion model

Jian Deng, Andreas Schmitt, Qun Wang

We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS) pairing to a Bose-Einstein condensate (BEC) in a relativistic superfluid within a boson-fermion model. The model includes, besides the fermions, separate bosonic degrees of freedom, accounting for the bosonic nature of the Cooper pairs. The crossover is realized by tuning the difference between the boson mass and boson chemical potential as a free parameter. The model yields populations of condensed and uncondensed bosons as well as gapped and ungapped fermions throughout the crossover region for arbitrary temperatures. Moreover, we observe the appearance of antiparticles for sufficiently large values of the crossover parameter. As an application, we study pairing of fermions with imbalanced populations. The model can potentially be applied to color superconductivity in dense quark matter at strong couplings.

arXiv:nucl-th/0611097•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Aug 22, 2007•46 citations

Role of the effective range in the density-induced BEC-BCS crossover

Hiroyuki Tajima, Haozhao Liang

We elucidate the role of the effective range in the Bose-Einstein-condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) crossover regime of two-component fermions in three dimensions. In contrast to ultracold Fermi gases near the broad Feshbach resonance, where the interaction can be characterized by the contact-type interaction, the interaction range in general becomes important in the density-induced BEC-BCS crossover discussed in the context of condensed-matter and nuclear systems. By characterizing the nonlocal interaction in terms of the low-energy constants such as scattering length $a$ and effective range $r$, we show how the crossover phenomena are affected by nonzero effective ranges. In particular, we show that the superfluid order parameter is strongly suppressed in the high-density regime and the sound velocity exhibits a nonmonotonic behavior reflecting the mechanical stability of the system. Moreover, we point out that the high-momentum tail associated with the contact parameter can be visible when the magnitude of momentum $k$ is much less than $1/r$. We also discuss the relation between the high-momentum tail and the nuclear contact formalism.

arXiv:2206.12599•Physical Review A•Oct 12, 2022•11 citations

Finite-range effect in the two-dimensional density-induced BCS–BEC crossover

Hikaru Sakakibara, Hiroyuki Tajima, Haozhao Liang

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.

arXiv:2306.02127•Progress of Theoretical and Experimental Physics•Jul 27, 2023•1 citation

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 +1 more

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.

arXiv:0902.3717•Physical Review C•May 6, 2009•16 citations

Equation of state of a superfluid Fermi gas in the BCS- BEC crossover

H. Hu, Xia-Ji Liu, P. D. Drummond

PACS. 03.75.Hh – Static properties of condensates; thermodynamical, statistical and structural properties. PACS. 03.75.Ss – Degenerate Fermi gases. PACS. 05.30.Fk – Fermion systems and electron gas. Abstract. – We present a theory for a superfluid Fermi gas near the BCS-BEC crossover, including pairing fluctuation contributions to the free energy similar to that considered by Nozières and Schmitt-Rink for the normal phase. In the strong coupling limit, our theory is able to recover the Bogoliubov theory of a weakly interacting Bose gas with a molecular scattering length very close to the known exact result. We compare our results with recent Quantum Monte Carlo simulations both for the ground state and at finite temperature. Excellent agreement is found for all interaction strengths where simulation results are available. The recent experimental realization of strongly interacting Fermi gases of 6 Li and 40 K atoms near a Feshbach resonance has opened up the exciting possibility of investigating the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC) [1–5]. In these systems, the inter-atomic interaction strength can be varied by tuning

•Jan 1, 2006•84 citations
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 \ensuremathνn{\ensuremath{\nu}}_{\mathrm{n}}\ensuremathνn​.
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.
We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS) pairing to a Bose-Einstein condensate (BEC) in a relativistic superfluid within a boson-fermion model. The model includes, besides the fermions, separate bosonic degrees of freedom, accounting for the bosonic nature of the Cooper pairs. The crossover is realized by tuning the difference between the boson mass and boson chemical potential as a free parameter. The model yields populations of condensed and uncondensed bosons as well as gapped and ungapped fermions throughout the crossover region for arbitrary temperatures. Moreover, we observe the appearance of antiparticles for sufficiently large values of the crossover parameter. As an application, we study pairing of fermions with imbalanced populations. The model can potentially be applied to color superconductivity in dense quark matter at strong couplings.
We elucidate the role of the effective range in the Bose-Einstein-condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) crossover regime of two-component fermions in three dimensions. In contrast to ultracold Fermi gases near the broad Feshbach resonance, where the interaction can be characterized by the contact-type interaction, the interaction range in general becomes important in the density-induced BEC-BCS crossover discussed in the context of condensed-matter and nuclear systems. By characterizing the nonlocal interaction in terms of the low-energy constants such as scattering length aaa and effective range rrr, we show how the crossover phenomena are affected by nonzero effective ranges. In particular, we show that the superfluid order parameter is strongly suppressed in the high-density regime and the sound velocity exhibits a nonmonotonic behavior reflecting the mechanical stability of the system. Moreover, we point out that the high-momentum tail associated with the contact parameter can be visible when the magnitude of momentum kkk is much less than 1/r1/r1/r. We also discuss the relation between the high-momentum tail and the nuclear contact formalism.
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.
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.
PACS. 03.75.Hh – Static properties of condensates; thermodynamical, statistical and structural properties. PACS. 03.75.Ss – Degenerate Fermi gases. PACS. 05.30.Fk – Fermion systems and electron gas. Abstract. – We present a theory for a superfluid Fermi gas near the BCS-BEC crossover, including pairing fluctuation contributions to the free energy similar to that considered by Nozières and Schmitt-Rink for the normal phase. In the strong coupling limit, our theory is able to recover the Bogoliubov theory of a weakly interacting Bose gas with a molecular scattering length very close to the known exact result. We compare our results with recent Quantum Monte Carlo simulations both for the ground state and at finite temperature. Excellent agreement is found for all interaction strengths where simulation results are available. The recent experimental realization of strongly interacting Fermi gases of 6 Li and 40 K atoms near a Feshbach resonance has opened up the exciting possibility of investigating the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC) [1–5]. In these systems, the inter-atomic interaction strength can be varied by tuning