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:0912.0273 · Physical Review C

Unitarity potentials and neutron matter at the unitary limit

Huan Dong, L.-W. Siu, T.T.S. Kuo, R. Machleidt

Published Mar 15, 2010• 12 citations
arXivHTMLPDF

Abstract

We study the equation of state of neutron matter using a family of unitarity potentials, all of which are constructed to have infinite ${}^{1}{S}_{0}$ scattering lengths ${a}_{s}$. For such a system, a quantity of much interest is the ratio $\ensuremath{\xi}={E}_{0}/{E}_{0}^{\mathrm{free}}$, where ${E}_{0}$ is the true ground-state energy of the system and ${E}_{0}^{\mathrm{free}}$ is that for the noninteracting system. In the limit of ${a}_{s}\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty}$, often referred to as the unitary limit, this ratio is expected to approach a universal constant, namely $\ensuremath{\xi}~0.44(1)$. In the present work we calculate this ratio $\ensuremath{\xi}$ using a family of hard-core square-well potentials whose ${a}_{s}$ can be exactly obtained, thus enabling us to have many potentials of different ranges and strengths, all with infinite ${a}_{s}$. We have also calculated $\ensuremath{\xi}$ using a unitarity CDBonn potential obtained by slightly scaling its meson parameters. The ratios $\ensuremath{\xi}$ given by these different unitarity potentials are all close to each other and also remarkably close to 0.44, suggesting that the above ratio $\ensuremath{\xi}$ is indifferent to the details of the underlying interactions as long as they have infinite scattering length. A sum-rule and scaling constraint for the renormalized low-momentum interaction in neutron matter at the unitary limit is studied. The importance of pairing in our all-order ring diagram and model-space HF calculations of neutron matter is discussed.

DOI
10.1103/physrevc.81.034003

Related papers

Low-momentum ring diagrams of neutron matter at and near the unitary limit

L.-W. Siu, T.T.S. Kuo, R. Machleidt

We study neutron matter at and near the unitary limit using a low-momentum ring diagram approach. By slightly tuning the meson-exchange CD-Bonn potential, neutron-neutron potentials with various ${}^{1}{S}_{0}$ scattering lengths such as ${a}_{s}=\ensuremath{-}12070$ fm and $+21$ fm are constructed. Such potentials are renormalized with rigorous procedures to give the corresponding ${a}_{s}$-equivalent low-momentum potentials ${V}_{\text{low-}k}$, with which the low-momentum particle-particle hole-hole ring diagrams are summed up to all orders, giving the ground state energy ${E}_{0}$ of neutron matter for various scattering lengths. At the limit of ${a}_{s}\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty}$, our calculated ratio of ${E}_{0}$ to that of the noninteracting case is found remarkably close to a constant of 0.44 over a wide range of Fermi-momenta. This result reveals an universality that is well consistent with the recent experimental and Monte Carlo computational study on low-density cold Fermi gas at the unitary limit. The overall behavior of this ratio obtained with various scattering lengths is presented and discussed. Ring-diagram results obtained with ${V}_{\text{low-}k}$ and those with $G$-matrix interactions are compared.

arXiv:0710.5717•Physical Review C•Mar 10, 2008•13 citations

Unitary limit and linear scaling of neutrons in harmonic trap with tuned CD-Bonn and square-well interactions

Y. Y. Cheng, T.T.S. Kuo, R. Machleidt +1 more

We study systems of finite-number neutrons in a harmonic trap at the unitary limit. Two very different types of neutron-neutron interactions are applied, namely, the meson-theoretic CD-Bonn potential and hard-core square-well interactions, all tuned to possess an infinite scattering length, and with effective ranges comparable to the trap size. The potentials are renormalized to equivalent, scattering-length preserving low-momentum potentials, Vlow−k, with which the particle-particle hole-hole ring diagrams are summed to all orders to yield the ground-state energy E0 of the finite neutron system. We find the ratio E0/E0free (where E0free denotes the ground-state energy of the corresponding non-interacting system) to be remarkably independent from variations of the harmonic trap parameter, the type and effective range of the unitarity interaction, and the decimation momentum of Vlow−k. Our results support a special linear scaling relation of E0 versus the trap parameter ħω. Certain properties of Landau's quasi-particles for trapped neutrons at the unitary limit are also discussed.

arXiv:1809.00205•Physics Letters B•Jul 30, 2019•3 citations

From low-density neutron matter to the unitary limit

Takumi Abe, R. Seki

Various quantities of an attractively interacting fermion system at the unitary limit are determined by extrapolating Monte Carlo results of low-density neutron matter. Smooth extrapolation in terms of $1/({k}_{F}{a}_{0})$ (${k}_{F}$ is the Fermi momentum, and ${a}_{0}$ is the ${}^{1}{S}_{0}$ scattering length) is found with the quantities examined: the ground-state energy, the pairing gap at $T\ensuremath{\approx}0$, and the critical temperature of the normal-to-superfluid phase transition. We emphasize proximity of the physics of low-density neutron matter to that at the unitary limit. The extrapolated quantities are in a reasonable agreement with those in the literature.

arXiv:0708.2524•Physical Review C•May 11, 2009•37 citations

Low-Density Neutron Matter and the Unitary Limit

Isaac Vidaña

We review the properties of neutron matter in the low-density regime. In particular, we revise its ground state energy and the superfluid neutron pairing gap and analyze their evolution from the weak to the strong coupling regime. The calculations of the energy and the pairing gap are performed, respectively, within the Brueckner–Hartree–Fock (BHF) approach of nuclear matter and the Bardeen–Cooper–Schrieffer (BCS) theory using the chiral nucleon-nucleon interaction of Entem and Machleidt at N3LO and the Argonne V18 phenomenological potential. Results for the energy are also shown for a simple Gaussian potential with a strength and range adjusted to reproduce the1S0neutron-neutron scattering length and effective range. Our results are compared with those of quantum Monte Carlo (QMC) calculations for neutron matter and cold atoms. The Tan contact parameter in neutron matter is also calculated, finding a reasonable agreement with experimental data from ultra-cold atoms only at very low densities. We find that low-density neutron matter exhibits a behavior close to that of a Fermi gas at the unitary limit, although, this limit is actually never reached. We also review the properties (energy, effective mass, and quasiparticle residue) of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons already studied by the author in a recent work where it was shown that these properties are very close to those of an attractive Fermi polaron in the unitary limit.

arXiv:2101.11903•Frontiers in Physics•May 10, 2021•16 citations

BCS variation method and universal behavior of trapped neutron systems at unitary limit

Y. Y. Cheng, Y. M. Zhao

In this work we study unitary neutron systems confined in a harmonic-oscillator trap, based on the BCS theory and the quasiparticle ring-diagram method. The low-momentum interaction ${V}_{\text{low-}k}$ renormalized from a fine-tuned CD-Bonn potential with the $^{1}S_{0}$ scattering length approaching the infinity is adopted. The energy ratios of trapped unitary neutron systems with various particle numbers, both those with magic numbers and those with nonmagic ones, to corresponding noninteracting systems, are shown to all flow to a constant value. The BCS wave functions for these trapped unitary systems, with different trap parameters and different particle numbers, manifest themselves with universal patterns: the effect of harmonic-oscillator shells is significant, and moreover, the orbits of the lowest valence shell are occupied with a uniform probability. We also discuss the self-energy given by the BCS calculation, and present a weighted sum rule satisfied by the monopole components of the unitary neutron-neutron interaction. In terms of these, the constant energy ratio independent of the trap parameter and the particle number can be interpreted.

Physical Review C•May 14, 2024•1 citation

Universal physics of two neutrons with one flavored meson

Udit Raha, Yuki Kamiya, Tetsuo Hyodo +1 more

We investigate the $s$-wave three-body system of two neutrons and one flavored meson with total spin-isospin $J=0,I=3/2$. The meson-neutron scattering length can become infinitely large in an unphysical region of the quark mass when extrapolated from strangeness to charm in the so-called zero coupling limit. Using a low-energy cluster effective field theory, we demonstrate that the Efimov effect is manifest in the three-body system when the meson-neutron scattering length is extrapolated to the unitary limit of the two-body interaction. We thereby discuss the consequence of universal physics in the physical $K^{-}nn$ and $D^{0}nn$ systems.

•Aug 10, 2017•0 citations
We study the equation of state of neutron matter using a family of unitarity potentials, all of which are constructed to have infinite 1S0{}^{1}{S}_{0}1S0​ scattering lengths as{a}_{s}as​. For such a system, a quantity of much interest is the ratio \ensuremathξ=E0/E0free\ensuremath{\xi}={E}_{0}/{E}_{0}^{\mathrm{free}}\ensuremathξ=E0​/E0free​, where E0{E}_{0}E0​ is the true ground-state energy of the system and E0free{E}_{0}^{\mathrm{free}}E0free​ is that for the noninteracting system. In the limit of as\ensuremath→\ifmmode±\else\textpm\fi\ensuremath∞{a}_{s}\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty}as​\ensuremath→\ifmmode±\else\textpm\fi\ensuremath∞, often referred to as the unitary limit, this ratio is expected to approach a universal constant, namely \ensuremathξ 0.44(1)\ensuremath{\xi}~0.44(1)\ensuremathξ 0.44(1). In the present work we calculate this ratio \ensuremathξ\ensuremath{\xi}\ensuremathξ using a family of hard-core square-well potentials whose as{a}_{s}as​ can be exactly obtained, thus enabling us to have many potentials of different ranges and strengths, all with infinite as{a}_{s}as​. We have also calculated \ensuremathξ\ensuremath{\xi}\ensuremathξ using a unitarity CDBonn potential obtained by slightly scaling its meson parameters. The ratios \ensuremathξ\ensuremath{\xi}\ensuremathξ given by these different unitarity potentials are all close to each other and also remarkably close to 0.44, suggesting that the above ratio \ensuremathξ\ensuremath{\xi}\ensuremathξ is indifferent to the details of the underlying interactions as long as they have infinite scattering length. A sum-rule and scaling constraint for the renormalized low-momentum interaction in neutron matter at the unitary limit is studied. The importance of pairing in our all-order ring diagram and model-space HF calculations of neutron matter is discussed.
We study neutron matter at and near the unitary limit using a low-momentum ring diagram approach. By slightly tuning the meson-exchange CD-Bonn potential, neutron-neutron potentials with various 1S0{}^{1}{S}_{0}1S0​ scattering lengths such as ${a}_{s}=\ensuremath{-}12070$ fm and +21+21+21 fm are constructed. Such potentials are renormalized with rigorous procedures to give the corresponding as{a}_{s}as​-equivalent low-momentum potentials Vlow-k{V}_{\text{low-}k}Vlow-k​, with which the low-momentum particle-particle hole-hole ring diagrams are summed up to all orders, giving the ground state energy E0{E}_{0}E0​ of neutron matter for various scattering lengths. At the limit of ${a}_{s}\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty}$, our calculated ratio of E0{E}_{0}E0​ to that of the noninteracting case is found remarkably close to a constant of 0.44 over a wide range of Fermi-momenta. This result reveals an universality that is well consistent with the recent experimental and Monte Carlo computational study on low-density cold Fermi gas at the unitary limit. The overall behavior of this ratio obtained with various scattering lengths is presented and discussed. Ring-diagram results obtained with Vlow-k{V}_{\text{low-}k}Vlow-k​ and those with GGG-matrix interactions are compared.
We study systems of finite-number neutrons in a harmonic trap at the unitary limit. Two very different types of neutron-neutron interactions are applied, namely, the meson-theoretic CD-Bonn potential and hard-core square-well interactions, all tuned to possess an infinite scattering length, and with effective ranges comparable to the trap size. The potentials are renormalized to equivalent, scattering-length preserving low-momentum potentials, Vlow−k, with which the particle-particle hole-hole ring diagrams are summed to all orders to yield the ground-state energy E0 of the finite neutron system. We find the ratio E0/E0free (where E0free denotes the ground-state energy of the corresponding non-interacting system) to be remarkably independent from variations of the harmonic trap parameter, the type and effective range of the unitarity interaction, and the decimation momentum of Vlow−k. Our results support a special linear scaling relation of E0 versus the trap parameter ħω. Certain properties of Landau's quasi-particles for trapped neutrons at the unitary limit are also discussed.
Various quantities of an attractively interacting fermion system at the unitary limit are determined by extrapolating Monte Carlo results of low-density neutron matter. Smooth extrapolation in terms of 1/(kFa0)1/({k}_{F}{a}_{0})1/(kF​a0​) (kF{k}_{F}kF​ is the Fermi momentum, and a0{a}_{0}a0​ is the 1S0{}^{1}{S}_{0}1S0​ scattering length) is found with the quantities examined: the ground-state energy, the pairing gap at $T\ensuremath{\approx}0$, and the critical temperature of the normal-to-superfluid phase transition. We emphasize proximity of the physics of low-density neutron matter to that at the unitary limit. The extrapolated quantities are in a reasonable agreement with those in the literature.
We review the properties of neutron matter in the low-density regime. In particular, we revise its ground state energy and the superfluid neutron pairing gap and analyze their evolution from the weak to the strong coupling regime. The calculations of the energy and the pairing gap are performed, respectively, within the Brueckner–Hartree–Fock (BHF) approach of nuclear matter and the Bardeen–Cooper–Schrieffer (BCS) theory using the chiral nucleon-nucleon interaction of Entem and Machleidt at N3LO and the Argonne V18 phenomenological potential. Results for the energy are also shown for a simple Gaussian potential with a strength and range adjusted to reproduce the1S0neutron-neutron scattering length and effective range. Our results are compared with those of quantum Monte Carlo (QMC) calculations for neutron matter and cold atoms. The Tan contact parameter in neutron matter is also calculated, finding a reasonable agreement with experimental data from ultra-cold atoms only at very low densities. We find that low-density neutron matter exhibits a behavior close to that of a Fermi gas at the unitary limit, although, this limit is actually never reached. We also review the properties (energy, effective mass, and quasiparticle residue) of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons already studied by the author in a recent work where it was shown that these properties are very close to those of an attractive Fermi polaron in the unitary limit.
In this work we study unitary neutron systems confined in a harmonic-oscillator trap, based on the BCS theory and the quasiparticle ring-diagram method. The low-momentum interaction Vlow-k{V}_{\text{low-}k}Vlow-k​ renormalized from a fine-tuned CD-Bonn potential with the 1S0^{1}S_{0}1S0​ scattering length approaching the infinity is adopted. The energy ratios of trapped unitary neutron systems with various particle numbers, both those with magic numbers and those with nonmagic ones, to corresponding noninteracting systems, are shown to all flow to a constant value. The BCS wave functions for these trapped unitary systems, with different trap parameters and different particle numbers, manifest themselves with universal patterns: the effect of harmonic-oscillator shells is significant, and moreover, the orbits of the lowest valence shell are occupied with a uniform probability. We also discuss the self-energy given by the BCS calculation, and present a weighted sum rule satisfied by the monopole components of the unitary neutron-neutron interaction. In terms of these, the constant energy ratio independent of the trap parameter and the particle number can be interpreted.
We investigate the sss-wave three-body system of two neutrons and one flavored meson with total spin-isospin J=0,I=3/2J=0,I=3/2J=0,I=3/2. The meson-neutron scattering length can become infinitely large in an unphysical region of the quark mass when extrapolated from strangeness to charm in the so-called zero coupling limit. Using a low-energy cluster effective field theory, we demonstrate that the Efimov effect is manifest in the three-body system when the meson-neutron scattering length is extrapolated to the unitary limit of the two-body interaction. We thereby discuss the consequence of universal physics in the physical K−nnK^{-}nnK−nn and D0nnD^{0}nnD0nn systems.