Static response, collective frequencies and ground state thermodynamical properties of spin saturated two-component cold atoms and neutron matter

Abstract

The thermodynamical ground-state properties and static response in both cold atoms at or close to unitarity and neutron matter are determined using a recently proposed Density Functional Theory (DFT) based on the s-wave scattering length $a_s$, effective range $r_e$, and unitary gas limit. In cold atoms, when the effective range may be neglected, we show that the pressure, chemical potential, compressibility modulus and sound velocity obtained with the DFT are compatible with experimental observations or exact theoretical estimates. The static response in homogeneous infinite systems is also obtained and a possible influence of the effective range on the response is analyzed. The neutron matter differs from unitary gas due to the non infinite scattering length and to a significant influence of effective range which affects all thermodynamical quantities as well as the static response. In particular, we show for neutron matter that the latter response recently obtained in Auxiliary-Field Diffusion Monte-Carlo (AFDMC) can be qualitatively reproduced when the p-wave contribution is added to the functional. Our study indicates that the close similarity between the exact AFDMC static response and the free gas response might stems from the compensation of the $a_s$ effect by the effective range and p-wave contributions. We finally consider the dynamical response of both atoms or neutron droplets in anisotropic traps. Assuming the hydrodynamical regime and a polytropic equation of state, a reasonable description of the radial and axial collective frequencies in cold atoms is obtained. Following a similar strategy, we estimate the equivalent collective frequencies of neutron drops in anisotropic traps.

arXiv comment12 pages, 17 figures

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• Energy-density functionals inspired by effective-field theories: Applications to neutron drops
• Non-perturbative Extraction of the Effective Mass in Neutron Matter
• Do we know how to count powers in pionless and pionful effective field theory?
• The Role of the Effective Range in Resonantly Interacting Fermi Gases: How Breaking Scale Symmetry Affects the Bulk Viscosity
• Satisfying the compressibility sum rule in neutron matter
• Towards a power counting in nuclear energy-density-functional theories through a perturbative analysis
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• Skyrme-based extrapolation for the static response of neutron matter
• Neutron matter at the interface(s): static response and effective mass
• Local energy density functional for superfluid Fermi gases from effective field theory