Unitarity potentials and neutron matter at the unitary limit

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 system, a quantity of much interest is the ratio $\xi =E_0/E_0^{free}$ where $E_0$ is the true ground-state energy of the system, and $E_0^{free}$ is that for the non-interacting system. In the limit of $a_s\to \pm \infty$, often referred to as the unitary limit, this ratio is expected to approach a universal constant, namely $\xi \sim 0.44(1)$. In the present work we calculate this ratio $\xi$ 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 $\xi$ using a unitarity CDBonn potential obtained by slightly scaling its meson parameters. The ratios $\xi$ given by these different unitarity potentials are all close to each other and also remarkably close to 0.44, suggesting that the above ratio $\xi$ 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 discussed.

7.5 pages, 7 figures

References in corpus (14)

• Theory of ultracold Fermi gases
• Nearly Perfect Fluidity: From Cold Atomic Gases to Hot Quark Gluon Plasmas
• Thermodynamics of the BCS-BEC crossover
• Strongly paired fermions: Cold atoms and neutron matter
• Shell-model calculations and realistic effective interactions
• Epsilon expansion for a Fermi gas at infinite scattering length
• The potential energy of a ${}^{40}$K Fermi gas in the BCS-BEC crossover
• Thermodynamic Measurements in a Strongly Interacting Fermi Gas
• Magnetic field control of elastic scattering in a cold gas of fermionic lithium atoms
• Dilute neutron matter on the lattice at next-to-leading order in chiral effective field theory
• Low-momentum NN interactions and all-order summation of ring diagrams of symmetric nuclear matter
• BEC-BCS Crossover in the Epsilon Expansion
• Neutron star, $\beta$-stable ring-diagram equation of state and Brown-Rho scaling
• Low-momentum ring diagrams of neutron matter at and near the unitary limit

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• Half-Skyrmions and the Equation of State for Compact-Star Matter
• Scale-Invariant Hidden Local Symmetry, Topology Change and Dense Baryonic Matter
• Low-momentum interactions with Brown-Rho-Ericson scalings and the density dependence of the nuclear symmetry energy
• Introduction to low-momentum effective interactions with Brown-Rho scaling and three-nucleon forces
• Unitary limit and linear scaling of neutrons in harmonic trap with tuned CD-Bonn and square-well interactions