Uniform neutron matter is approximated by a cubical box containing a finite number of neutrons, with periodic boundary conditions. We report variational and Green's function Monte Carlo calculations of the ground state of fourteen neutrons in a periodic box using the Argonne v8 ′ two-nucleon interaction at densities up to one and half times the nuclear matter density. The effects of the finite box size are estimated using variational wave functions together with cluster expansion and chain summation techniques. They are small at subnuclear densities. We discuss the expansion of the energy of low-density neutron gas in powers of its Fermi momentum. This expansion is strongly modified by the large nn scattering length, and does not begin with the Fermi-gas kinetic energy as assumed in both Skyrme and relativistic mean field theories. The leading term of neutron gas energy is ∼ half the Fermi-gas kinetic energy. The quantum Monte Carlo results are also used to calibrate the accuracy of variational calculations employing Fermi hypernetted and single operator chain summation methods to study nucleon matter over a larger density range, with more realistic Hamiltonians including three-nucleon interactions. PACS: 21.65.+f, 26.60.+c

We calculate the energy and condensate fraction for a dense system of bosons interacting through an attractive short range interaction with positive s-wave scattering length a. At high densities, n ≫ a −3 , the energy per particle, chemical potential, and square of the sound speed are independent of the scattering length and proportional to n 2/3 , as in Fermi systems. The condensate is quenched at densities na 3 ≃ 1.PACS numbers: 03.75. Fi, 21.65.+f, 74.20.Fg, The densities of atomic vapors under experimental conditions are generally low, in the sense that the distance between particles is typically much larger than the magnitude of the atomic scattering length a, which characterizes the strength of two-body interactions. Recently, it has become possible to tune atomic scattering lengths to essentially any value, positive or negative, by exploiting Feshbach resonances [1]. This opens up the possibility of creating systems which are dense, in the sense that the "gaseousness parameter", n|a| 3 , where n is the particle density, is large compared with unity [2].In dilute alkali gases, the bare two-body interaction at distances large compared with the atomic size is attractive due to the van der Waals interaction, but the effective two-body interaction at low energies, which is given by 4πh 2 a/m, may be large and positive due to the existence of a bound state just below threshold.One of the novel features of such gases is that the characteristic length R associated with the range of the interatomic potential is of order 10 −6 cm. The quantity r 0 = (3/4πn) 1/3 , which is a measure of the atomic separation, is typically of order 10 −4 cm, and therefore much larger than R. In this Letter we consider the properties of a Bose gas for arbitrary n|a| 3 , assuming that R ≪ r 0 . The corresponding problem for a Fermi gas has been considered previously [3].We begin by reviewing briefly the properties of the dilute Bose gas with repulsive interactions, a > 0. At low densities (na 3 ≪ 1) the interaction energy is proportional to the scattering length and the density, as was first found by Lenz [4]. With higher order terms calculated by Huang, Lee, and Yang [5] and Wu [6] included, the energy per particle is E N = 2πh 2 a m n 1 + 128 15To this order, the only property of the two-body interaction that enters is the scattering length. These results have been used to calculate the leading corrections beyond mean-field theory to the properties of trapped Bose gases [7]. Terms of order na 3 and higher depend on other properties of the interaction, as discussed in detail recently in Ref. [8].The expansions leading to the above results are asymptotic, and consequently they give little guidance to the properties of a dense gas, na 3 > ∼ 1. Even though the range of the interaction is small compared with the particle separation, correlations between particles are very important, as one can see from the fact that all terms in the low-density expansion Eq. (1) are formally of the same order of magnitude when na 3 ≃ 1. The Jastrow wave fu...

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We review recent progress in the theory of neutron matter with particular emphasis on its superfluid properties. Results of quantum Monte Carlo calculations of simple and realistic models of uniform superfluid neutron gas are discussed along with those of neutrons interacting in a potential well chosen to approximate neutron-rich oxygen isotopes. The properties of dilute superfluid Fermi gases that may be produced in atom traps, and their relations with neutron matter, are illustrated. The density dependence of the effective interaction between neutrons, used to describe neutron-rich systems with the mean field approximations, is also discussed.

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