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arXiv:0809.1467 · Physical Review C

Hot neutron matter from a self-consistent Green's-functions approach

Arnau Rios, A. Polls, Isaac Vidaña

Published Feb 6, 2009• 73 citations
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Abstract

A systematic study of the microscopic and thermodynamical properties of pure neutron matter at finite temperature within the self-consistent Green's-function approach is performed. The model dependence of these results is analyzed by both comparing the results obtained with two different microscopic interactions, the CD Bonn and the Argonne V18 potentials, and by analyzing the results obtained with other approaches, such as the Brueckner-Hartree-Fock approximation, the variational approach, and the virial expansion.

DOI
10.1103/physrevc.79.025802

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A systematic study of the microscopic and thermodynamical properties of pure neutron matter at finite temperature within the self-consistent Green's-function approach is performed. The model dependence of these results is analyzed by both comparing the results obtained with two different microscopic interactions, the CD Bonn and the Argonne V18 potentials, and by analyzing the results obtained with other approaches, such as the Brueckner-Hartree-Fock approximation, the variational approach, and the virial expansion.
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A method for choosing and deriving a suitable single-particle potential for many-body calculations at finite temperature is suggested. With this potential one can readily determine the self-consistent correlated chemical potential and consequently the resulting equations of state rigorously satisfy a number of basic thermodynamic relations. Application of our method to a Brueckner-Hartree-Fock nuclear matter calculation yields results in remarkably good agreement with the Hugenholtz--Van Hove theorem.
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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 ${v8}^{\ensuremath{'}}$ 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\mathrm{nn}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 approximately 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.
We compute continuum and infinite volume limit extrapolations of the structure factors of neutron matter at finite temperature and density. Using a lattice formulation of leading-order pionless effective field theory, we compute the momentum dependence of the structure factors at finite temperature and at densities beyond the reach of the virial expansion. The Tan contact parameter is computed and the result agrees with the high momentum tail of the vector structure factor. All errors, statistical and systematic, are controlled for. This calculation is a first step towards a model-independent understanding of the linear response of neutron matter at finite temperature.