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arXiv:1207.6314 · Physical Review C

Comparative study of neutron and nuclear matter with simplified Argonne nucleon-nucleon potentials

M. Baldo, A. Polls, Arnau Rios, H.-J. Schulze, Isaac Vidaña

Published Dec 3, 2012• 84 citations
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Abstract

We present calculations of the energy per particle of pure neutron and symmetric nuclear matter with simplified Argonne nucleon-nucleon potentials for different many-body theories. We compare critically the Brueckner-Hartree-Fock results to other formalisms, such as the Brueckner-Bethe-Goldstone expansion up to third order, self-consistent Green's functions, auxiliary field diffusion Monte Carlo, and Fermi hypernetted chain. We evaluate the importance of spin-orbit and tensor correlations in the equation of state and find these to be important in a wide range of densities.

DOI
10.1103/physrevc.86.064001

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Canadian Journal of Physics•Aug 4, 2021•1 citation
We present calculations of the energy per particle of pure neutron and symmetric nuclear matter with simplified Argonne nucleon-nucleon potentials for different many-body theories. We compare critically the Brueckner-Hartree-Fock results to other formalisms, such as the Brueckner-Bethe-Goldstone expansion up to third order, self-consistent Green's functions, auxiliary field diffusion Monte Carlo, and Fermi hypernetted chain. We evaluate the importance of spin-orbit and tensor correlations in the equation of state and find these to be important in a wide range of densities.
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.
Abstract This chapter discusses the significance of two body interactions to many-body properties, beginning with a schematic model showing the relevance of short-range correlations beyond those of the Fermi gas. These correlations are studied within Brueckner theory and the help of the Bethe-Goldstone equation, mainly for nuclear matter proper but extensions to finite temperature are presented. Effective forces of Skyrme type are derived through an expansion of the G-matrix to small relative momenta. This scheme hinges essentially on the Brueckner-Hartree-Fock approximation, for which results for binding energy and equilibrium density are presented. An alternative variational method based on Jastrow functions is sketched, which demonstrates the necessity for considering effective three body forces. The concept of the nuclear equation of state is presented and parameterized by Skyrme forces with density dependent parameters. Finally, a semi-classical transport theory is presented which accounts for statistical collisions of the nucleons.
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.
The tensor optimized Fermi sphere (TOFS) method is applied first for the study of the property of nuclear matter using the Argonne V4' NNNNNN potential. In the TOFS method, the correlated nuclear matter wave function is taken to be a power-series-type of the correlation function FFF, where FFF can induce central, spin-isospin, tensor, etc.~correlations. This expression has been ensured by a cluster expansion theory. In the TOFS calculation, we take into account the contributions from all the many body terms arising from the product of the nuclear-matter Hamiltonian H\mathcal{H}H and FFF. It is found that the density dependence of the energy per particle in nuclear matter is reasonably reproduced, in comparison with other methods such as the Brueckner-Hartree-Fock (BHF) approach.
Abstract The tensor-optimized Fermi sphere (TOFS) theory is applied first for the study of the property of nuclear matter using the Argonne V4′^\prime′NNNNNN potential. In the TOFS theory, the correlated nuclear matter wave function is taken to be a power-series type of the correlation function FFF, where FFF can induce central, spin–isospin, tensor, etc. correlations. This expression has been ensured by a linked cluster expansion theorem established in the TOFS theory. We take into account the contributions from all the many-body terms arising from the product of the nuclear matter Hamiltonian H\mathcal{H}H and FFF. The correlation function is optimally determined in the variation of the total energy of nuclear matter. It is found that the density dependence of the energy per particle in nuclear matter is reasonably reproduced up to the nuclear matter density ρ≃0.20\rho \simeq 0.20ρ≃0.20 fm−3^{-3}−3 in the present numerical calculation, in comparison with other methods such as the Brueckner–Hartree–Fock approach.
In this work, the static fluctuation approximation (SFA) is used to investigate the thermodynamic properties of spin-polarized neutron matter. The energy per particle, pressure, entropy per particle, specific heat capacity, and effective magnetic field are studied as functions of density, temperature, and polarization fraction. The Argonne v18 nucleon–nucleon potential is used here. It is found that the energy per particle, pressure, entropy per particle, and effective magnetic field increase as the density or temperature increases. Also, the energy per particle and pressure are linearly dependent on the quadratic spin polarization δ2. The system becomes more ordered as δ increases. Our calculations are found to be in good agreement with previously published results obtained with different many-body techniques, such as the lowest order constrained variational (LOCV) method, the Brueckner–Hartree–Fock (BHF) approach, and the Dirac–Brueckner–Hartree–Fock (DBHF) technique.