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arXiv:1410.8789 · Physical Review C

Effective-interaction approach to the Fermi hard-sphere system

Angela Mecca, Alessandro Lovato, Omar Benhar A, A. Polls

Published Mar 24, 2015• 9 citations
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Abstract

The formalism based on correlated basis functions and the cluster-expansion technique has been recently employed to derive an effective interaction from a realistic nuclear Hamiltonian. To gauge the reliability of this scheme, we perform a systematic comparison between the results of its application to the Fermi hard-sphere system and the predictions obtained from low-density expansions, as well as from other many-body techniques. The analysis of a variety of properties, including the ground-state energy, the effective mass, and the momentum distribution, shows that the effective-interaction approach is quite accurate, thus suggesting that it may be employed to achieve a consistent description of the structure and dynamics of nuclear matter in the density region relevant to astrophysical applications.

DOI
10.1103/physrevc.91.034325

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The formalism based on correlated basis functions and the cluster-expansion technique has been recently employed to derive an effective interaction from a realistic nuclear Hamiltonian. To gauge the reliability of this scheme, we perform a systematic comparison between the results of its application to the Fermi hard-sphere system and the predictions obtained from low-density expansions, as well as from other many-body techniques. The analysis of a variety of properties, including the ground-state energy, the effective mass, and the momentum distribution, shows that the effective-interaction approach is quite accurate, thus suggesting that it may be employed to achieve a consistent description of the structure and dynamics of nuclear matter in the density region relevant to astrophysical applications.
I discuss the derivation of an effective interaction, obtained from a realistic nuclear Hamiltonian using the formalism of Correlated Basis Functions (CBF) and the cluster expansion technique. Unlike the bare nucleon-nucleon potential, this effective interaction is well behaved, and suitable for carrying out perturbative calculations of a variety of equilibrium and non-equilibrium properties of nuclear matter using the basis of eigenstates of the non interacting system. The robustness and accuracy of the proposed approach are thoroughly examined, comparing the results of its application to the Femi hard-sphere system to the predictions of low-density expansions. Selected properties of nuclear matter, at both zero and nonzero temperatures, are reported and discussed.
The formalism based on Correlated Basis Functions (CBF) and the cluster-expansion technique has been recently employed to derive an effective interaction from a realistic nuclear Hamiltonian. One of the main objectives of the work described in this Thesis is establishing the accuracy of this novel approach--that allows to combine the flexibility of perturbation theory in the basis of eigenstates of the noninteracting system with a realistic description of short-range correlations in coordinate space--by focusing on the hard-sphere fermion system. As a first application of the formalism, the quasiparticle properties of hard spheres of degeneracy four have been determined from the two-point Green's function. The calculation has been performed carrying out a perturbative expansion of the self-energy, up to the second order in the CBF effective interaction. The main results of this study are the momentum distributions, the quasiparticle spectra and their description in terms of effective mass. The investigation of the hard-sphere fermion fluid has been extended to study the shear viscosity and thermal conductivity coefficients of the system with degeneracy two, that can be regarded as a model of pure neutron matter. The resulting transport coefficients show a strong sensitivity to the quasiparticle effective mass, reflecting the effect of second order contributions to the self-energy which are not taken into account in nuclear matter studies available in the literature. The difference between first and second order results is likely to play an important role in astrophysical applications and needs to be carefully investigated extending our analysis to nuclear matter.
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.
We evaluate the fourth-order Hugenholtz diagrams from the Rayleigh-Schr\"odinger many-body perturbation series for a repulsive, square-well potential. We consider a system containing four different equal-mass identically interacting particle species, similar to nuclear matter when only the repulsive core is considered. We use the results of these calculations to extend the L expansion of the ground-state energy of a Fermi fluid by one more term. From this extension, we are able to provide accurate values of the ground-state energy over a density range which includes that for infinite nuclear matter.
The methods of quantum statistics previously developed by the author are applied to the determination of properties of the ground state of nuclear matter. An expansion in powers of the pair-function of quantum statistics is made and expressions are derived for the momentum distribution, pair-correlation function, binding energy, and effective single-particle energies. The leading terms of these expressions can be interpreted in terms of an effective two-body interaction, and a model of nuclear matter which consists of interacting quasi-particles whose energies are the effective single-particle energies is thereby suggested. The theory is compared with Brueckner's theory and also with Landau's phenomenological theory of the Fermi liquid.
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.