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Physical Review C

Role of single-particle spectrum in the ring-diagram approach for nuclear matter

Meng Jiang, R. Machleidt, T.T.S. Kuo

Published Mar 1, 1991• 4 citations
Publisher

Abstract

A previously developed ring-diagram formalism, which substantially improves the predictions for the saturation density of nuclear matter, is employed for different choices for the single-particle (s.p.) spectrum. Three types of s.p. spectra are studied: a gap spectrum, a continuous choice, and a model-space spectrum. It is found that the choice of the s.p. spectrum has some influence on the saturation energy, but little influence on the saturation density. Thus, the main virtue of the ring-diagram approach turns out to be independent of the choice of the s.p. spectrum. We also give a clear demonstration of the strongly density-dependent ring effect and compare our results with those obtained using other many-body methods.

DOI
10.1103/physrevc.43.1469

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A previously developed ring-diagram formalism, which substantially improves the predictions for the saturation density of nuclear matter, is employed for different choices for the single-particle (s.p.) spectrum. Three types of s.p. spectra are studied: a gap spectrum, a continuous choice, and a model-space spectrum. It is found that the choice of the s.p. spectrum has some influence on the saturation energy, but little influence on the saturation density. Thus, the main virtue of the ring-diagram approach turns out to be independent of the choice of the s.p. spectrum. We also give a clear demonstration of the strongly density-dependent ring effect and compare our results with those obtained using other many-body methods.
We recently proposed a nonlocal form for the 3-body induced interaction that is consistent with the Fock space representation of interaction operators but leads to a fractional power dependence on the density. Here we examine the implications of the nonlocality for the excitation spectrum. In the two-component weakly interacting Fermi gas, we find that it gives an effective mass that is comparable to the one in many-body perturbation theory. Applying the interaction to nuclear matter, it predicts a huge enhancement to the effective mass. Since the saturation of nuclear matter is partly due to the induced 3-body interaction, fitted functionals should treat the effective mass as a free parameter, unless the 2- and 3-body contributions are determined from basic theory.
By the method of ``modes'' introduced by Sawada, the excitation spectra of a fermion system with singular interactions have been obtained in three cases; (1) with one additional particle above and and one hole below the Fermi surface, (2) with one additional particle above the Fermi surface, and (3) with two particles above the Fermi surface. The argument holds not only for the system of low density (nuclear matter with a hard-core repulsion), but also for the case of the interacting electron gas in the high-density region. The results have been compared with the Brueckner-Goldstone perturbation-expansion formulas, by using diagrams in the second- and third-order of the expansion in interaction strength. We show that in the approximation of our treatment, the occupation probability function at temperature T has the same form as the Fermi distribution function.
We calculate the single-particle spectral function for the Hubbard model within the framework of a projection technique equivalent to the two-pole approximation. We show that the two-pole approximation can be well understood as an average characterization of the upper and the lower Hubbard bands, rather than describing a dispersive quasiparticle. By comparing with numerical spectra of finite Hubbard rings and of a 4\ifmmode\times\else\texttimes\fi{}4 cluster [P. W. Leung et al., Phys. Rev. B 46, 11 779 (1992)], we show that the present approximation is capable of reproducing essential properties of the single-particle spectral function. In particular, the two-pole spectrum is characterized by a direct gap, in agreement with the exact spectrum. We emphasize the role of local antiferromagnetic correlations.
Background: Idealized systems are commonly used in nuclear physics and condensed matter. For instance, the construction of nuclear energy density functionals involves properties of infinite matter, whereas neutron drops are used to test nuclear interactions and approximations to the nuclear many-body problem. In condensed matter, quantum rings are also used to study properties of electron systems.Purpose: To investigate the possibility to use quantum rings with systems of nucleons including many-body correlations.Methods: A quantum ring model of a finite number of same spin fermions is developed. Several attractive and repulsive interactions with finite and infinite ranges are considered. Quantum Monte Carlo calculations are used to provide exact ground-state energies. Comparisons with analytical Hartree-Fock solutions are used to get an insight into the role of correlations.Results: Hartree-Fock results with no breaking of space translational symmetry are able to describe many systems. However, additional spatial correlations are required in the case of dense systems with a strong short-range repulsion or with attractive interactions in large rings.Conclusions: Self-bound systems of fermions with spatial correlations produced by basic features of the nuclear interactions can be described on a quantum ring, encouraging applications with realistic interactions, as well as investigations with higher-dimensional geometries, such as spherium.
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.
We carry out nonperturbative calculations of the single-particle excitation spectrum in strongly interacting neutron matter. These are microscopic quantum Monte Carlo computations of many-neutron energies at different densities as well as several distinct excited states. As input, we employ both phenomenological and chiral two- and three-nucleon interactions. We use the single-particle spectrum to extract the effective mass in neutron matter. With a view to systematizing the error involved in this extraction, we carefully assess the impact of finite-size effects on the quasiparticle dispersion relation. We find an effective-mass ratio that drops from 1 as the density is increased. We conclude by connecting our results with the physics of ultracold gases as well as with energy-density functional theories of nuclei and neutron-star matter.