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arXiv:nucl-th/0012087

Few-Body Correlations in Fermi Systems

M. Beyer

Published Dec 23, 2000• 0 citations
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Abstract

I present recent results on few-body correlations in nuclear matter at finite temperatures and densities. In particular I focus on the four-body correlations. The alpha-particle is the strongest bound state. The investigation is done based on effective in-medium few-body equations that consistently include self energy corrections and Pauli blocking effects. I address the question of four-body condensates as well.

DOI
10.48550/arxiv.nucl-th/0012087

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I present recent results on few-body correlations in nuclear matter at finite temperatures and densities. In particular I focus on the four-body correlations. The alpha-particle is the strongest bound state. The investigation is done based on effective in-medium few-body equations that consistently include self energy corrections and Pauli blocking effects. I address the question of four-body condensates as well.
We are concerned with few-particle correlations in a fermionic system at finite temperature and density. Within the many-body Green functions formalism the description of correlations is provided by the Dyson equation approach that leads to effective few-body equations. They contain the dominant medium effects, which are self energy corrections and the Pauli blocking. Hence the effective two-body interactions between quasiparticles are momentum/energy-dependent and therefore they can be usesed in the medium modified, momentum space, integral AGS equations for three- and four-body systems. To investigate correlations and clusters beyond four-body, we employ, instead, the configuration space two-variable integro-differential equations (IDEA) for AAA-body bound systems which are based on Hyperspherical Harmonics and the Faddeev decomposition of the wave function in two-body amplitudes. This requires the transformation of the energy dependent two-body interactions to equivalent local, energy independent, ones. To achieve this we use inverse scattering techniques the resulting interactions being, on-- and (to all practical purposes) off--shell equivalent to the energy dependent potentials. In this way we obtain binding energy results for the 2--, 3--, 4--, and 16--particle in a medium at a finite temperature and various densities. Several aspects of the problem are discussed and the behavior of the potential surfaces obtained in the extreme adiabatic approximation, below and above the Mott transition, is investigated.
We derive three-body equations valid at finite densities and temperatures. The equations are based on the cluster mean field approach consistently including proper self-energy corrections and Pauli blocking. As an application we investigate the binding energies of triton and determine the Mott densities and momenta relevant for a many particle description of nuclear matter in a generalized Beth-Uhlenbeck approach. The method, however, is not restricted to nuclear physics problems but may also be relevant, e.g., to treat three-particle correlations in weakly doped semiconductors or strongly coupled dense plasmas.
Overview of the recent advances in description of the few two-component fermions is presented. The model of zero-range interaction is generally considered to discuss the principal aspects of the few-body dynamics. Particular attention is paid to detailed description of two identical fermions of mass mmm and a distinct particle of mass m1m_1m1​: it turns out that two LP=1−L^P = 1^-LP=1− three-body bound states emerge if mass ratio m/m1m/m_1m/m1​ increases up to the critical value μc≈13.607μ_c \approx 13.607μc​≈13.607, above which the Efimov effect takes place. The topics considered include rigorous treatment of the few-fermion problem in the zero-range interaction limit, low-dimensional results, the four-body energy spectrum, crossover of the energy spectra for m/m1m/m_1m/m1​ near $μ_c $, and properties of potential-dependent states. At last, enlisted are the problems, whose solution is in due course.
Realistic nucleon-nucleon interactions induce correlations to the nuclear many-body system, which lead to a fragmentation of the single-particle strength over a wide range of energies and momenta. We address the question of how this fragmentation affects the thermodynamical properties of nuclear matter. In particular, we show that the entropy can be computed with the help of a spectral function, which can be evaluated in terms of the self-energy obtained in the self-consistent Green's function approach. Results for the density and temperature dependences of the entropy per particle for symmetric nuclear matter are presented and compared to the results of lowest order finite-temperature Brueckner-Hartree-Fock calculations. The effects of correlations on the calculated entropy are small, if the appropriate quasiparticle approximation is used. The results demonstrate the thermodynamical consistency of the self-consistent TTT-matrix approximation for the evaluation of the Green's functions.