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Nuclear Matter Spectral Functions by Transport Theory

J. Lehr A, H. Lenske, Stefan Leupold, U. Mosel

Published Aug 4, 2001• 14 citations
OpenAlex

Abstract

Quantum transport theory is used to calculate the nucleon spectral function in infinite nuclear matter. A self-consistent description is obtained by utilizing the relations between collision rates and correlation functions. Static and dynamical self-energies are taken into account in the single particle propagators. The real parts of the non-static self-energy contributions are calculated by dispersion theory thus conserving the analyticity of momentum distributions. The transport theoretical spectral functions, momentum distributions, occupation probabilities and responce functions are in close agreement with results of variational and other many-body theoretical calculations. The results indicate that the nucleon spectral functions are determined only by the average short-range correlation strength.

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Quantum transport theory is used to calculate the nucleon spectral function in infinite nuclear matter. A self-consistent description is obtained by utilizing the relations between collision rates and correlation functions. Static and dynamical self-energies are taken into account in the single particle propagators. The real parts of the non-static self-energy contributions are calculated by dispersion theory thus conserving the analyticity of momentum distributions. The transport theoretical spectral functions, momentum distributions, occupation probabilities and responce functions are in close agreement with results of variational and other many-body theoretical calculations. The results indicate that the nucleon spectral functions are determined only by the average short-range correlation strength.
Recent developments in the many-body theory of interacting fermions are discussed employing a self-consistent Green function approach. This scheme is outlined and its application to nuclear systems is presented. Special attention is paid to the consistent inclusion of short-range and long-range correlations induced by realistic nucleon-nucleon interactions. Such correlations lead to occupation probabilities which deviate from the simple mean-field or shell-model description. The scheme is extended to incorporate relativistic effects. Also applications of field theoretical models for hadrons in a nuclear medium and their relation to QCD are discussed.
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.
Widths of low-lying states in nuclei are of the order of 30 MeV. These large widths are a consequence of the strong interactions leading to a strongly correlated many body system at the typical densities of nuclear matter. Nevertheless ''traditional'' Brueckner calculations treat these states as quasiparticles i.e. with spectral functions of zero widths. The width is related to the imaginary part of the selfenergy and is included selfconsistently in an extension of the Brueckner theory using T -matrix and Green's function (GF) techniques. A more general formulation applicable also to non-equilibrium systems is contained in the Kadanoff-Baym (KB) equations while still maintaining the basic many-body techniques of Brueckner theory. In the present work the two-time KB-equations are timestepped along the imaginary timeaxis to calculate the binding energy of nuclear matter as a function of density, including the spectral widths self-consistently. These zero temperature calculations are compared with quasiparticle calculations. The inclusion of the selfconsistent widths are found to add several MeV to the binding. The spectral widths are due to the long-ranged correlations. Short ranged correlations decrease rather than increase the binding. The method is easily extended to nonzero temperatures where the importance of the widths are expected to increase.
The properties of symmetric nuclear matter are investigated within Green's functions approach. We have implemented an iterative procedure allowing for a self-consistent evaluation of the single-particle and two-particle propagators. The in-medium scattering equation is solved for a realistic (nonseparable) nucleon-nucleon interaction including both particle-particle and hole-hole propagation. The corresponding two-particle propagator is constructed explicitly from the single-particle spectral functions. Results are obtained for finite temperatures and an extrapolation to T=0T=0T=0 is presented.
We review self-consistent spectral methods for nuclear matter calculations. The in-medium T −matrix approach is conserving and thermodynamically consistent. It gives both the global and the single-particle properties the system. The T −matrix approximation allows to address the pairing phenomenon in cold nuclear matter. A generalization of nuclear matter calculations to the superfluid phase is discussed and numerical results are presented for this case. The linear response of a correlated system going beyond the Hartree-Fock+ Random-Phase-Approximation (RPA) scheme is studied. The polarization is obtained by solving a consistent Bethe-Salpeter (BS) equation for the coupling of dressed nucleons to an external field. We find that multipair contributions are important for the spin(isospin) response when the interaction is spin(isospin) dependent. 1