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arXiv:nucl-th/0605080 · Physical Review C

Entropy of a correlated system of nucleons

Arnau Rios, A. Polls, Angels Ramos, H. Müther

Published Nov 28, 2006• 29 citations
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Abstract

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 $T$-matrix approximation for the evaluation of the Green's functions.

DOI
10.1103/physrevc.74.054317

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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.
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.
The self-consistent Green’s function method within the ladder approximation provides a microscopic description of correlated nuclear systems which properly treats the nucleon-nucleon correlations induced by the short-range and tensor components present in any realistic interaction. These correlations produce a sizable depletion of low momenta below the Fermi surface as well as the occupation of high momenta in the nuclear ground state. A few representative results for nuclear matter are presented to illustrate the present progress in the application of this method to nuclear systems.
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 super.uid 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.
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
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.
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.