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Deuterization and Mott density in nuclear matter at finite temperatures

G. Roepke, M. Schlauges, D. Kremp, L. Muenchow, H. Schulz

Published Sep 1, 1982• 0 citations
OpenAlex

Abstract

The theory of the thermodynamic properties of nuclear matter at finite temperatures is developed on the basis of thermodynamic Green functions for a system of interacting nucleons. The influence of the surrounding nuclear matter on the two-nucleon system leads to a weakening of the effective nucleon-nucleon interaction and at the Mott density, which depends on the temperature and total momentum of the two-nucleon system, the bound state disappears. The deuteron degree of association and the phase diagram of nuclear matter are discussed.

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The theory of the thermodynamic properties of nuclear matter at finite temperatures is developed on the basis of thermodynamic Green functions for a system of interacting nucleons. The influence of the surrounding nuclear matter on the two-nucleon system leads to a weakening of the effective nucleon-nucleon interaction and at the Mott density, which depends on the temperature and total momentum of the two-nucleon system, the bound state disappears. The deuteron degree of association and the phase diagram of nuclear matter are discussed.
The equation of state of symmetric nuclear matter is addressed starting both from a realistic interaction derived from nucleon-nucleon scattering processes and from a low-momentum effective potential. The approach is based on finite temperature Green’s functions. The internal energy per particle is estimated from the summation of diagrams and through the Galitskii-Koltun’s sum rule. At present, there is not a unique and reliable theory of nuclear interactions. From the study of nucleon-nucleon scattering processes different models for the basic interaction between nucleons have been developed, but difficulties arise when they are used in calculations which aim to reproduce the properties of bound nuclei. These models all reproduce the experimental N-N phase shifts up to the threshold for pion production with high accuracy, but differ in the short-wavelength region, where less experimental constraints are available. In deriving the properties of dense nuclear matter, if we start from a bare N-N potential we have to take into account the complex correlations induced
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.
A systematic development of the theory of finite Fermi systems for non-zero temperatures (Tnot =0) is undertaken on the basis of the method of temperature Green's functions. The properties of compound nuclear states are considered. The variations of the density matrix deltarho, the self-energy part delta..sigma.., the mean square radius delta , the quadrupole moment delta, etc, are studied in a transition from the ground state (T=0) to an excited state with temperature T. The relationship connecting the excitation energy with temperature is obtained. Consistently taken into account is the strong interaction of the nucleons, in particular, the change in the one-particle nuclear potential as the temperature T is varied. Qualitative quasi-classical estimates are given for the effects considered, and the limits on the applicability of the statistical description of nuclei at large T are discussed.
For one decade, several fields in physics as well microscopic as macroscopic benefit from the computational particle-models (astrophysics, electronics, fluids mechanics...). In particular, the nuclear matter offers an interesting challenge as many body problem, owing to the quantal nature of its components and the complexity of the in-medium interaction. Using a model derived from semi-classical Vlasov equation and the projection of the Wigner function on a Gaussian coherent states basis (pseudo-particles), static and dynamical properties of nuclear matter are studied, featuring the growing of bulk instabilities in dilute matter. Using different zero and finite range effective interactions, the effect of the model parameters upon the relation total energy - density - temperature and surface energy of the pseudo-particles fluid is pointed out. The dynamical feature is first based upon a model of the 2-body Uehling-Ulhenbeck collisionnal term. A study of the relaxation of a nucleonic system is performed. At last, the pseudo-particle model is used in order to extract time scale for the growing of density fluctuations. This process is supposed to be a possible way to clusterization during heavy nuclei collisions.
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 short-range and tensor components of the bare nucleon-nucleon interaction induce a sizable depletion of low momenta in the ground state of a nuclear many-body system. The self-consistent Green's function method within the ladder approximation provides an ab initio description of correlated nuclear systems that accounts properly for these effects. The momentum distribution predicted by this approach is analyzed in detail, with emphasis on the depletion of the lowest momentum state. The temperature, density, and nucleon asymmetry (isospin) dependence of the depletion of the Fermi sea is clarified. A connection is established between the momentum distribution and the time-ordered components of the self-energy, which allows for an improved interpretation of the results. The dependence on the underlying nucleon-nucleon interaction provides quantitative estimates of the importance of short-range and tensor correlations in nuclear systems.