Semiclassical expansions of the relativistic nuclear Hartree-Fock theory at finite temperature

Abstract

The Wigner-Kirkwood semiclassical expansion of the relativistic nuclear Hartree-Fock theory is generalized for finite temperatures by utilizing the spectral representation of the Green function for non-zero temperatures. The expansion is described in greater detail up to second order and the thermostatic properties of nuclear systems are discussed in the same order. For finite nuclear systems static Hartree-Fock calculations at finite temperature describe a hot nucleus in equilibrium with an external vapour. A subtraction scheme is needed to extract the properties of the hot nucleus from those of the system 'gas+hot nucleus'. In the spectral representation method we achieve this goal by subtracting the parts of the occupation probabilities which are related solely to the external gas (vapour phase).

Recent Progress in Quantum Hadrodynamics

“…Systematic studies at this level are contained in [Vo92a,Sh93,Zh93,Su93,Bo94,Ha94,Sc95a]. In nonrelativistic HartreeFock calculations with Skyrme interactions, one makes a phenomenological fit to nuclei using a contact NN interaction containing various powers of the density.…”

“…A great deal of work has been done on the extended Thomas-Fermi model, where it is relatively straightforward to generalize the results of infinite nuclear matter calculations to finite systems. The extended Thomas-Fermi approach is discussed in detail in [Ce92b,Mu92,Vo92b,Ce93a,Ce93b,Sp93,Ce94,Ha94,Vo94a,Vo94b,Sc95,Sc95a].…”

“…The charged mesons (π, ρ) first enter these calculations at the relativistic Hartree-Fock (HF) level, where the exchange interaction is included. Systematic studies at this level are contained in [Vo92a,Sh93,Zh93,Su93,Bo94,Ha94,Sc95a]. In nonrelativistic Hartree-Fock calculations with Skyrme interactions, one makes a phenomenological fit to nuclei using a contact NN interaction containing various powers of the density.…”

Isovector coupling channel and central properties of the charge density distribution in heavy spherical nuclei

“…The first remark is that the Strutinsky averaging method goes beyond the TF approximation, but the evaluation of nuclear one-and two-body matrix elements shows that the semiclassical TF calculations provide the smoothly varying part of these matrix elements, dropping the shell effects in accordance with the Strutinsky averaging method [13]. The second remark is that extending the TF approximation leads to a better reproduction of the exponentially decreasing tail of the density distribution and the binding energy, but has a negligible effect on the central part of the density distribution, which is very well reproduced by the TF approximation [14].…”

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“…[9,17], for instance, for a detailed description of the relativistic density dependent hadron field theory, and Refs. [12,18] for more details on the introduction of the temperature and the calculation of energy and entropy.…”