Fock Terms Research Articles

Renormalization of Nucleon Self-Energy in Nuclear Matter by Dispersion Relation Method**The project supported by National Natural Science Foundation of China

Taking -exchange Fock term of nucleon self-energy in nuclear matter as an example, we renormalized the nucleon self-energy by both dimensional regularization method and dispersion relation method in the Walecka model. We compared them numerically and found them identical, independent of the renormalization methods.

Momentum projection of a soliton in the massive Gross-Neveu model

Abstract We study a solitonic state in the SU ( N c ) Gross-Neveu model using the Peierls-Yoccoz projection. It is found by an order estimation that the Fock term and the det B term, are the leading order corrections in 1 N c of the spurious zero-point energy of translational motion. We calculate these terms numerically in the scalar approximation. It is shown numerically that the corrected energy estimated by replacing the inertial mass by the soliton energy agrees reasonably well with that estimated by the Fock term and the det B term when the coupling constant is large.

Investigations of the scalar field self-interactions generated by a chiral model in the Hartree-Fock approach to nuclear structure

We have investigated the role of the exchange effects in a chiral theory (including self-interactions of the scalar field) in the framework of the self-consistent Hartree-Fock approximation to nuclear matter and finite nuclei. The properties of normal solutions are found to be in better agreement with the experiment than in the Hartree case. The stability of abnormal solutions decreases as a consequence of the Fock terms.

On the momentum dependence of the nucleon-nucleus optical potential

The momentum dependence of the mean-field contribution to the real part of the optical-model potential is investigated employing realistic nucleon-nucleon interactions. Within a non-relativistic approacg a momentum dependence originates from the non-locality of the Fock exchange term. Deducing the real part of the optical model from a relativistic Dirac-Brueckner-Hartree-Fock approximation for the self-energy of the nucleons yields an additional momentum dependence originating from the non-relativistic reduction of the self-energy. It is demonstrated that large Fock terms are required in the non-relativistic approach to simulate these relativistic features. A comparison is made between a local-density approximation for the optical model and a direct evaluation in finite nuclei.

Interpretation of the scalar fields of the relativistic Brueckner-Hartree-Fock formalism.

We discuss matrix elements of the axial current and the Gell-Mann-Oakes-Renner relation in the presence of nuclear matter. The density dependence of hadron masses and of the pion decay constant is also considered. We define a scalar order parameter that describes the modification of the quark scalar density in the presence of nuclear matter and go on to relate that parameter to the scalar field that appears in the relativistic Brueckner-Hartree-Fock (RBHF) theory. We suggest that the field-theoretic formulation provides a value for only the Hartree term in the calculation of the nucleon self-energy and present some estimates of how exchange (Fock) terms and short-range correlations modify the value obtained for the nucleon self-energy when calculations are made in the RBHF formalism. [Because of various cancellations, it is seen that the magnitude of the scalar part of the nucleon self-energy is largely unchanged when exchange (Fock) terms and short-range correlations are taken into account.]

Relativistic field theory of superfluidity in nuclei

Starting from a Lagrangian with nucleonic and mesonic degrees of freedom, a relativistic theory of pairing correlations in nuclei is presented. Based on an extended mean field approximationDirac-Hartree-Fock-Bogoliubov equations are derived, which contain apart from the kinetic term of Dirac and the self-consistent mesonic fields, known from relativistic mean field theory, a Fock term and a pairing potential. This theory is applied to a relativistic description of pairing correlations in symmetric nuclear matter. Several phenomenological models are investigated.

Magnetic susceptibility of neutron matter in a relativistic approach

A relativistic Hartree-Fock approach ( σ+ ω) is used to study the magnetic susceptibility of a pure neutron system at densities in the range of gravitationally stable neutron stars. A significant correlation is found between the expectation value of the relativistic spin operator and the magnetic susceptibility throughout this density range. The ferromagnetic transition is crucially determined by the Fock terms.

Semiclassical kinetic equation and the WKB approximation

We study the connection between the classical response function of a nucleus described by the Vlasov equation and the corresponding quantum response function. In the limit of large quantum numbers, the Fourier coefficients which appear in the Vlasov theory correspond to the quantum matrix elements evaluated in the WKB approximation. The classical frequencies of motion give the quantum excitation energies according to the correspondence principle. For a central potential, we identify the normal modes of the classical systems with the corresponding shell-model transitions. Thus we can improve the Vlasov theory by excluding excitation modes which correspond to forbidden quantum transitions. Also, we study the effect of a spin-orbit force in the context of the Vlasov theory. Finally, always by exploiting the close analogy between the classical and the quantum response functions, we introduce exchange (Fock) term in the semiclassical RPA equation given by the Vlasov theory.

A relativistic description of nuclei

The usual Dirac-Hartree description of nuclei is extended to the case where Fock terms are included, with the addition ofπ- andϱ-meson degrees of freedom. Preliminary results show the important role played by theπ and the tensor ϱ coupling, and are in good agreement with the properties of finite nuclei.

Ground States, Configurations, and Truncated Orbital Bases of the Iron-Series Atoms

This article presents an analysis of several related topics of importance to the orbital theory of electronic states of transition-metal atoms in the framework of the Hartree–Fock approximation. First, it is shown that the principle experimental features of the term separations for these atoms are determined primarily by the Hartree–Fock wavefunction. Within the framework of this one-particle description, it is then demonstrated that subtle competing electrostatic effects are responsible for the well-known inversions of ground-state configurations. Beyond the one-particle description, electron correlation contributions, determined as differences between experimental and Hartree–Fock term separations, are demonstrated to have remarkably systematic trends that enable predictions to be made of term values of stable but unobserved excited states of the ions. Finally, useful small bases that maintain the principal features of the Hartree–Fock description for reliable exploratory SCF calculations on these atoms and their molecules are presented and discussed.