On the nucleon self-energy in nuclear matter

We consider the nucleon self-energy in nuclear matter in the absence of Pauli blocking. It is evaluated using the partial-wave analysis of scattering data. Our results are compared with that of a realistic calculation to estimate the effect of this blocking. It is also possible to use our results as a check on the realistic calculations.PACS: 21.30.-x Nuclear forces - 21.65. + f Nuclear matter     

On the Dirac structure of the nucleon self-energy in nuclear matter

The relativistic structure of the self-energy of a nucleon in nuclear matter is investigated including the imaginary and real components which arise from the terms of first and second order in the NN interaction. A parameterized form of the Brueckner G-matrix is used for the NN interaction. The effects of the terms beyond the DBHF approximation on quasiparticle energies and the optical potential for nucleon-nucleus scattering are discussed.     

Nuclear binding energy and symmetry energy of nuclear matter with modern nucleon–nucleon potentials

The binding energy of nuclear matter at zero temperature in the Brueckner–Hartree–Fock approximation with modern nucleon–nucleon potentials is studied. Both the standard and continuous choices of single particle energies are used. These modern nucleon–nucleon potentials fit the deuteron properties and are phase shifts equivalent. Comparison with other calculations is made. In addition we present results for the symmetry energy obtained with different potentials, which is of great importance in astrophysical calculation.     

Isospin splitting of nucleon effective mass and symmetry energy in isotopic nuclear reactions

Within an isospin and momentum dependent transport model, the dynamics of isospin particles(nucleons and light clusters) in Fermi-energy heavy-ion collisions are investigated for constraining the isospin splitting of nucleon effective mass and the symmetry energy at subsaturation densities. The impacts of the isoscalar and isovector parts of the momentum dependent interaction on the emissions of isospin particles are explored, i.e., the mass splittings of m_n~*=m_p~* and m_n~* m_p~*(m_n~* m_p~*). The single and double neutron to proton ratios of free nucleons and light particles are thoroughly investigated in the isotopic nuclear reactions of ~(112)Sn+~(112)Sn and ~(124)Sn+~(124)Sn at incident energies of 50 and 120 MeV/nucleon, respectively. It is found that both the effective mass splitting and symmetry energy impact the kinetic energy spectra of the single ratios, in particular at the high energy tail(larger than 20 Me V). The isospin splitting of nucleon effective mass slightly impacts the double ratio spectra at the energy of 50 MeV/nucleon. A soft symmetry energy with stiffness coefficient of γ_s =0.5 is constrained from the experimental data with the Fermi-energy heavy-ion collisions.     

The spin-isospin decomposition of the nuclear symmetry energy from low to high density

The energy per particle BA in nuclear matter is calculated up to high baryon density in the whole isospin asymmetry range from symmetric matter to pure neutron matter.The results,obtained in the framework of the Brueckner-Hartree-Fock approximation with two-and three-body forces,confirm the well-known parabolic dependence on the asymmetry parameterβ=(N?Z)/A(β^2 law)that is valid in a wide density range.To investigate the extent to which this behavior can be traced back to the properties of the underlying interaction,aside from the mean field approximation,the spin-isospin decomposition of BA is performed.Theoretical indications suggest that theβ^2 law could be violated at higher densities as a consequence of the three-body forces.This raises the problem that the symmetry energy,calculated according to theβ^2 law as a difference between BA in pure neutron matter and symmetric nuclear matter,cannot be applied to neutron stars.One should return to the proper definition of the nuclear symmetry energy as a response of the nuclear system to small isospin imbalance from the Z=N nuclei and pure neutron matter.     

Correlations and the Dirac structure of the nucleon self-energy

The Dirac structure of the nucleon self-energy in symmetric nuclear matter as well as neutron matter is derived from a realistic meson exchange model for the nucleon-nucleon (NN) interaction. It is demonstrated that the effects of correlations on the effective NN interaction in the nuclear medium can be parameterized by means of an effective meson exchange. This analysis leads to a very intuitive interpretation of correlation effects and also provides an efficient parametrization of an effective interaction to be used in relativistic structure calculations for finite nuclei. Received: 29 January 2001 / Accepted: 5 May 2001     

Lorentz covariant approach in the gravitation theory

The gravitation theory is constructed in the framework of the flat Minkowski space-time. The approach is found that provides unambiguity of the construction. The derived formulas coincide in form with the formulas of general relativity theory.     

Energy-dependent Lorentz covariant representation of the NN interaction

A phenomenological Lorentz covariant representation of the NN t-matrix has been obtained with parameters that are explicitly energy dependent. The real and imaginary parts of the t-matrix are separately expanded in a complete set of on-shell Lorentz invariant amplitudes, each of which is represented by the exchange of isoscalar and isovector “mesons” modified by form factors. Direct and exchange contributions are handled explicitly in the model. The model parameters are fit to the summer 1994 Arndt amplitudes over the laboratory kinetic energy range from 200 to 500 MeV. In contrast to the earlier work of Horowitz, a single χ² minimization is carried out over the full energy range considered. Two separate fits are obtained, one with energy dependence confined to the coupling strengths, the other with energy dependence in the form factor masses as well. Although the second fit is somewhat better, both fits reproduce the empirical amplitudes reasonably well. Results are also given for various np and pp observables and compared with the data.     

Density content of nuclear symmetry energy from nuclear observables

The nuclear symmetry energy at a given density measures the energy transferred in converting symmetric nuclear matter into the pure neutron matter. The density content of nuclear symmetry energy remains poorly constrained. Our recent results for the density content of the nuclear symmetry energy, around the saturation density, extracted using experimental data for accurately known nuclear masses, giant resonances and neutron-skin thickness in heavy nuclei are summarized.     

Probing the density content of the nuclear symmetry energy

The nature of equation of state for the neutron star matter is crucially governed by the density dependence of the nuclear symmetry energy. We attempt to probe the behaviour of the nuclear symmetry energy around the saturation density by exploiting the empirical values for volume and surface symmetry energy coefficients extracted from the precise data on the nuclear masses.     

High density behaviour of nuclear symmetry energy

There exists profound discrepancy in the high density behaviour of the nuclear symmetry energy obtained in realistic variational many-body (VMB) calculations and in relativistic mean-field (RMF) calculations. While the symmetry energy decreases to negative values in the former approach it increases monotonically in the latter one. The origin of this discrepancy is discussed and it is argued that VMB prediction is more reliable. It is shown that vanishing of the symmetry energy implies proton-neutron separation instability in dense matter.This work was partially supported by KBN grants 2 0204 91 01 and 2 0054 91 01.     

Double neutron/proton ratio of nucleon emissions in isotopic reaction systems as a robust probe of nuclear symmetry energy

The double neutron/proton ratio of nucleon emissions taken from two reaction systems using four isotopes of the same element, namely, the neutron/proton ratio in the neutron-rich system over that in the more symmetric system, has the advantage of reducing systematically the influence of the Coulomb force and the normally poor efficiencies of detecting low energy neutrons. The double ratio thus suffers less systematic errors. Within the IBUU04 transport model the double neutron/proton ratio is shown to have about the same sensitivity to the density dependence of nuclear symmetry energy as the single neutron/proton ratio in the neutron-rich system involved. The double neutron/proton ratio is therefore more useful for further constraining the symmetry energy of neutron-rich matter.     

Classical radiation reaction off-shell corrections to the covariant Lorentz force

We show that the problem of radiation reaction may be formulated in a space of five dimensions, with five corresponding gauge fields in the framework of the classical version of a fully gauge covariant form of the Stueckelberg–Feynman–Schwinger covariant mechanics (the zero mode fields of the 0,1,2,3 components correspond to the Maxwell fields). The particles and fields are not confined to their mass shells. We show that in the mass-shell limit, the generalized Lorentz force obtained by means of the retarded Green's functions for the five-dimensional field equations provides the classical Abraham–Lorentz–Dirac radiation reaction terms (with renormalized mass and charge). We also obtain general coupled equations for the orbit and the off-shell dynamical mass during the evolution as well as an autonomous nonlinear equation of third order for the off-shell mass. The theory does not admit radiation if the particle does not move off-shell. The structure of the equations implies that the mass-shell deviation is bounded when the external field is removed.     

Influence of coupling constants on nuclear symmetry energy

By studying the energy of neutron star matter, we discuss the nuclear symmetry energy at different baryon densities and different coupling constants in the relativistic mean field approximation. The results show that the symmetry energy increases with baryon density at various coupling constants and incompressibilities. Further-more, the symmetry energy at saturation density increases with increasing incompressibility at fixed d, and decreases at fixed c. Specifically, when coupling constants gv and gs are fixed, respectively, the symmetry energy has a little change with increasing incompressibility. It is demonstrated that the NN coupling constants have greater influences on the symmetry energy than the self-coupling constants.     

Towards understanding astrophysical effects of nuclear symmetry energy

The European Physical Journal A - The properties of the quantum electrodynamic (QED) vacuum in general, and of the nuclear vacuum (ground) state in particular, are determined by virtual processes...     

The nuclear symmetry energy from relativistic Brueckner-Hartree-Fock model

The microscopic mechanisms of the symmetry energy in nuclear matter are investigated in the framework of the relativistic Brueckner-Hartree-Fock (RBHF) model with a high-precision realistic nuclear potential, pvCDBonn A. The kinetic energy and potential contributions to symmetry energy are decomposed. They are explicitly expressed by the nucleon self-energies, which are obtained through projecting the G-matrices from the RBHF model into the terms of Lorentz covariants. The nuclear medium effects on the nucleon self-energy and nucleon-nucleon interaction in symmetry energy are discussed by comparing the results from the RBHF model and those from Hartree-Fock and relativistic Hartree-Fock models. It is found that the nucleon self-energy including the nuclear medium effect on the single-nucleon wave function provides a largely positive contribution to the symmetry energy, while the nuclear medium effect on the nucleon-nucleon interaction, i.e., the effective G-matrices provides a negative contribution. The tensor force plays an essential role in the symmetry energy around the density. The scalar and vector covariant amplitudes of nucleon-nucleon interaction dominate the potential component of the symmetry energy. Furthermore, the isoscalar and isovector terms in the optical potential are extracted from the RBHF model. The isoscalar part is consistent with the results from the analysis of global optical potential, while the isovector one has obvious differences at higher incident energy due to the relativistic effect.