Relativistic Hartree Calculations Research Articles

Study of relativistic bound state wave functions in quasielastic ( e, e′ p) reactions

The unpolarized response functions of the quasielastic 16O( e, e′ p) 15N reaction are calculated for three different types of relativistic bound-state wave functions. The wave functions are obtained from relativistic Hartree, relativistic Hartree-Fock and density-dependent relativistic Hartree calculations that reproduce the experimental rms charge radius of 16O. The sensitivity of the unpolarized response functions to the single-particle structure of the different models is investigated in the relativistic plane-wave impulse approximation. Redistributions of the momentum dependence in the longitudinal and transverse response function can be related to the binding energy of the single-particle states. The interference responses R LT and R TT reveal a strong sensitivity to the small component of the relativistic bound-state wave function.

Skyrme representation of a relativistic spin-orbit field

We find that a spin-orbit force with the conventional Skyrme form reproduces satisfactorily the isospin dependence of the spin-orbit field generated in relativistic Hartree calculations on semi-infinite nuclear matter with different neutron excesses. We also examine a generalization of the Skyrme-type energy-density functional that leads to still better agreement with the relativistic Hartree calculations. {copyright} {ital 1997} {ital The American Physical Society}

Symmetric and asymmetric nuclear matter in the relativistic approach.

Symmetric and asymmetric nuclear matter is studied in the framework of the relativistic Brueckner-Hartree-Fock and in the relativistic version of the so-called ${\mathrm{\ensuremath{\Lambda}}}^{00}$ approximation. The equations are solved self-consistently in the full Dirac space, so avoiding the ambiguities in the choice of the effective scattering amplitude in matter. The calculations were performed for some modern meson-exchange potentials constructed by Brockmann and Machleidt. In some cases we used also the Groningen potentials. First, we examine the outcome for symmetric matter with respect to other calculations, which restrict themselves to positive-energy states only. The main part is devoted to the properties of asymmetric matter. In this case we obtain additionally to the good agreement with the parameters of symmetric matter, also a quite satisfactory agreement with the semiempirical macroscopic coefficients of asymmetric matter. Furthermore, we tested the assumption of a quadratic dependence of the asymmetry energy for a large range of asymmetries. Included is also the dependence of nucleon self-energies on density and neutron excess. For the purpose of comparison we discuss further the similarities and differences with relativistic Hartree and Hartree-Fock calculations and nonrelativistic Skyrme calculations.

Relativistic Hartree calculations of nuclear compressional properties.

Using the scaling model, we calculate within the framework of relativistic Hartree theory the nuclear breathing-model energies corresponding to the NL1 and NL-SH parameter sets of the nonlinear \ensuremath{\sigma}-\ensuremath{\omega}-\ensuremath{\rho} model. Both of these sets are found to be in disagreement with experiment and there is a clear need for an improved fit. However, as far as the nuclear-matter incompressibility ${\mathit{K}}_{\mathit{v}}$ is concerned, neither the NL1 value, 212 MeV, nor the NL-SH value, 356 MeV, can be excluded.

Relativistic mean-field theory and a density-dependent spin-orbit Skyrme force.

We generalize the Skyrme force by making its spin-orbit component density dependent. One of the two extra parameters thereby introduced is fixed by performing Hartree-Fock calculations on semi-infinite nuclear matter, and comparing with relativistic Hartree calculations performed on the same system in the nonlinear \ensuremath{\sigma}-\ensuremath{\omega} model. In this way an essential feature of the relativistic theory is incorporated into the nonrelativistic framework of Skyrme forces.

Systematic relativistic Hartree-Fock calculation of deformed nuclei in s-d shell.

A systematic study of even-even deformed nuclei in [ital s]-[ital d] shell is performed in the QHD framework by using relativistic Hartree-Fock calculations. The exchange of [sigma], [omega], [rho], and [pi] mesons and photons are included, the parameters of the model (meson masses and coupling constants) adopted are from an earlier least-squares fit to finite nuclear ground-state properties. We compare to the results of a similar calculation using parameters adjusted to fit the nuclear matter saturation data. We found great improvement in the total binding energy, however the deformation pattern is essentially not changed; for closed subshell nuclei we still find that the ground state favors a spherical solution. A well-defined constant Fermi surface in the [ital s]-[ital d] shell is obtained which is consistent with the experiment observation. The results are also compared to the corresponding relativistic Hartree calculations.

Methodology for relativistic Hartree calculations

An efficient method for performing relativistic Hartree calculations for finite systems is described. The method combines a derivative expansion of the high-energy contributions to the induced vacuum polarization density with a numerical evaluation of the low-energy contributions, allowing calculations to be performed with a minimum of numerical work. The method is applied to theories of fermions coupled to scalar mesons in 1 + 1 dimensions as an illustration.

Relativistic Hartree study of deformed nuclei

Relativistic Hartree calculations are performed for axially symmetric solutions of deformed nuclei in the sd shell. Both even-even and selected odd- A nuclei are included. The systematic behavior of quadrupole moments and binding energies are reproduced; the deformations being solely determined by self-consistency. The states are expanded in a spherical basis of states obtained by solving the same or neighboring nucleus with a constraint to retain spherical symmetry. The continuum states are artificially discretized by applying a boundary condition; both the positive and negative energy states are included in the expansion. The effects of tensor coupling of the rho meson and of the pion are included. The contribution of the former are small in the nuclei studied here; however, the pion has a large effect on the magnetic moment of odd- A nuclei. The binding energies, quadrupole moments, magnetic moments and single particle spectra are presented and compared with similar calculations, both relativistic and non-relativistic.

Vacuum polarization currents in finite nuclei

Self-consistent relativistic Hartree calculations of odd-A nuclei, including vacuum polarization, are presented. The contribution to the baryon current from the deformed Dirac sea is calculated using a derivative expansion. This vacuum current does not affect magnetic moments; however, at intermediate momentum transfers it tends to cancel the current from the deformed occupied core, as expected from the random-phase approximation response in nuclear matter. Wave function mixing for the valence state, which arises in the self-consistent solution but not in random-phase approximations, significantly affects both Dirac and anomalous currents.

Systematic study of potential energy surfaces of light nuclei in relativistic Hartree calculations

Potential energy surfaces of light even-even nuclei are calculated within a relativistic mean field theory using an axially symmetric space lattice and a quadrupole constraint. Pairing effects are included within the constant gap approach. It is shown that the potential energy surfaces are sensitive to the parametrisations used. The calculated deformations generally are in good agreement with experimental data. Calculations of fission/fusion potentials are presented.

Effect of vacuum polarization on nuclear structure

We perform self-consistent relativistic Hartree calculations of finite nuclei using the derivative expansion of the effective action to calculate the effect of vacuum polarization. The presence of derivative terms in this expansion allows non-vanishing baryon density fluctuations in the Dirac sea that contribute five percent of the baryon density on the surface of nuclei and also significantly in the interior of light nuclei. As a result, the RMS radius of the valence nucleons is reduced and the binding energy is increased. This effect is greatest in the lightest nuclei and improves the agreement with the experimental binding energies. The value of the scalar meson mass parameter necessary to fit the RMS radius of 40Ca is 550 MeV, which is significantly different from the value of 458 MeV obtained if one ignores the derivative terms, but is similar to that obtained when the entire vacuum structure is ignored.

Comment on "Relativistic Hartree calculations for axially deformed nuclei"

Comment on "Relativistic Hartree calculations for axially deformed nuclei"

Relativistic Hartree Calculations for Axially Deformed Nuclei

Relativistic Hartree Calculations for Axially Deformed Nuclei

Relativistic Hartree calculations for axially deformed nuclei.

Properties of deformed light nuclei are calculated within a relativistic mean-field theory with use of an axially symmetric space lattice. The axial results are in good agreement with the results of previous calculations for spherical nuclei. For deformed nuclei, parameters fitted to describe spherical nuclei fail to reproduce energies and deformations.

Relativistic Hartree theory of finite nuclei: The role of the quantum vacuum

One-baryon-loop fluctuation contributions to the vacuum energy are included in relativistic Hartree calculations of closed-shell nuclei. These corrections decrease the nuclear scalar density by approximately 15% in the nuclear interior and may be observable in medium-energy proton-nucleus scattering. Their omission could significantly distort empirically determined neutron densities.

Relativistic calculation of nuclear matter and the nuclear surface

Relativistic mean field Hartree and Thomas-Fermi calculations are made for infinite and semiinfinite symmetric nuclear matter. Cubic and quartic scalar meson self-interactions are included. The strength of these self-interactions, the scalar and vector meson coupling constants, and the scalar meson mass are considered as parameters chosen to fit the empirical properties of nuclear matter and of the nuclear surface. Acceptable fits imply large self-interactions. No abnormal nuclear matter solutions are found. The best fit of the nuclear surface yields a compressibility coefficient of 150 ± 50 MeV. The Hartree and TF results are in good agreement for larger surface thicknesses.