Relativistic nuclear structure. II. Finite nuclei.

Lattice quantum hadrodynamics

Quantum corrections to the mean-field equation of state for nuclear matter are estimated in a lattice simulation of quantum hadrodynamics. In contrast with the standard coordinate-space methods used in lattice QCD, the calculations are carried out here in momentum space and on nonhypercubic (irregular) lattices. The quantum corrections to the known mean-field equation of state were found to be considerable.

Quasi-free electron scattering in a relativistic model of the nucleus

Longitudinal and transverse response functions of quasi-free electron scattering have been calculated in mean field approximation for a relativisticσ-ω model, including non-linearities in theσ-field. As a consequence of the completely consistent and fully relativistic treatment of wave functions and current operators, gauge invariance is perfectly satisfied throughout the calculation. The results indicate that models with the same nuclear bulk properties lead to similar response functions within 10%. Our results agree with the experimental data for12C and238U, but cannot describe the longitudinal response in the Ca-Fe region. Predictions for208Pb are given for comparison with future experim…

Relativistic density-dependent Hartree approach for finite nuclei.

We develop a relativistic density-dependent Hartree approach for finite nuclei, where the coupling constants of the relativistic Hartree Lagrangian are made density dependent and are obtained from the relativistic Brueckner-Hartree-Fock results of nuclear matter. The calculated results on binding energies and root mean square radii of {sup 16}O and {sup 40}Ca agree very well with experiment. The charge densities from electron scattering are also calculated and their dependence on the nucleon-nucleon interaction is discussed in relation with nuclear matter properties.

Quark mean field model for nucleons in nuclei

We propose the quark mean field model for nucleons in nuclei, where the meson mean fields created by other nucleons act on quarks in a nucleon and change the nucleon properties in nuclei. We take the constituent quark model for the nucleon, which naturally allows the direct coupling of pions and in turn other mesons as $\ensuremath{\sigma}$ and $\ensuremath{\omega}$ mesons. We find very good nuclear matter properties with the use of the nonlinear self-energy terms in the meson Lagrangian. We expect the spin-orbit splitting in finite nuclei to be large due to the large reduction of the nucleon mass, which is in agreement with experiment. The nucleon size increases by about 7% at the normal m…

The relativistic mean-field model at large densities

The extrapolation properties of the relativistic mean-field model are investigated in nuclear matter. The results of a recent relativistic Bethe-Brueckner-Gatdstone calculation are taken as ‘data”. Fits in a window of normal nuclear densities are extrapolated to large densities and compared with the ‘data’. We find large discrepancies which hint at an insufficiency of the model in its present parametrisation.

Relativistic nuclear structure. I. Nuclear matter.

The formalism for the Dirac-Brueckner approach to the nuclear many-body problem is described including its basis in relativistic two-nucleon scattering. A family of relativistic meson-exchange potentials is constructed which (apart from the usual coupling terms for heavy mesons) apply the pseudovector (gradient) coupling for the interaction of pseudoscalar mesons (\ensuremath{\pi},\ensuremath{\eta}) with nucleons. These potentials describe low-energy two-nucleon scattering and the deuteron data accurately. Using these potentials, the properties of nuclear matter are calculated in the Dirac-Brueckner-Hartree-Fock approximation, in which the empirical nuclear matter saturation is explained qu…

Peripheral nucleon-nucleon phase shifts and chiral symmetry

Within the one-loop approximation of baryon chiral perturbation theory we calculate all one-pion and two-pion exchange contributions to the nucleon-nucleon interaction. In fact we construct the elastic NN-scattering amplitude up to and including third order in small momenta. The phase shifts with orbital angular momentum $L\geq2 $ and the mixing angles with $J\geq2$ are given parameterfree and thus allow for a detailed test of chiral symmetry in the two-nucleon system. We find that for the D-waves the $2\pi$-exchange corrections are too large as compared with empirical phase shifts, signaling the increasing importance of shorter range effects in lower partial waves. For higher partial waves…

Decay modes of sigma and lambda hypernuclei

Abstract A review is presented of the problem of Σ and Λ decay in nuclei. By means of handy, yet reliable approximations, an approach to Σ decay is developed which allows a clear insight into the different aspects of the problem. The role of nuclear polarization, due to the spin-isospin ΣN → ΛN interaction, in the reduction of the Σ widths is discussed. Many experimentally observable Σ hypernuclei are predicted by showing that their widths are narrower than the separation energies between levels. The mesonic and non-mesonic decays of Λ hypernuclei are analyzed. The non-mesonic width is fairly well reproduced by simplified models for the ΛN → NN weak transition, but quantities like the ratio…

Properties of dense nuclear and neutron matter with relativistic nucleon-nucleon interactions.

Within the framework of the Dirac-Brueckner (DB) approach, the properties of dense nuclear and neutron matter are investigated using realistic nucleon-nucleon (NN) interactions which are derived from relativistic meson-field theory and describe the two-nucleon system quantitatively. Single-particle potentials, equations of state, nucleon effective masses, Landau parameters, and speeds of sound are calculated and analyzed as functions of density, for both nuclear and neutron matter. In the DB approach, the equation of state comes out stiffer than in the most sophisticated nonrelativistic calculation, but softer than in the Walecka model. Possible extensions of the present approach to nucleon…