A new scheme to study the properties of finite nuclei is proposed based on the Dirac-Brueckner-Hartree-Fock (DBHF) approach starting from a realistic nucleon-nucleon interaction. The relativistic structure of the nucleon self-energies in nuclear matter depending on density, momentum, and isospin asymmetry is determined through a subtracted $T$-matrix technique. The scalar and vector potentials in nuclear matter are parametrized and extrapolated around the very low density region to provide the necessary basis for the finite nuclei calculation. The potentials of a single particle in finite nuclei are generated via a local density approximation (LDA). The surface effect of finite nuclei can be taken into account by an improved LDA. The bulk properties of nuclei can be determined in a self-consistent scheme, and the spherical nuclei $^{16}\mathrm{O},\phantom{\rule{0.16em}{0ex}}^{40,48}\mathrm{Ca},\phantom{\rule{0.16em}{0ex}}^{90}\mathrm{Zr},\phantom{\rule{0.16em}{0ex}}^{116,132}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$ are sampled for validation. The results show that the calculated binding energies are coincident with the experimental data, and the predicted values for radii and spin-orbit splitting of single-particle energies are reasonably described with an underestimation of about 10%. Basic features of finite nuclei in this scheme are consistent with those of more sophisticated DBHF calculations.

A relativistic microscopic optical model potential, named CTOM, for nucleon-nucleus scattering is investigated in the framework of Dirac-Brueckner-Hartree-Fock approach. The microscopic feature of CTOM is guaranteed through rigorously adopting the isospin dependent DBHF calculation within the subtracted T matrix scheme. In order to verify its prediction power, a global study n, p + A scattering are carried out. The predicted scattering observables coincide with experimental data within a good accuracy over a broad range of targets and a large region of energies only with two free items, namely the free-range factor t in the applied improved local density approximation and minor adjustments of the scalar and vector potentials in the low-density region. In addition, to estimate the uncertainty of the theoretical results, the deterministic simple least square approach is preliminarily employed to derive the covariance of predicted angular distributions, which is also briefly contained in this paper.

Background: For the study of exotic nuclei it is important to have an optical model potential that is reliable not only for stable nuclei but can also be extrapolated to nuclear systems with exotic numbers of protons and neutrons. An efficient way to obtain such a potential is to develop a microscopic optical potential (MOP) based on a fundamental theory with a minimal number of free parameters, which are adjusted to describe stable nuclei all over the nuclide chart.Purpose: The choice adopted in the present work is to develop the MOP within a relativistic scheme which provides a natural and consistent relation between the spin-orbit part and the central part of the potential. The Dirac-Brueckner-Hartree-Fock (DBHF) approach provides such a microscopic relativistic scheme, which is based on a realistic nucleon-nucleon interaction and reproduces the saturation properties of symmetric nuclear matter without any adjustable parameter. Its solution using the projection technique within the subtracted T-matrix representation provides a reliable extension to asymmetric nuclear matter, which is important to describe the features of isospin asymmetric nuclei. The present work performs a global analysis of the isospin dependent nucleon-nucleus MOP based on the DBHF calculation in symmetric and asymmetric nuclear matter.Methods: The DBHF approach is used to evaluate the relativistic structure of the nucleon self-energies in nuclear matter at various densities and asymmetries. The Schrodinger equivalent potentials of finite nuclei are derived from these Dirac components by a local density approximation (LDA). The density distributions of finite nuclei are taken from the Hartree-Fock-Bogoliubov approach with Gogny D1S force. An improved LDA approach (ILDA) is employed to get a better prediction of the scattering observables. A chi(2) assessment system based on the global simulated annealing algorithm is developed to optimize the very few free components in this study.Results: The nucleon-nucleus scattering calculations are carried out for a broad spectrum of n and p scattering experiments below 200 MeV with targets ranging from C-12 to Pb-208. The scattering observables including the neutron total cross section, proton reaction cross section, elastic scattering angular distribution, analyzing power, and spin rotation are evaluated and compared with the experimental data, as well as with results derived from the widely used phenomenological Koning-Delaroche global potential.Conclusions: Results with the present relativistic MOP reproduce the n, p + A scattering observables with good accuracy over a broad range of targets and a large region of energies fitting only the free-range factor t in ILDA and minor adjustments of the scalar and vector potentials in the low-density region.

We present a simultaneous calculation of heavy single-Λ hypernuclei and compact stars containing hypernuclear core within a relativistic density functional theory based on a Lagrangian which includes the hyperon octet and lightest isoscalar-isovector mesons which couple to baryons with density-dependent couplings. The corresponding density functional allows for SU(6) symmetry breaking and mixing in the isoscalar sector, whereby the departures in the σ–Λ and σ–Σ couplings away from their values implied by the SU(3) symmetric model are used to adjust the theory to the laboratory and astronomical data. We fix σ–Λ coupling using the data on the single-Λ hypernuclei and derive an upper bound on the σ–Σ from the requirement that the lower bound on the maximum mass of a compact star is 2M⊙.

We present a simultaneous calculation of heavy single-$\Lambda$ hypernuclei and compact stars containing hypernuclear core within a relativistic density functional theory based on a Lagrangian which includes the hyperon octet and lightest isoscalar-isovector mesons which couple to baryons with density-dependent couplings. The corresponding density functional allows for SU(6) symmetry breaking and mixing in the isoscalar sector, whereby the departures in the $\sigma$-$\Lambda$ and $\sigma$-$\Sigma$ couplings away from their values implied by the SU(3) symmetric model are used to adjust the theory to the laboratory and astronomical data. We fix $\sigma$-$\Lambda$ coupling using the data on the single-$\Lambda$ hypernuclei and derive an upper bound on the $\sigma$-$\Sigma$ from the requirement that the lower bound on the maximum mass of a compact star is $2 M_{\odot}$.

The structure of finite nuclei is investigated by employing an interaction model which is based on the low-momentum interaction $V_{lowk}$. It is supplemented by a density-dependent contact interaction fitted to reproduce the saturation properties of infinite nuclear matter within the Hartree-Fock approach. The calculations of finite nuclei are performed in a basis of plane waves discretized in a cartesian box of appropriate size. As a first example the structure of Ne isotopes is considered ranging from $^{18}$Ne to the neutron drip line. Rather good agreement is obtained for the bulk properties of these nuclei without any free parameter. The basis is also appropriate to describe other deformed nuclei and the transition from discrete nuclei to homogeneous matter which is supposed to occur in the crust of neutron stars.

A density dependent relativistic mean-field model is determined to reproduce the components of the nucleon self-energy at low densities. This model is used to investigate spinodal instabilities in isospin asymmetric nuclear matter at finite temperatures. The inhomogeneous density distributions in the spinodal region are investigated through calculations in a cubic Wigner-Seitz cell. Compared to results obtained in phenomenological calculations the spinodal region is large, i.e. the spinodal region at zero temperature can reach densities above 0.12 fm$^{-3}$. The predicted spinodal region is concentrated around isospin symmetric nuclear matter and the critical temperature is considerably lower than in the previous microscopic based investigation within a non-relativistic Brueckner-Hartree-Fock approach.

The relativistic optical model potential (OMP) for nucleon-nucleus scattering is investigated in the framework of Dirac-Brueckner-Hartree-Fock (DBHF) approach using the Bonn-B One-Boson- Exchange potential for the bare nucleon-nucleon interaction. Both real and imaginary parts of isospin-dependent nucleon self-energies in nuclear medium are derived from the DBHF approach based on the projection techniques within the subtracted T -matrix representation. The Dirac potentials as well as the corresponding Schrodinger equivalent potentials are evaluated. An improved local density approximation is employed in this analysis, where a range parameter is included to account for a finite-range correction of the nucleon-nucleon interaction. As an example the total cross sections, differential elastic scattering cross sections, analyzing powers for n, p + 27Al at incident energy 100 keV < E < 250 MeV are calculated. The results derived from this microscopic approach of the OMP are compared to the experimental data, as well as the results obtained with a phenomenological OMP. A good agreement between the theoretical results and the measurements can be achieved for all incident energies using a constant value for the range parameter.

A set of relativistic mean-field models is constructed, which includes the Hartree and Hartree-Fock (HF) approximations accounting for the exchange of isoscalar and isovector mesons as well as the pion. Density-dependent coupling functions are determined to reproduce the components of the nucleon self-energy at the Fermi surface, obtained within the Dirac-Brueckner-HF (DBHF) approach by using a realistic nucleon-nucleon interaction. It is investigated to which extent the various mean-field models can reproduce the DBHF results for the momentum dependence of the self-energies and the total energy of infinite matter. Also, the mean-field models are used to evaluate the bulk properties of spherical closed-shell nuclei. We find that the HF model, which allows for the exchange of sigma, omega, rho, and delta mesons and pions, yields the best reproduction of the DBHF results in infinite matter and also provides a good description of the properties of finite nuclei without any adjustment of parameters.

The off-shell behavior of the nucleon self-energy in isospin asymmetric nuclear matter is investigated within the framework of relativistic Dirac-Brueckner-Hartree-Fock approach based on projection techniques. The dependence of the Dirac components of the self-energy on momentum as well as energy is evaluated for symmetric as well as asymmetric nuclear matter. Special attention is paid to the various contributions to the momentum dependence of the real and imaginary part of the optical potential. The consequences to the different definitions of the effective nucleon mass and particle spectral functions are discussed.

The low-momentum interaction Vlow-k derived from realistic models of the nucleon-nucleon interaction is presented in a separable form. This separable force is supported by a contact interaction to achieve the saturation properties of symmetric nuclear matter. Bulk properties of nuclear matter and finite nuclei are investigated for the separable form of Vlow-k and two different parametrizations of the contact term. The accuracy of the separable force in Hartree-Fock calculations with respect to the original interaction Vlow-k is discussed. For a cutoff parameter Lambda of 2 fm(-1), a representation by a rank-2 separable force yields sufficient accuracy, while higher ranks are required for larger cutoff parameters. The resulting separable force is parametrized in a simple way to allow for an easy application in other nuclear structure calculations.

The status of relativistic nuclear many-body calculations of nuclear systems to be built up in terms of protons and neutrons is reviewed. In detail, relativistic effects on several aspects of nuclear matter such as the effective mass, saturation mechanism, and the symmetry energy are considered. This review will especially focus on isospin asymmetric issues, since these aspects are of high interest in astrophysical and nuclear structure studies. Furthermore, from the experimental side these aspects are experiencing an additional boost from a new generation of radioactive beam facilities, e.g., the future GSI facility FAIR in Germany or SPIRAL2 at GANIL/France. Finally, the prospects of studying finite nuclei in microscopic calculations which are based on realistic NN interactions by including relativistic effects in calculations of low momentum interactions are discussed.

Nuclei close to the neutron drip line are described employing an interaction model which is based on the low-momentum interaction Vlowk. This effective two-body interaction which is determined to reproduce the nucleon-nucleon (NN) scattering data at energies below the pion thresh-hold is supplemented by a density-dependent contact interaction fitted to reproduce the saturation properties of infinite nuclear matter within the Hartree-Fock approach. It is demonstrated that corresponding calculations for closed shell-nuclei using this interaction model reproduce the bulk properties of these nuclei, independent whether the wave functions are expanded in terms of harmonic oscillator waves or in a basis of plane waves discretized in a spherical box of appropriate size. This plane wave basis, however, is more appropriate to describe weakly bound nuclei and the transition from discrete nuclei to homogeneous matter which is supposed to occur e.g. in the crust of neutron stars. Properties of exotic nuclei are studied within a Hartree-Fock plus BCS approximation.

Relativistic effects are investigated in nuclear matter calculations employing renormalized low-momentum nucleon-nucleon (NN) interactions. It is demonstrated that the relativistic effects cure a problem of nonrelativistic low-momentum interactions, which fail to reproduce saturation of nuclear matter. Including relativistic effects, one already obtains saturation in a Hartree-Fock calculation. Brueckner-Hartree-Fock calculations lead to a further improvement of the saturation properties. The results are rather insensitive to the realistic NN interaction on which they are based.

Properties of asymmetric nuclear matter are derived from various many-body approaches. This includes phenomenological ones like the Skyrme Hartree-Fock and relativistic mean field approaches, which are adjusted to fit properties of nuclei, as well as more microscopic attempts like the Brueckner-Hartree-Fock approximation, a self-consistent Greens function method and the so-called Vlow-k approach, which are based on realistic nucleonnucleon interactions which reproduce the nucleon-nucleon phase shifts. These microscopic approaches are supplemented by a density-dependent contact interaction to achieve the empirical saturation property of symmetric nuclear matter. The predictions of all these approaches are discussed for nuclear matter at high densities in β-equilibrium. Special attention is paid to behavior of the isovector component of the effective mass in neutronrich matter.

Properties of inhomogeneous nuclear matter are evaluated within a relativistic mean-field approximation by using density-dependent coupling constants. A parametrization for these coupling constants is presented that reproduces the properties of the nucleon self-energy obtained in Dirac-Brueckner-Hartree-Fock calculations of asymmetric nuclear matter but also provides a good description for bulk properties of finite nuclei. The inhomogeneous infinite matter is described in terms of cubic Wigner-Seitz cells, which allows for a microscopic description of the structures in the so-called pasta-phase of nuclear configurations and provides a smooth transition to the limit of homogeneous matter. The effects of pairing properties and finite temperature are considered. A comparison is made to corresponding results by employing the phenomenological Skyrme Hartree-Fock approach, and the consequences for the Thomas-Fermi approximation are discussed.

We present Dirac-Brueckner-Hartree-Fock calculations for isospin asymmetric nuclear matter which are based on improved approximations schemes. The potential matrix elements have been adapted for isospin asymmetric nuclear matter in order to account for the proton-neutron mass splitting in a more consistent way. The proton properties are particularly sensitive to this adaption and its consequences, whereas the neutron properties remains almost unaffected in neutron-rich matter. Although at present full Brueckner calculations are still too complex to apply to finite nuclei, these relativistic Brueckner results can be used as a guidance to construct a density-dependent relativistic mean-field theory, which can be applied to finite nuclei. It is found that an accurate reproduction of the Dirac-Brueckner-Hartree-Fock equation of state requires a renormalization of these coupling functions.

T. Klähn, 2, ∗ D. Blaschke, 4, † S. Typel, E.N.E. van Dalen, A. Faessler, C. Fuchs, T. Gaitanos, H. Grigorian, 6 A. Ho, E.E. Kolomeitsev, M.C. Miller, G. Röpke, J. Trümper, D.N. Voskresensky, 11 F. Weber, and H.H. Wolter 1 Institut für Physik, Universität Rostock, 18051 Rostock, Germany 2 Institut für Theoretische Physik, Universität Tübingen, 72076 Tübingen, Germany 3 Gesellschaft für Schwerionenforschung mbH (GSI), 64291 Darmstadt, Germany 4 Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia 5 Department für Physik, Universität München, 85748 Garching, Germany 6 Department of Physics, Yerevan State University, 375049 Yerevan, Armenia 7 Department of Physics, San Diego State University, 5500 Campanile Drive, San Diego, California 92182, USA 8 School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA 9 Department of Astronomy, University of Maryland, College Park, MD 20742-2421, USA 10 Max-Planck-Institut für extraterrestrische Physik, 85741 Garching, Germany 11 Moscow Engineering Physical Institute, Kashirskoe Shosse 31,11549 Moscow, Russia (Dated: February 14, 2006)

Relativistic and nonrelativistic modern nucleon-nucleon potentials are mapped on a relativistic operator basis using projection techniques. This allows us to compare the various potentials at the level of covariant amplitudes were a remarkable agreement is found. In nuclear matter large scalar and vector mean fields of several hundred MeV magnitude are generated at tree level. This is found to be a model independent feature of the nucleon-nucleon interaction.