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A new scheme to study the properties of finite nuclei is proposed based on the Dirac-Brueckner-Hartree-Fock (DBHF) approach starting from a bare nucleon-nucleon interaction. The relativistic structure of the nucleon self-energies in nuclear matter depending on density, momentum and isospin asymmetry are determined through a subtracted T-matrix technique and parameterized, which makes them easily accessible for general use. The scalar and vector potentials of a single particle in nuclei are generated via a local density approximation (LDA). The surface effect of finite nuclei can be taken into account by an improved LDA (ILDA), which has successfully been applied in microscopic derivations of the optical model potential for nucleon-nucleus scattering. The bulk properties of nuclei can be determined in a self-consistent scheme for nuclei all over the nuclear mass table. Calculated binding energies agree very well with the empirical data, while the predicted values for radii and spin-orbit splitting of single-particle energies are about 10 \% smaller than the experimental data. Basic features of more sophisticated DBHF calculations for finite nuclei are reproduced.

The Microscopic Otical Model Potential is evaluated 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 reproduce the saturation properties of symmetric nuclear matter without any adjustable parameter. Its solution using the projection technique within the subtracted T-matrix (STM) representation provides a reliable extension to asymmetric nuclear matter, which is important to describe the features of the isospin asymmetric nuclei. Therefore, the present work aims to perform a global analysis of the isospin-dependent nucleon-nucleus MOP based on the DBHF calculation in symmetric and asymmetric nuclear matter. The DBHF is used to evaluate the relativistic structure of the nucleon self-energies in nuclear matter at various densities and asymmetries. The Schr\"odinger equivalent potentials of finite nuclei are derived from these Dirac components by a local density approximation (LDA). The nucleon-nucleus scattering calculations are carried out for a broad spectrum $n$ and $p$ scattering experiments below 200 MeV with targets ranging from $^{12}$C to $^{208}$Pb.

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 $2 M_{\odot}$., Comment: 10 pages, 4 figures, to appear in Phys. Lett. B, v2: minor editorial corrections

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., Comment: 11 pages, 7 figures

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., Comment: 10 pages, 16 figures

A set of relativistic mean field models is constructed including the Hartree and Hartree-Fock approximation 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-Hartree-Fock (DBHF) approach using a realistic nucleon-nucleon interaction. It is investigated, to which extend 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. The mean field models are also used to evaluate the bulk properties of spherical closed-shell nuclei. We find that the Hartree-Fock model allowing for the exchange of $\sigma,\,\omega,\,\rho,\,\delta$ mesons and pions, yield 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., Comment: 12 pages, 6 figures

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., Comment: 13 pages, 8 figures

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., Comment: 57 pages, 16 figures

The low-momentum interaction $V_{\text{low-k}}$ derived from realistic models of the nucleon-nucleon interaction is presented in a separable form. This separable force is supported by a contact interaction in order to achieve the saturation properties of symmetric nuclear matter. Bulk properties of nuclear matter and finite nuclei are investigated for the separable form of $V_{\text{low-k}}$ and two different parameterizations of the contact term. The accuracy of the separable force in Hartree-Fock calculations with respect to the original interaction $V_{\text{low-k}}$ is discussed. For a cutoff parameter $\Lambda$ of 2 fm$^{-1}$ a representation by a rank 2 separable force yields a sufficient accuracy, while higher ranks are required for larger cut-off parameters. The resulting separable force is parameterized in a simple way to allow for an easy application in other nuclear structure calculations., Comment: 11 pages, 7 figures

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 non-relativistic 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., Comment: 4 pages, 3 figures

Nuclei close to the neutron drip line are described employing an interaction model which is based on the low-momentum interaction $V_{lowk}$. 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., Comment: 13 pages, 8 figures

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 $V_{lowk}$ approach, which are based on realistic nucleon-nucleon 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 $\beta$-equilibrium. Special attention is paid to behavior of the isovector component of the effective mass in neutron-rich matter., Comment: 16 pages, 7 figures

Properties of inhomogeneous nuclear matter are evaluated within a relativistic mean field approximation using density dependent coupling constants. A parameterization for these coupling constants is presented, which 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 employing the phenomenological Skyrme Hartree-Fock approach and the consequences for the Thomas-Fermi approximation are discussed., Comment: 16 pages 7, Figs

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., Comment: 34 pages, 9 figures, submitted to Eur. Phys. J. A

A new scheme for testing nuclear matter equations of state (EsoS) at high densities using constraints from neutron star phenomenology and a flow data analysis of heavy-ion collisions is suggested. An acceptable EoS shall not allow the direct Urca process to occur in neutron stars with masses below $1.5~M_{\odot}$, and also shall not contradict flow and kaon production data of heavy-ion collisions. Compact star constraints include the mass measurements of 2.1 +/- 0.2 M_sun (1 sigma level) for PSR J0751+1807, of 2.0 +/- 0.1 M_sun from the innermost stable circular orbit for 4U 1636-536, the baryon mass - gravitational mass relationships from Pulsar B in J0737-3039 and the mass-radius relationships from quasiperiodic brightness oscillations in 4U 0614+09 and from the thermal emission of RX J1856-3754. This scheme is applied to a set of relativistic EsoS constrained otherwise from nuclear matter saturation properties with the result that no EoS can satisfy all constraints simultaneously, but those with density-dependent masses and coupling constants appear most promising., Comment: 15 pages, 8 figures, 5 tables

Properties of symmetric and asymmetric nuclear matter have been investigated in the relativistic Dirac-Brueckner-Hartree-Fock approach based on projection techniques using the Bonn A potential. The momentum, density, and isospin dependence of the optical potentials and nucleon effective masses are studied. It turns out that the isovector optical potential depends sensitively on density and momentum, but is almost insensitive to the isospin asymmetry. Furthermore, the Dirac mass $m^*_D$ and the nonrelativistic mass $m^*_{NR}$ which parametrizes the energy dependence of the single particle spectrum, are both determined from relativistic Dirac-Brueckner-Hartree-Fock calculations. The nonrelativistic mass shows a characteristic peak structure at momenta slightly above the Fermi momentum $\kf$. The relativistic Dirac mass shows a proton-neutron mass splitting of $m^*_{D,n} m^*_{NR,p}$ which is in agreement with the results from nonrelativistic calculations., Comment: 25 pages, 12 figures, to appear in Physical Review C

Relativistic and non-relativistic modern nucleon-nucleon potentials are mapped on a relativistic operator basis using projection techniques. This allows 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., Comment: 5 pages, 2 figures, results for V_lowk added, to appear in PRC

The momentum and isospin dependence of the in-medium nucleon mass are studied. Two definitions of the effective mass, i.e. the Dirac mass $m^*_D$ and the nonrelativistic mass $m^*_{NR}$ which parameterizes the energy spectrum, are compared. Both masses are determined from relativistic Dirac-Brueckner-Hartree-Fock calculations. The nonrelativistic mass shows a distinct peak around the Fermi momentum. The proton-neutron mass splitting in isospin asymmetric matter is $m^*_{D,n} m^*_{NR,p}$, which is consistent with nonrelativistic approaches., Comment: 11 pages, 4 figures, minor changes, to appear in Physical Review Letters

The properties of asymmetric nuclear matter have been investigated in a relativistic Dirac-Brueckner-Hartree-Fock framework using the Bonn A potential. The components of the self-energies are extracted by projecting on Lorentz invariant amplitudes. Furthermore, the optimal representation scheme for the $T$ matrix, the subtracted $T$ matrix representation, is applied and the results are compared to those of other representation schemes. Of course, in the limit of symmetric nuclear matter our results agree with those found in literature. The binding energy $E_b$ fulfills the quadratic dependence on the asymmetry parameter and the symmetry energy is 34 MeV at saturation density. Furthermore, a neutron-proton effective mass splitting of $m_n^* < m_p^*$ is found. In addition, results are given for the mean-field effective coupling constants., Comment: 28 pages, 7 figures, to appear in Nucl. Phys. A, added additional references

The contribution from hyperons to the bulk viscosity of neutron star matter is calculated. Compared to previous works we use for the weak interaction the one-pion exchange model rather than a current-current interaction, and include the neutral current $nn \leftrightarrow n\Lambda$ process. Also the sensitivity to details of the equation of state is examined. Compared to previous works we find that the contribution from hyperons to the bulk viscosity is about two orders of magnitude smaller., Comment: 18 pages, to appear in Physical Review C

Neutrino emissivities in a neutron star are computed for the neutrino bremsstrahlung process. In the first part the electro-weak nucleon-nucleon bremsstrahlung is calculated in free space in terms of a on-shell $T$-matrix using a generalized Low energy theorem. In the second part the emissivities are calculated in terms of the hadronic polarization at the two-loop level. Various medium effects, such as finite particle width, Pauli blocking in the $T$-matrix are considered. Compared to the pioneering work of Friman and Maxwell in terms of (anti-symmetrized) one-pion exchange the resulting emissivity is about a factor 4 smaller at saturation density., Comment: 36 pages, accepted for publication in Physical Review C

Cooling of neutrons stars proceeds mainly via neutrino emission; As an example we study the modified neutrino bremsstrahlung process $nn \to nn\nu\bar{\nu}.$ The radiated energy is small compared to other scales in the system. Hence one can use low-energy theorems to compute the neutrino emissivity in terms of the non-radiative process, ie the on-shell $T$ matrix. We find that the use of the $T-$matrix as compared to previous estimates based upon one pion exchange leads a substantial reduction of the predicted emissivity., Comment: 6 pages, 2 figures. To appear in the Proceedings of "Bologna 2000: Structure of the Nucleus at the Dawn of the Century",May 29 - June 3, 2000, Bologna,Italy

We study the neutrino emissivity of strongly magnetized neutron stars due to the charged and neutral current couplings of neutrinos to baryons in strong magnetic fields. The leading order neutral current process is the one-body neutrino-pair bremsstrahlung, which does not have an analogue in the zero field limit. The leading order charged current reaction is the known generalization of the direct Urca processes to strong magnetic fields. While for superstrong magnetic fields in excess of $10^{18}$ G the direct Urca process dominates the one-body bremsstrahlung, we find that for fields on the order $10^{16}-10^{17}$ G and temperatures a few times $10^9$ K the one-body bremsstrahlung is the dominant process. Numerical computation of the resulting emissivity, based on a simple parametrization of the equation of state of the $npe$-matter in a strong magnetic field, shows that the emissivity of this reaction is of the same order of magnitude as that of the modified Urca process in the zero field limit., Comment: 11 pages, 6 figures, to appear in A&A