Dirac-Brueckner Approach Research Articles

Analysis of reaction cross sections of Ne and Mg isotopes at 240 MeV/u in the Dirac-Brueckner approach and Glauber model

Within a relativistic effective complex nucleon-nucleon interaction derived by solving the Dirac-Brueckner-Bethe-Goldstone equation, locally, starting from the one-boson-exchange potential (OBEP) as a bare NN interaction, the optical potentials and reaction cross sections of the 20-36Ne , 24-38Mg + 12C reactions, recently observed at 240MeV/u , are calculated. The proton and neutron density distributions of target and projectile are derived from Skyrme-Hartree-Fock calculations, employing SKRA and SKM* interactions. A comparison between the experimental data as well as recent theoretical calculations of Horiuchi et al. (Phys. Rev. C 86, 024614 (2012)) and Panda et al. (Mod. Phys. Lett. A 29, 1450013 (2014)) show that the data are well reproduced by the present relativistic calculations.

Isospin splitting of the nucleon mean field

The isospin splitting of the nucleon mean field is derived from the Brueckner theory extended to asymmetric nuclear matter. The Argonne V18 has been adopted as bare interaction in combination with a microscopic three body force. The isospin splitting of the effective mass is determined from the Brueckner-Hartree-Fock self-energy: It is linear acording to the Lane ansatz and such that $m^*_n > m^*_p$ for neutron-rich matter. The symmetry potential is also determined and a comparison is made with the predictions of the Dirac-Brueckner approach and the phenomenological interactions. The theoretical predictions are also compared with the empirical parametrizations of neutron and proton optical-model potentials based on the experimental nucleon-nucleus scattering and the phenomenological ones adopted in transport-model simulations of heavy-ion collisions. The direct contribution of the rearrangement term due to three-body forces to the single particle potential and symmetry potential is discussed.

Effect of three-body interaction on phase transition of hot asymmetric nuclear matter

The properties and the isospin dependence of the liquid–gas phase transition in hot asymmetric nuclear matter have been investigated within the framework of the finite temperature Brueckner–Hartree–Fock approach extended to include the contribution of a microscopic three-body force. A typical Van der Waals structure has been observed in the calculated isotherms (of pressure) for symmetric nuclear matter implying the presence of the liquid–gas phase transition. The critical temperature of the phase transition is calculated and its dependence on the proton-to-neutron ratio is discussed. It is shown that the three-body force gives a repulsive contribution to the nuclear equation of state and reduces appreciably the critical temperature and the mechanical instable region. At fixed temperature and density the pressure of asymmetric nuclear matter increases monotonically as a function of isospin asymmetry. In addition, it turns out that the domain of mechanical instability for hot asymmetric nuclear matter gradually shrinks with increasing asymmetry and temperature. We have compared our results with the predictions of other theoretical models especially the Dirac–Brueckner approach. A possible explanation for the discrepancy between the values of the critical temperature predicted by the present non-relativistic Brueckner calculations including the three-body force and the relativistic Dirac–Brueckner method is given.

The relativistic Dirac–Brueckner approach to asymmetric nuclear matter

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.

Interplay of three-body interactions in the EOS of nuclear matter

The equation of state of symmetric nuclear matter has been investigated within Brueckner approach adopting the charge-dependent Argonne V 18 two-body force plus a microscopic three-body force based on a meson-exchange model. The effects on the equation of state of the individual processes giving rise to the three-body force are explored up to high baryonic density. It is found that the major role is played by the competition between the strongly repulsive ( σ, ω)-exchange term with virtual nucleon–antinucleon excitation and the large attractive contribution due to ( σ, ω) exchange with N ∗(1440) resonance excitation. The net result is a repulsive term which shifts the saturation density corresponding to the only two-body force much closer to the empirical value, while keeping constant the saturation energy per particle. The contribution from ( π, ρ)-exchange 3BF is shown to be attractive and rather small. The analysis of the separate three-body force contributions allows to make a comparison with the prediction of Dirac–Brueckner approach which is supposed to incorporate via the dressed Dirac spinors the same virtual nucleon–antinucleon excitations as in the present three-body force. The numerical results suggest that the three-body force components missing from the Dirac–Brueckner approach are not negligible, especially at high density. The calculation of the nuclear mean field and the effective mass shows that the three-body force affects to a limited extent such properties.

Testing microscopic medium effects on nucleons and mesons using polarization observables in high-spin, unnatural-parity(p→,p′)reactions at 200 MeV

We compare measurements of the cross section, analyzing power, induced polarization, and polarization transfer coefficients for $(\stackrel{\ensuremath{\rightarrow}}{p},{p}^{\ensuremath{'}})$ reactions leading to unnatural-parity, high-spin states in ${}^{16}\mathrm{O}$ and ${}^{28}\mathrm{Si}$ with distorted wave impulse approximation calculations. We use an effective nucleon-nucleon (NN) interaction obtained from a microscopic treatment of nuclear medium effects. The NN potential is generated from a one-boson-exchange model of the nuclear force that reproduces NN scattering data well. Medium effects are incorporated through a G matrix obtained within a Dirac-Brueckner approach to nuclear matter. While agreement for some observables is good, differences for the polarization transfer coefficients indicate that systematic problems with the relative sizes of the spin-orbit and tensor interaction components exist. The differences are larger for ${}^{28}\mathrm{Si}$ than for ${}^{16}\mathrm{O}.$ A new model that incorporates density-dependent meson mass reductions produces only small effects that do not change the quality of the agreement. Connections to previous calculations are investigated.

Heavy ion collisions and non-equilibrium mean fields

Methods and difficulties of the determination of the equation-of-state of nuclear matter by means of relativistic heavy ion collisions are reviewed. The decription of nuclear structure in the framework of a hadronic field theory is discussed and it is argued that the Dirac-Brueckner approach represents a framework that allows to unify the description of NN-scattering, nuclear matter and finite nuclei, and heavy ion reactions. In the latter case, however, non-equilibrium features of the phase space distribution have to be taken into account to reliably extract the equation-of-state. This is done here in a local phase space configuration approximation. An examplary application to flow observables in relativistic Au+Au collisions is presented. It is seen that the microscopic Dirac Brueckner fields reproduce experimental data reasonably well if non-equlibrium effects are accounted for approximately.

Nuclear symmetry energy

To study the nuclear symmetry energy, we extend the Dirac-Brueckner approach with a Bonn one-boson-exchange nucleon-nucleon interaction to the general case of asymmetric nuclear matter. We extract the symmetry energy coefficient at the saturation to be about 31 MeV, which is in good agreement with the empirical value of 30{plus_minus}4thinspMeV. The symmetry energy is found to increase almost linearly with the density, which differs considerably from the results of nonrelativistic approaches. This finding also supports the linear parametrization of Prakash, Ainsworth, and Lattimer. We find, furthermore, that the higher-order dependence of the nuclear equation of state on the asymmetry parameter is unimportant. {copyright} {ital 1998} {ital The American Physical Society}

Momentum dependence of single particle potential in Dirac Brueckner approach

The momentum dependence of the empirical scalar and vector potentials needed for describing relativistic heavy-ion collisions at 1 GeV/nucleon is compared with that derived from self-consistent Dirac-Brueckner calculations using the Bonn-A potential. Our calculated scalar and vector potentials exhibit a weak momentum dependence and their magnitudes decrease with nucleon momentum, in close similarity with the momentum dependence required by the empirical potentials. The effects of explicit momentum dependence on the properties of equilibrium nuclear matter are found to be small.

RMF parametrization of relativistic effective NN interaction

The relativistic energy density of nuclear matter derived in the Dirac-Brueckner approach, by solving the Dirac-Bethe-Goldstone equation, is parametrized in terms of the relativistic mean field (RMF) theory. The obtained mean field parameters represent a parametrization of effective interaction in nuclear medium. The RMF model of this interaction is used to calculate the properties of finite nuclei. A good agreement with experiments is obtained.

Quark condensate in nuclear matter

Higher-order contributions to the quark condensate in nuclear matter due to nucleon-nucleon interactions are evaluated in the Dirac-Brueckner approach with the Bonn one-boson-exchange potential. We find that at normal nuclear matter density the quark condensate with higher-order contributions is about 5% larger than the model-independent leading-order result obtained from the pion-nucleon sigma term and usually used in theoretical discussions. At higher densities, the higher-order contributions become increasingly important, leading to a hindrance of chiral restoration. Possible reasons for this behaviour are discussed.

Microscopic calculation of in-medium proton-proton cross sections.

We derive in-medium proton-proton cross sections in a microscopic model based upon the Bonn nucleon-nucleon potential and the Dirac-Brueckner approach for nuclear matter. We demonstrate the difference between proton-proton and neutron-proton cross sections and point out the need to distinguish carefully between the two cases. We also find substantial differences between our in-medium cross sections and phenomenological parametrizations that are commonly used in heavy-ion reactions.

Momentum-dependent mean field based upon the Dirac-Brueckner approach for nuclear matter.

A momentum-dependent mean field potential, suitable for application in the transport-model description of nucleus-nucleus collisions, is derived in a microscopic way. The derivation is based upon the Bonn meson-exchange model for the nucleon-nucleon interaction and the Dirac-Brueckner approach for nuclear matter. The properties of the microscopic mean field are examined and compared with phenomenological parametrizations which are commonly used in transport-model calculations.

Relativistic microscopic description of proton-nucleus scattering at intermediate energies.

We study elastic proton-nucleus scattering at intermediate energies. The nucleon-nucleus optical potential is derived from the Bonn nucleon-nucleon potential and the Dirac-Brueckner approach for nuclear matter. Our calculations, which do not contain any adjustable parameters, yield good agreement with experiment.

Microscopic calculation of in-medium nucleon-nucleon cross sections.

We derive in-medium nucleon-nucleon (NN) cross sections in a microscopic model. Our calculations are based upon the Bonn NN potential and the Dirac-Brueckner approach for nuclear matter. We consider energies up to 300 MeV (in the laboratory frame) and densities up to twice nuclear matter density. Our results deviate substantially from cross section parametrizations that are commonly used in the nuclear medium.

Effect of charge dependence of the nucleon-nucleon interaction on the properties of nuclear and neutron matter.

We calculate the properties of nuclear matter and neutron matter with charge dependent potentials using the Dirac-Brueckner approach. It turns out that the charge dependence of the NN interaction has no significant influence on the properties of nuclear matter and neutron matter.

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-nucleus scattering and nucleus-nucleus collisions are also discussed.

Nuclear-matter properties based on a relativistic model of the nucleon-nucleon interaction.

Saturation properties of nuclear matter are determined within a Dirac-Brueckner approach. Relativistic covariance is implemented by constructing the complete representation of the nucleon-nucleon amplitude in the Dirac space. As a dynamical model the relativistic one-boson-exchange model is used, including also the negative-energy-state components. A consistent treatment is discussed of nucleon propagation in the nuclear medium. The compressibility obtained for symmetric matter is rather low as compared to other calculations and more in agreement with the value suggested by astrophysical studies.

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 quantitatively. The effective two-body interaction in the nuclear matter medium (G matrix) is calculated directly in the nuclear matter rest frame. Thus, cumbersome transformations between the two-nucleon center-of-mass frame and the nuclear matter rest frame are avoided. Size and nature of relativistic effects included in the present approach are examined in detail. The formalism, the potentials, and the results of this paper may also serve as a basis and a realistic starting point for systematic relativistic nuclear structure studies as well as for the investigation of further relativistic many-body corrections and of contributions of higher order.

Ambiguities in the dirac-brueckner approach

The neglect of an explicit coupling to antiparticles when solving the relativistic Brueckner-Bethe-Goldstone (RBBG) equation leads to ambiguities of the calculated self-energy. We show that it is possible to obtain a family of weakly momentum-dependent self-energies from the RBBG equation which are consistent despite several hundred MeV differences in their magnitudes.