Starting from the Bonn potential, relativistic Brueckner-Hartree-Fock (RBHF) equations are solved for nuclear matter in the full Dirac space, which provides a unique way to determine the single-particle potentials and avoids the approximations applied in the RBHF calculations in the Dirac space with positive-energy states (PESs) only. The uncertainties of the RBHF calculations in the Dirac space with PESs only are investigated, and the importance of the RBHF calculations in the full Dirac space is demonstrated. In the RBHF calculations in the full Dirac space, the empirical saturation properties of symmetric nuclear matter are reproduced, and the obtained equation of state agrees with the results based on the relativistic Green's function approach up to the saturation density.
Starting with a bare nucleon-nucleon interaction, for the first time the full relativistic Brueckner-Hartree-Fock equations are solved for finite nuclei in a Dirac-Woods-Saxon basis. No free parameters are introduced to calculate the ground-state properties of finite nuclei. The nucleus $^{16}$O is investigated as an example. The resulting ground-state properties, such as binding energy and charge radius, are considerably improved as compared with the non-relativistic Brueckner-Hartree-Fock results and much closer to the experimental data. This opens the door for \emph{ab initio} covariant inv…
We have performed self-consistent Brueckner-Hartree-Fock (BHF) and its renormalized theory to the structure calculations of finite nuclei. The $G$-matrix is calculated within the BHF basis, and the exact Pauli exclusion operator is determined by the BHF spectrum. Self-consistent occupation probabilities are included in the renormalized Brueckner-Hartree-Fock (RBHF). Various systematics and convergences are studies. Good results are obtained for the ground-state energy and radius. RBHF can give a more reasonable single-particle spectrum and radius. We present a first benchmark calculation with …
We have calculated the proton spectral functions in finite nuclei based on the local density approximation where the properties of finite nuclei and nuclear matter are calculated by the Skyrme-Hartree-Fock method and the extended Brueckner-Hartree-Fock approach, respectively. The scaled spectral function from our calculation is in good agreement with experimental results at small momenta while the difference between them becomes apparent at high momenta. Besides, a target dependence of the scaled proton spectral function is also obtained in our calculation as was observed in experiment. A furt…
On the way of a microscopic derivation of covariant density functionals, the first complete solution of the relativistic Brueckner-Hartree-Fock (RBHF) equations is presented for symmetric nuclear matter. In most of the earlier investigations, the $G$-matrix is calculated only in the space of positive energy solutions. On the other side, for the solution of the relativistic Hartree-Fock (RHF) equations, also the elements of this matrix connecting positive and negative energy solutions are required. So far, in the literature, these matrix elements are derived in various approximations. We discus…
Neutron drops confined in an external field are studied in the framework of relativistic Brueckner-Hartree-Fock theory using the bare nucleon-nucleon interaction. The ground state energies and radii of neutron drops with even numbers from $N = 4$ to $N=50$ are calculated and compared with results obtained from other nonrelativistic \textit{ab initio} calculations and from relativistic density functional theory. Special attention has been paid to the magic numbers and to the sub-shell closures. The single-particle energies are investigated and the monopole effect of the tensor force on the evol…
Starting from the relativistic form of the Bonn potential as a bare nucleon-nucleon interaction, the full Relativistic Brueckner-Hartree-Fock (RBHF) equations are solved for finite nuclei in a fully self-consistent basis. This provides a relativistic ab initio calculation of the ground state properties of finite nuclei without any free parameters and without three-body forces. The convergence properties for the solutions of these coupled equations are discussed in detail at the example of the nucleus $^{16}$O. The binding energies, radii, and spin-orbit splittings of the doubly magic nuclei $^…
We investigate the appearance of di-neutron bound states in pure neutron matter within the Brueckner-Hartree-Fock approach at zero temperature. We consider Argonne $v_{18}$ and Paris bare interactions as well as chiral two- and three-nucleon forces. Self-consistent single-particle potentials are calculated controlling explicitly singularities in the $g$ matrix associated with bound states. Di-neutrons are loosely bound, with binding energies below $1$ MeV, but are unambiguously present for Fermi momenta below $1$ fm$^{-1}$ for all interactions. Within the same framework we are able to calculat…
We study the properties of nuclear matter with lattice nucleon-nucleon ($NN$) potential in the relativistic Brueckner-Hartree-Fock (RBHF) theory. To use this potential in such a microscopic many-body theory, we firstly have to construct a one-boson-exchange potential (OBEP) based on the latest lattice $NN$ potential. Three mesons, pion, $σ$ meson, and $ω$ meson, are considered. Their coupling constants and cut-off momenta are determined by fitting the on-shell behaviors and phase shifts of the lattice force, respectively. Therefore, we obtain two parameter sets of the OBEP potential (named as …
Brueckner-Hartree-Fock theory allows to derive the $G$-matrix as an effective interaction between nucleons in the nuclear medium. It depends on the center of mass momentum $\bm{P}$ of the two particles and on the two relative momenta $\bm{q}$ and $\bm{q'}$ before and after the scattering process. In the evaluation of the total energy per particle in nuclear matter usually the angle averaged center of mass momentum approximation has been used. We derive in detail the exact expressions of the angular integrations of the momentum $\bm{P}$ within relativistic Brueckner-Hartree-Fock (RBHF) theory, …
Recently, a microscopically motivated nuclear energy density functional was derived by applying the density matrix expansion to the Hartree-Fock (HF) energy obtained from long-range chiral effective field theory two- and three-nucleon interactions. However, the HF approach cannot account for all many-body correlations. One class of correlations is included by Brueckner-Hartree-Fock (BHF) theory, which gives an improved definition of the one-body HF potential by replacing the interaction by a reaction matrix $G$. In this paper, we find that the difference between the $G$-matrix and the nucleon-…
The microscopic mechanisms of the symmetry energy in nuclear matter are investigated in the framework of the relativistic Brueckner-Hartree-Fock (RBHF) model with a high-precision realistic nuclear potential, pvCDBonn A. The kinetic energy and potential contributions to symmetry energy are decomposed. They are explicitly expressed by the nucleon self-energies, which are obtained through projecting the $G$-matrices from the RBHF model into the terms of Lorentz covariants. The nuclear medium effects on the nucleon self-energy and nucleon-nucleon interaction in symmetry energy are discussed by co…
We consider the thermal conductivity, shear viscosity, and momentum relaxation rates in the nucleon cores of the neutron stars. We study how the choice of the nuclear interaction and the model for three-body forces may affect these transport coefficients calculated within the Brueckner-Hartree-Fock many-body nuclear theory. We find that at relatively large densities the model dependence of the results is substantial. In addition we provide the analytical approximations which allow to incorporate our results in practical simulations.
Microscopic Optical Potential from Brueckner-Hartree-Fock Theory
Beijing Normal University（北京师范大学）；Beijing Academy of Science and Technology（北京科学院）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Dipartimento di Fisica and Laboratori Nazionali del Sud (INFN)（物理系和南实验室（意大利国家核物理研究所））
We derive the values of nuclear symmetry energy, its components, as well as pressure in finite nuclei at saturation density from their corresponding values in nuclear matter obtained in non-relativistic Brueckner-Hartree-Fock calculations with the realistic Bonn B and Bonn CD potentials using the coherent density fluctuation model in the framework of a self-consistent Skyrme-Hartree-Fock plus BCS method. We focus on three isotopic chains of spherical nuclei (Ni, Sn, and Pb) and compare our results with those obtained with an effective Brueckner density-dependent potential. The role of the thre…
Properties of nuclear matter are investigated in the framework of relativistic Brueckner-Hartree-Fock model with the latest high-precision charge-dependent Bonn (pvCD-Bonn) potentials, where the coupling between pion and nucleon is adopted as pseudovector form. These realistic pvCD-Bonn potentials are renormalized to effective nucleon-nucleon ($NN$) interactions, $G$ matrices. They are obtained by solving the Blankenbecler-Sugar (BbS) equation in nuclear medium. Then, the saturation properties of symmetric nuclear matter are calculated with pvCD-Bonn A, B, C potentials. The energies per nucleo…
The momentum and isospin dependence of the single-particle potential for the in-medium nucleon are the key quantities in the Relativistic Brueckner-Hartree-Fock (RBHF) theory. It depends on how to extract the scalar and the vector components of the single-particle potential inside nuclear matter. In contrast to the RBHF calculations in the Dirac space with the positive-energy states (PESs) only, the single-particle potential can be determined in a unique way by the RBHF theory together with the negative-energy states (NESs), i.e., the RBHF theory in the full Dirac space. The saturation propert…
As the interior density of a neutron star can become very high, it has been expected and discussed that quark matter may exist inside it. To describe the transition from hadron to quark phases (and vice versa), there are mainly two methods; one is the first-order phase transition, and the other is the crossover phenomenon. In the present study, using the flavor-SU (3) NJL model with the vector coupling interaction, we have calculated the equation of state for the quark phase at high density. Furthermore, for the hadron phase at low density, we have used two kinds of the equations of state; one…
