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Staring from the Lagrangian density that foots on the meson-propagated picture of nuclear force, the full Hamiltonian, that contains both mean field and pairing contributions, is derived by quantizing the Dirac spinor field in the Bogoliubov quasi-particle space, and the expectation with respect to the Bogoliubov ground state gives the full energy functional. As an extension of the D-RHF model, the degree of freedom associated with the $\rho$-tensor ($\rho$-T) coupling is implemented, and incorporating with the Bogoliubov scheme the finite-range Gogny force D1S is utilized as the pairing force. Moreover, qualitative analysis on the nature of the $\pi$-PV and $\rho$-T couplings are presented for better understanding their enhancements on the deformation effects. Space convergence related to the spherical DWS base is confirmed for the D-RHFB model by taking light nucleus $^{24}$Mg and mid-heavy one $^{156}$Sm as candidates. Compared to light nuclei, extraordinary more negative energy states are necessitated to keep the expansion completeness on the spherical DWS base for mid-heavy and heavy nuclei, due to the enhanced correlations between the expansion components with large $\kappa$-quantity as indicated by the nature of the $\pi$-PV and $\rho$-T couplings. Furthermore, because of the enhanced deformation effects by the $\pi$-PV and $\rho$-T couplings, the RHF Lagrangian PKA1 presents deeper bound ground state for $^{24}$Mg than the other selected Lagrangians, in addition to predicting a fairly deep bound local minimum with large oblate deformation., Comment: 27 pages, 4 figures and 2 tables

In the framework of Thomas-Fermi approximation, we study systematically the EOSs and microscopic structures of neutron star matter in a vast density range with $n_\mathrm{b}\approx 10^{-10}$-2 $\mathrm{fm}^{-3}$, where various covariant density functionals are adopted, i.e., those with nonlinear self couplings (NL3, PK1, TM1, GM1, MTVTC) and density-dependent couplings (DD-LZ1, DDME-X, PKDD, DD-ME2, DD2, TW99). It is found that the EOSs generally coincide with each other at $n_\mathrm{b}\lesssim 10^{-4}$ fm${}^{-3}$ and 0.1 fm${}^{-3}\lesssim n_\mathrm{b} \lesssim 0.3$ fm${}^{-3}$, while in other density regions they are sensitive to the effective interactions between nucleons. By adopting functionals with larger slope of symmetry energy $L$, the curvature parameter $K_\mathrm{sym}$ and neutron drip density generally increase, while the droplet size, proton number of nucleus, core-crust transition density, and onset density of non-spherical nuclei decrease. All functionals predict neutron stars with maximum masses exceeding the two-solar-mass limit, while those of DD2, DD-LZ1, DD-ME2, and DDME-X predict optimum neutron star radii according to the observational constraints. Nevertheless, the corresponding skewness coefficients $J$ are much lager than expected, while only the functionals MTVTC and TW99 meet the start-of-art constraints on $J$. More accurate measurements on the radius of PSR J0740+6620 and the maximum mass of neutron stars are thus essential to identify the functional that satisfies all constraints from nuclear physics and astrophysical observations. Approximate linear correlations between neutron stars' radii at $M=1.4 M_{\odot}$ and $2 M_{\odot}$, the slope $L$ and curvature parameter $K_\mathrm{sym}$ of symmetry energy are observed as well, which is mainly attributed to the curvature-slope correlations in the functionals adopted here., Comment: The EOS tables can be found at: teacher.yzu.edu.cn/CJXia/en/lwcg/492393/content/79242.htm

Properties of the liquid-gas (LG) phase transition of thermal nuclear matter are investigated within the relativistic Hartree-Fock (RHF) theory, focusing on the role played by the in-medium balance between nuclear attraction and repulsion. Applying the RHF Lagrangian PKA1, rather different critical properties and LG phase diagrams are obtained in contrast to the other popular relativistic Lagrangians. Aiming at such notable model deviations, a series of testing parametrizations $x{\ensuremath{\kappa}}_{\ensuremath{\rho}}$ (${\ensuremath{\kappa}}_{\ensuremath{\rho}}$ being the $\ensuremath{\rho}$-tensor coupling strength) are proposed to bridge PKA1 and other popular Lagrangians. Along the systematics from PKA1 to the $x{\ensuremath{\kappa}}_{\ensuremath{\rho}}$ series and further to other popular Lagrangians, it is illustrated that the in-medium balance of nuclear attraction and repulsion, manifested as various modeling of the nuclear in-medium effects, is essential for the van der Waals-like behaviors of thermal nuclear matter, in which the residual nuclear in-medium effects deduced from the dominant attractive and repulsive channels play a significant role. Our study paves a way to model the in-medium nuclear interactions from the thermal statistic aspects of nuclear systems, e.g., referring to the critical temperature from future delicate experiments.

The framework of the random-phase approximation (RPA) based on the relativistic Hartree-Fock (RHF) theory is extended to achieve a self-consistent calculation with the $\ensuremath{\rho}$-meson tensor coupling. The model self-consistency is verified by the check of the isobaric analog state, and it is found that the $\ensuremath{\rho}$-tensor and $\ensuremath{\rho}$-vector-tensor couplings play significant roles in maintaining the self-consistency. Using the RHF Lagrangian PKA1, the properties of the Gamow-Teller resonances (GTR) are investigated, in which the roles played by the particle-hole residual interaction of various meson-nucleon couplings are clarified in details. Furthermore, the effects of the tensor force, which is introduced naturally via the Fock terms, are analyzed by comparing the calculations with full Lagrangians and the ones artificially dropping the tensor force components. It is found that for the RHF Lagrangians $\mathrm{PKO}i$ $(i=1,2,3)$ and PKA1, the tensor forces play the role mainly via the RHF mean field rather than via the RPA residual interaction in determining the GTR. Moreover, the tensor-force effects are not as strong as those indicated by the Skyrme Hartree-Fock calculations.

Axially deformed relativistic Hartree-Fock (RHF) model with density-dependent meson-nucleon couplings is established in this work, in which the integrodifferential Dirac equations are solved by expanding the Dirac spinor on the spherical Dirac Woods-Saxon base. Using the RHF Lagrangians $\mathrm{PKO}i$ ($i=1,2,3$), the reliability of the method has been illustrated by taking the light $^{20}\mathrm{Ne}$, midheavy $^{56}\mathrm{Fe}$, and heavy Pb isotopes as examples. As a preliminary application, the systematic study of $^{20}\mathrm{Ne}$ shows that PKO1 and PKO3, which contain the $\ensuremath{\pi}$-pseudovector ($\ensuremath{\pi}$-PV) coupling, improve the description of the binding energy of $^{20}\mathrm{Ne}$, as compared to PKO2 and the selected RMF Lagrangian. Moreover, it is found that the tensor force components carried by the $\ensuremath{\pi}$-PV coupling can present substantial effects in determining the shape evolution of nucleus.

We study the $K^0_S-K^0_L$ asymmetries and $CP$ violations in charm-baryon decays with neutral kaons in the final state. The $K^0_S-K^0_L$ asymmetry can be used to search for two-body doubly Cabibbo-suppressed amplitudes of charm-baryon decays, with the one in $\Lambda^+_c\to pK^0_{S,L}$ as a promising observable. Besides, it is studied for a new $CP$-violation effect in these processes, induced by the interference between the Cabibbo-favored and doubly Cabibbo-suppressed amplitudes with the neutral kaon mixing. Once the new CP-violation effect is determined by experiments, the direct $CP$ asymmetry in neutral kaon modes can then be extracted and used to search for new physics. The numerical results based on $SU(3)$ symmetry will be tested by the experiments in the future., Comment: 15 pages, 3 tables. Version published in JHEP

The tensor-force effects on the evolution of the spin-orbit splittings in the neutron drops are investigated within the framework of the relativistic Hartree-Fock theory. For fair comparisons on the pure mean-field level, the results of the relativistic Brueckner-Hartree-Fock calculation with the Bonn A interaction are adopted as meta-data. Through a quantitative analysis, we certify that the $\pi$-pseudovector ($\pi$-PV) coupling affects the evolutionary trend through the tensor force embedded. The strength of the tensor force is explored by enlarging the strength $f_{\pi}$ of the $\pi$-PV coupling. It is found that weakening the density dependence of $f_{\pi}$ is slightly better than enlarging it with a factor. We thus provide a semiquantitative support for the \textit{renormalization persistency} of the tensor force within the framework of density functional theory. This will serve as an important guidance for the further development of the relativistic effective interactions with particular focus on the tensor force., Comment: 9 pages, 4 figures, 2 tables

Nuclear $\ensuremath{\beta}$ decay is a key process to understand the origin of heavy elements in the universe, while the accuracy is far from satisfactory for the predictions of $\ensuremath{\beta}$-decay half-lives by nuclear models to date. In this work, we pave a novel way to accurately predict $\ensuremath{\beta}$-decay half-lives with the machine learning based on the Bayesian neural network, in which the known physics has been explicitly embedded, including the ones described by the Fermi theory of $\ensuremath{\beta}$ decay, and the dependence of half-lives on pairing correlations and decay energies. The other potential physics, which is not clear or even missing in nuclear models nowadays, will be learned by the Bayesian neural network. The results well reproduce the experimental data with a very high accuracy and further provide reasonable uncertainty evaluations in half-life predictions. These accurate predictions for half-lives with uncertainties are essential for the $r$-process simulations.

Restoration of pseudo-spin symmetry (PSS) along the $N=32$ and $34$ isotonic chains and the physics behind are studied by applying the relativistic Hartree-Fock theory with effective Lagrangian PKA1. Taking the proton pseudo-spin partners $(\pi2s_{1/2},\pi1d_{3/2})$ as candidates, systematic restoration of PSS along both isotonic chains is found from sulphur (S) to nickel (Ni), while distinct violation from silicon (Si) to sulphur is discovered near the drip lines. The effects of the tensor-force components introduced naturally by the Fock terms are investigated, which can only partly interpret the systematics from calcium to nickel, but fail for the overall trends. Further analysis following the Schr\"{o}dinger-like equation of the lower component of Dirac spinor shows that the contributions from the Hartree terms dominate the overall systematics of the PSS restoration, and such effects can be self-consistently interpreted by the evolution of the proton central density profiles along both isotonic chains. Specifically the distinct PSS violation is found to tightly relate with the dramatic changes from the bubble-like density profiles in silicon to the central-bumped ones in sulphur., Comment: 4 figures, to be published in Chinese Physics C

Nuclear structure models built from phenomenological mean fields, the effective nucleon-nucleon interactions (or Lagrangians), and the realistic bare nucleon-nucleon interactions are reviewed. The success of covariant density functional theory (CDFT) to describe nuclear properties and its influence on Brueckner theory within the relativistic framework are focused upon. The challenges and ambiguities of predictions for unstable nuclei without data or for high-density nuclear matter, arising from relativistic density functionals, are discussed. The basic ideas in building an ab initio relativistic density functional for nuclear structure from ab initio calculations with realistic nucleon-nucleon interactions for both nuclear matter and finite nuclei are presented. The current status of fully self-consistent relativistic Brueckner-Hartree-Fock (RBHF) calculations for finite nuclei or neutron drops (ideal systems composed of a finite number of neutrons and confined within an external field) is reviewed. The guidance and perspectives towards an ab initio covariant density functional theory for nuclear structure derived from the RBHF results are provided., 67 pages, 26 figures, version accepted for publication in "Progress in Particleand Nuclear Physics"

Using the relativistic Hartree–Fock Lagrangian PKA1, we investigate the properties of the exotic nucleus 48Si, which is predicted to be an atypical nucleus characterized by i) the onset of doubly magicity, ii) its location at the drip line, iii) the presence of dual semi-bubble structure (distinct central depletion in both of neutron and proton density profiles) in the ground state, and iv) the occurrence of pairing reentrance at finite temperature. While not being new for each, these phenomena are found to simultaneously occur in 48Si. For instance, the dual semi-bubble structure reduces the spin–orbit splitting of low-ℓ orbitals and upraises the s orbitals, leading therefore to distinct N=34 and Z=14 magic shells in 48Si. Consequently, the doubly magicities provide extra stability for such extreme neutron-rich system at the drip line. Associating with the neutron shell N=34 and continuum above, the pairing correlations are reengaged interestingly at finite temperature. Theoretical nuclear modelings are known to be poorly predictive in general, and we asset our confidence in the prediction of our modeling on the fact that the predictions of PKA1 in various regions of the nuclear chart have systematically been found correct and more specifically in the region of pf shell. Whether our predictions are confirmed or not, 48Si provides a concrete benchmark for the understanding of the nature of nuclear force. Keywords: New magicity, Drip-line nucleus, Bubble-like structure, Pairing reentrance

The mechanism that restores the pseudo-spin symmetry (PSS) are investigated under the relativistic Hartree-Fock (RHF) approach, by focusing on the in-medium balance between nuclear attractive and repulsive interactions. It is illustrated that the modelings of both the equilibrium of nuclear dynamics and the in-medium effects can be essentially changed by the $\rho$-tensor coupling that play the role almost fully via the Fock terms, from which the model discrepancy on the PSS restoration is verified. Specifically, the largely different density-dependent behaviors of the isoscalar coupling strengths $g_\sigma$ and $g_\omega$, deduced from the parametrization of the RHF Lagrangian PKA1, play an essential role in restoring the PSS of the high-$l'$ pseudo-spin doublets around the Fermi levels. Qualitatively, a guidance is provided for the modelings of both the equilibrium of nuclear dynamics and the in-medium effects via the PSS restoration., Comment: 3 figures and 2 tables

The formation of new shell gaps in intermediate mass neutron-rich nuclei is investigated within the relativistic Hartree-Fock-Bogoliubov theory, and the role of the Lorentz pseudo-vector and tensor interactions is analyzed. Based on the Foldy-Wouthuysen transformation, we discuss in detail the role played by the different terms of the Lorentz pseudo-vector and tensor interactions in the appearing of the $N=16$, 32 and 34 shell gaps. The nuclei $^{24}$O, $^{48}$Si and $^{52,54}$Ca are predicted with a large shell gap and zero ($^{24}$O, $^{52}$Ca) or almost zero ($^{48}$Si, $^{54}$Ca) pairing gap, making them candidates for new magic numbers in exotic nuclei. We find from our analysis that the Lorentz pseudo-vector and tensor interactions induce very specific evolutions of single-particle energies, which could clearly sign their presence and reveal the need for relativistic approaches with exchange interactions., 7 pages, 5 figures, 1 table

The relativistic mean field (RMF) model has achieved great success in describing various nuclear phenomena. However, several serious defects are common. For instance, the pseudo-spin symmetry of high-l orbits is distinctly violated in general, leading to spurious shell closures and . This leads to problems in describing structure properties, including shell structures, nuclear masses, etc. Guided by the pseudo-spin symmetry restoration [Geng et al., Phys. Rev. C, 100: 051301 (2019)], a new RMF Lagrangian DD-LZ1 is developed by considering the density-dependent meson-nucleon coupling strengths. With the newly obtained RMF Lagrangian DD-LZ1, satisfactory descriptions can be obtained for the bulk properties of nuclear matter and finite nuclei. In particular, significant improvements on describing the single-particle spectra are achieved by DD-LZ1. In particular, the spurious shell closures and , commonly found in previous RMF calculations, are eliminated by the new effective interaction DD-LZ1, and consistently the pseudo-spin symmetry (PSS) around the Fermi levels is reasonably restored for both low-l and high-l orbits. Moreover, the description of nuclear masses is also notably improved by DD-LZ1, as compared to the other RMF Lagrangians.

The hypernuclear matter is studied within the relativistic Hartree-Fock theory employing several parametrizations of the hypernuclear density functional with density-dependent couplings. The equations of state and compositions of hypernuclear matter are determined for each parametrization and compact stars are constructed by solving their structure equations in spherical symmetry. We quantify the softening effect of Fock terms on the equation of state, as well as discuss the impact of tensor interactions, which are absent in the Hartree theories. Starting from models of density functionals which are fixed in the nuclear sector to the nuclear phenomenology, we vary the couplings in the hyperonic sector around the central values which are fitted to the hyperon potentials in nuclear matter. We use the SU(6) spin-flavor and SU(3) flavor symmetric quark models to relate the hyperonic couplings to the nucleonic ones. We find, consistent with previous Hartree studies, that for the SU(6) model the maximal masses of compact stars are below the two-solar mass limit. In the SU(3) model we find sufficiently massive compact stars with cores composed predominantly of $\Lambda$ and $\Xi$ hyperons and a low fraction of leptons (mostly electrons). The parameter space of the SU(3) model is identified where simultaneously hypernuclear compact stars obey the astrophysical limits on pulsar masses and the empirical hypernuclear potentials in nuclear matter are reproduced., Comment: v2: 22 pages, 14 figures, minor changes and clarifications, matches published version

Tensor force is identified in each meson-nucleon coupling in the relativistic Hartree-Fock theory. It is found that all the meson-nucleon couplings, except the $\sigma$-scalar one, give rise to the tensor force. The effects of tensor force on various nuclear properties can now be investigated quantitatively, which allows fair and direct comparisons with the corresponding results in the non-relativistic framework. The tensor effects on nuclear binding energies and the evolutions of the $Z,\,N = 8,\,20$, and $28$ magic gaps are studied. The tensor contributions to the binding energies are shown to be tiny in general. The $Z,\,N = 8$ and $20$ gaps are sensitive to the tensor force, but the $Z,\,N = 28$ gaps are not., Comment: 21 pages, 9 figures, 6 tables

The structure of low-lying excitation states of even–even N = 40 isotones is studied using a five-dimensional collective Hamiltonian with the collective parameters determined from the relativistic mean-field plus BCS method with the PC-PK1 functional in the particle-hole channel and a separable paring force in the particle–particle channel. The theoretical calculations can provide a reasonable description not only for the systematics of the low-lying states along the isotonic chain but also for the detailed structure of the spectroscopy in a single nucleus. We find a picture of spherical-oblate-prolate shape transition along the isotonic chain of N = 40 by analyzing the potential energy surfaces. The coexistence of low-lying excited states has also been shown to be a common feature in neutron-deficient N = 40 isotones.

Several topics on the isospin properties of nuclear matter studied within the density-dependent relativistic Hartree-Fock theory are summarized. In detail, the effects of the Fock terms on the nuclear symmetry energy are listed, including the extra enhancement from the Fock terms of the isoscalar meson-nucleon coupling channels, the extra hyperon-induced suppression effect originating from the Fock channel, self-consistent tensor effects embedded automatically in the Fock diagrams, the enhanced density-dependent isospin-triplet potential part of the symmetry energy at high densities, a reduced kinetic symmetry energy at supranuclear density and so on. The results demonstrate the importance of the Fork diagram, especially from the isoscalar mesonnucleon coupling channels, on the isospin properties of the in-medium nuclear force.

The occurrence of the bubble-like structure has been studied, in the light of pseudospin degeneracy, within the relativistic Hartree-Fock-Bogoliubov (RHFB) theory. It is concluded that the charge/neutron bubble-like structure is predicted to occur in the mirror system of {$^{34}\mathrm{Si},\phantom{\rule{0.16em}{0ex}}^{34}\mathrm{Ca}$} commonly by the selected Lagrangians, due to the persistence of $Z(N)=14$ subshell gaps above which the $\ensuremath{\pi}(\ensuremath{\nu})2{s}_{1/2}$ states are not occupied. However, for the popular candidate $^{46}\mathrm{Ar}$, the RHFB Lagrangian PKA1 does not support the occurrence of the bubble-like structure in the charge (proton) density profiles, due to the almost degenerate pseudospin doublet ${\ensuremath{\pi}2{s}_{1/2},\ensuremath{\pi}1{d}_{3/2}}$ and coherent pairing effects. The formation of a semibubble in heavy nuclei is less possible as a result of small pseudospin-orbit (PSO) splitting, while it tends to appear at $Z=120$ superheavy systems which coincides with large PSO splitting of the doublet ${\ensuremath{\pi}3{p}_{3/2},\ensuremath{\pi}2{f}_{5/2}}$ and couples with significant shell effects. Pairing correlations, which can work against bubble formation, significantly affect the PSO splitting. Furthermore, we found that the influence on semibubble formation due to different types of pairing interactions is negligible. The quenching of the spin-orbit splitting in the $p$ orbit has been also stressed, and it may be considered the hallmark for semibubble nuclei.

The recent progress of the relativistic many-body approach by the group at Peking University will be reviewed. In particular, axially deformed relativistic Hartree-Bogoliubov approach in Woods-Saxon basis aiming at halo nucleus, time-odd triaxial RMF approach, the adiabatic and configuration-fixed constrained triaxial RMF approaches, a Reflection ASymmetric RMF (RAS-RMF) approach, and a new relativistic Hartree-Fock (RHF) approach with density-dependent σ,ω,ρ and π meson-nucleon couplings for finite nuclei and nuclear matter, will be highlighted.

Background: The relativistic Hartree-Fock-Bogoliubov (RHFB) theory has recently been developed and it provides a unified and highly predictive description of both nuclear mean field and pairing correlations. Ground state properties of finite nuclei can accurately be reproduced without neglecting exchange (Fock) contributions. Purpose: Finite-temperature RHFB (FT-RHFB) theory has not yet been developed, leaving yet unknown its predictions for phase transitions and thermal excitations in both stable and weakly bound nuclei. Method: FT-RHFB equations are solved in a Dirac Woods-Saxon (DWS) basis considering two kinds of pairing interactions: finite or zero range. Such a model is appropriate for describing stable as well as loosely bound nuclei since the basis states have correct asymptotic behaviour for large spatial distributions. Results: Systematic FT-RH(F)B calculations are performed for several semi-magic isotopic/isotonic chains comparing the predictions of a large number of Lagrangians, among which are PKA1, PKO1 and DD-ME2. It is found that the critical temperature for a pairing transition generally follows the rule $T_c = 0.60\Delta(0)$ for a finite-range pairing force and $T_c = 0.57\Delta(0)$ for a contact pairing force, where $\Delta(0)$ is the pairing gap at zero temperature. Two types of pairing persistence are analysed: type I pairing persistence occurs in closed subshell nuclei while type II pairing persistence can occur in loosely bound nuclei strongly coupled to the continuum states. Conclusions: This first FT-RHFB calculation shows very interesting features of the pairing correlations at finite temperature and in finite systems such as pairing re-entrance and pairing persistence., Comment: 13 pages, 11 figures, accepted version in Phys. Rev. C

With the relativistic representation of the nuclear tensor force that is included automatically by the Fock diagrams, we explored the self-consistent tensor effects on the properties of a nuclear matter system. The analysis was performed within the density-dependent relativistic Hartree-Fock (DDRHF) theory. The tensor force is found to notably influence the saturation mechanism, the equation of state, and the symmetry energy of nuclear matter, as well as the neutron star properties. Without introducing any additional free parameters, the DDRHF approach is a natural way to reveal the tensor effects on the nuclear matter system.

The recent progress of the relativistic many-body approach by the group at Peking University will be reviewed. In particular, the adiabatic and configuration-fixed constrained triaxial RMF approaches, triaxial RMF approach with time-odd components, a Shell-model-Like APproach (SLAP), a Reflection ASymmetric RMF (RAS-RMF) approach, and a new relativistic Hartree-Fock (RHF) approach with density-dependent σ, ω, ρ and π meson-nucleon couplings for finite nuclei and nuclear matter, will be highlighted.

The pseudo-spin symmetry (PSS) is investigated in the density-dependent relativistic Hartree-Fock theory by taking {the} doubly magic nucleus $^{132}$Sn as a representative. It is found that the Fock terms bring significant contributions to the pseudo-spin orbital potentials (PSOP) and make it comparable to the pseudo-centrifugal barrier (PCB). However, these Fock terms in the PSOP are counteracted by other exchange terms due to the non-locality of the exchange potentials. The pseudo-spin orbital splitting indicates that the PSS is preserved well for the partner states $\lrb{\nu 3s_{1/2}, \nu2d_{3/2}}$ of $^{132}$Sn in the relativistic Hartree-Fock theory., Comment: 6 figues

Half-life of proton radioactivity of spherical proton emitters is studied within the scheme of covariant density functional (CDF) theory, and for the first time the potential barrier that prevents the emitted proton is extracted with the similarity renormalization group (SRG) method, in which the spin-orbit potential along with the others that turn out to be non-negligible can be derived automatically. The spectroscopic factor that is significant is also extracted from the CDF calculations. The estimated half-lives are found in good agreement with the experimental values, which not only confirms the validity of the CDF theory in describing the proton-rich nuclei, but also indicates the prediction power of present approach to calculate the half-lives and in turn to extract the structural information of proton emitters., 6 pages, 2 figures

Recent works on the relativistic description of exotic nuclei and nuclear matter at extreme conditions are reviewed. New parameter sets for the Lagrangian density in the relativistic mean field (RMF) theory, PK1, PK1r, and PKDD are proposed with the center-of-mass correction included in a microscopic way. The density-dependences of effective interactions in RMF for nuclear matter and neutron stars are discussed. They are able to provide an excellent description not only for the properties of nuclear matter and neutron stars, but also for the nuclei near or far from the beta-stability line, including halos and giant halos at the neutron drip line in nuclei and hypernuclei. As a step toward the investigation of deformed nuclei close to the drip line, the Woods-Saxon basis has been suggested to replace the widely used harmonic oscillator basis for solving the RMF equations. Based on the two-neutron separation energy, shell correction energy, and effective pairing gaps, etc., new magic numbers for superheavy nuclei are suggested.

The origin of the nuclear tensor interaction in the covariant energy density functional (EDF) is presented in this work, associated with the Fock diagrams of Lorentz scalar and vector couplings. With this newly obtained relativistic formalism of the nuclear tensor interaction, more distinct tensor effects are found in the Fock diagrams of the Lorentz scalar and vector couplings, as compared to the Lorentz pseudo-vector and tensor channels. A unified and self-consistent treatment on both the nuclear tensor and spin-orbit interactions, which dominate the spin-dependent features of the nuclear force, is then achieved by the relativistic models. Moreover, careful analysis on the tensor strengths indicates the reliability of the nuclear tensor interaction in the covariant EDF for exploring the nuclear structure, excitation and decay modes., 5 pges, 3 figures

International audience; The occurrence of the spherical shell closures in superheavy nuclear systems is explored within the relativistic Hartree-Fock-Bogoliubov (RHFB) theory with density- dependent meson-nucleon couplings. We use the two-nucleon gaps δ2n(p) and pairing gaps Δv(π) to characterize the shell effects. The results depend slightly on the forces used, but the general set of magic numbers beyond 208Pb are Z = 120, 138 and N = 172, 184, 228 and 258. Our calculations are in favor of the nuclide 304120 as the next spherical doubly magic nucleus. Combined with the bulk properties of symmetric matter, we find that the shell effects are sensitive to the values of both scalar mass and effective mass. These two masses essentially determine the spin-orbit splittings and single-particle level density, respectively. Furthermore, the breaking of relativistic pseudo-spin symmetry influences the level structure and the occurrence of closed shells.

Institute of Modern Physics, Chinese Academy of Science, Lanzhou 730000, China(Dated: January 10, 2014)The odd-even staggerings (OES) on nuclear binding energies are studied systematically within the covariantdensity functional (CDF) theories, specifically the relativistic Hartree-Fock-Bogoliubov (RHFB) and the rela-tivistic Hartree-Bogoliubov (RHB) theories. Taking the finite-range Gogny force D1S as an e ective pairinginteraction, both CDF models can provide appropriate descriptions on the OESs of nuclear binding energies forC, O, Ca, Ni, Zr, Sn, Ce, Gd and Pb isotopes as well as for N = 50 and 82 isotones. However, due to the in-consistence between the non-relativistic pairing interaction and the relativistic e ective Lagrangians, there existsome systematical discrepancies from the data, i.e., the underestimated OESs in light C and O isotopes and theoverestimated ones in heavy region, respectively. Such discrepancies can be eliminated partially by introducinga Z- or N-dependent strength factor into the pairing force Gogny D1S. In addition, successful descriptions ofthe occupation numbers of Sn isotopes are achieved with the optimized Gogny pairing force. Furthermore, theanalysis of the systematics of both pairing e ects and nuclear binding energy indicate the requirement of anunified relativistic mechanism in both p-p and p-h channels to improve the quantitative precision of the theory.

Tensor effects on the N=40 gap evolution of N=40 isotones are studied by employing the Skyrme-Hartree-Fock-Bogoliubov (SHFB) and relativistic Hartree-Fock-Bogoliubov (RHFB) theories. The results with and without the inclusion of the tensor component are compared with the experimental data. When the tensor force is included, both of the two different approaches are found to give the same trend and agree with the experimental one, which indicates the necessity of introducing the tensor force in the evolution of N=40 subshell and on the other hand the reliability of the methods. Furthermore, it is shown that the gap evolution is primarily determined by the corresponding tensor contributions from $\pi$ and $\rho$-tensor coupling in the relativistic framework.

Within the relativistic Hartree-Fock-Bogoliubov (RHFB) theory, the structure properties of Carbon isotopes are systematically studied. In order to reproduce the experiment data, we take the finite-range Gogny D1S with a strength factor $f$ as the pairing force. The self-consistent RHFB calculations with density-dependent meson-nucleon couplings indicate the single-neutron halo structures in both $^{17}$C and $^{19}$C, whereas the two-neutron halo in $^{22}$C is not well supported. It is also found that close to the neutron drip line there exists distinct odd-even staggering on neutron radii, which is tightly related with the blocking effects and correspondingly the blocking effect plays a significant role in halo formation., Comment: 8 pages, 5 figures, 5 table

The $\beta$-decay half-lives of neutron-rich nuclei with $20 \leqslant Z \leqslant 50$ are systematically investigated using the newly developed fully self-consistent proton-neutron quasiparticle random phase approximation (QRPA), based on the spherical relativistic Hartree-Fock-Bogoliubov (RHFB) framework. Available data are reproduced by including an isospin-dependent proton-neutron pairing interaction in the isoscalar channel of the RHFB+QRPA model. With the calculated $\beta$-decay half-lives of neutron-rich nuclei a remarkable speeding up of $r$-matter flow is predicted. This leads to enhanced $r$-process abundances of elements with $A \gtrsim 140$, an important result for the understanding of the origin of heavy elements in the universe., Comment: 14 pages, 4 figures

Low-lying nuclear states of Sm isotopes are studied in the framework of a collective Hamiltonian based on covariant energy density functional theory. Pairing correlation are treated by both BCS and Bogoliubov methods. It is found that the pairing correlations deduced from relativistic Hartree-Bogoliubov (RHB) calculations are generally stronger than those by relativistic mean-field plus BCS (RMF+BCS) with same pairing force. By simply renormalizing the pairing strength, the diagonal part of the pairing field is changed in such a way that the essential effects of the off-diagonal parts of the pairing field neglected in the RMF+BCS calculations can be recovered, and consequently the low-energy structure is in a good agreement with the predictions of the RHB model., Comment: 5 figures, 5 pages

Motivated by recent observational data, the equations of state with the inclusion of strangeness-bearing $\Lambda$-hyperons and the corresponding properties of neutron stars are studied, based on the covariant density functional (CDF) theory. To this end, we specifically employ the density dependent relativistic Hartree-Fock (DDRHF) theory and the relativistic mean field theory (RMF). The inclusion of $\Lambda$-hyperons in neutron stars shows substantial effects in softening the equation of state. Because of the extra suppression effect originated from the Fock channel, large reductions on both the star mass and radius are predicted by the DDRHF calculations. It is also found that the mass-radius relations of neutron stars with $\Lambda$-hyperons determined by DDRHF with the PKA1 parameter set are in fairly good agreement with the observational data where a relatively small neutron stars radius is required. Therefore, it is expected that the exotic degrees of freedom such as the strangeness-bearing structure may appear and play significant roles inside the neutron stars, which is supported further by the systematical investigations on the consistency between the maximum neutron star mass and $\Lambda$-coupling strength., Comment: 3figures, 3 tables, 7pages

Nuclear halo structure and restoration of relativistic symmetry are studied within the framework of the relativistic Hartree-Fock-Bogoliubov (RHFB) theory. Giant halos as well as ordinary ones are found in Cerium isotopes close to the neutron drip line. Bridged by T=0 {channel}, the restoration of pseudo-spin symmetry (PSS) plays an essential role in stabilizing the neutron halo structures. The Fock terms, especially the $\rho$-tensor couplings, not only play significant role in the PSS restoration but also present substantial contributions to the T=0 {channel}, from which is well demonstrated the necessity of Fock terms., Comment: 5pages, 4figures, 1table

The spin symmetry in the Dirac negative energy spectrum and its origin are investigated for the first time within the density-dependent relativistic Hartree-Fock (DDRHF) theory. Taking the nucleus $^{16}$O as an example, the spin symmetry in the negative energy spectrum is found to be a good approximation and the dominant components of the Dirac wave functions for the spin doublets are nearly identical. In comparison with the relativistic Hartree approximation where the origin of spin symmetry lies in the equality of the scalar and vector potentials, in DDRHF the cancellation between the Hartree and Fock terms is responsible for the better spin symmetry properties and determines the subtle spin-orbit splitting. These conclusions hold even in the case when significant deviations from the G-parity values of the meson-antinucleon couplings occur., 13 pages, 7 figures, 1 table, accepted by Eur. Phys. J. A

The nucleus-nucleus interaction potential has been studied within the relativistic mean field theory. The systematics of the relativistic effects have been investigated by analyzing the relation between the potential and the bombarding energy as a function of the impact parameter. It is shown that the potential barriers are noticeably sensitive to the bombarding energy for a given impact parameter. At large bombarding energies the slope at the potential edge decreases with the impact parameter. Comparisons with a non-relativistic treatment shows that relativistic effects cannot be ignored at bombarding energies around and larger than 100 MeV/nucleon., Comment: 5 figures

Evolutions of single-particle energies and Z=64 sub-shell along the isotonic chain of N=82 are investigated in the density dependent relativistic Hartree-Fock (DDRHF) theory in comparison with other commonly used mean field models such as Skyrme HF, Gogny HFB and density dependent relativistic Hartree model (DDRMF). The pairing is treated in the BCS scheme, except for Gogny HFB. It is pointed out that DDRHF reproduces well characteristic features of experimental $Z$-dependence of both spin orbital and pseudo-spin orbital splittings around the sub-shell closure Z=64. Non-local exchange terms of the isoscalar $\sigma$ and $\omega$ couplings play dominant roles in the enhancements of the spin-orbit splitting of proton 2d states, which is the key ingredient to give the Z=64 sub-shell closure properly. On the other hand, the $\pi$ and $\rho$ tensor contributions for the spin-orbit splitting cancel each other and the net effect becomes rather small. The enhancement of the sub-shell gaps towards Z=64 is studied by the DDRHF, for which the local terms of the scalar and vector meson couplings are found to be important., Comment: 4 figures

The relativistic mean field theory cannot describe pion-induced effects because exchange terms are dropped. The relativistic Hartree-Fock (RHF) approach allows for the treatment of such effects. A density-dependent RHF model is presented and it is applied to the study of single-particle spectra along the chains of N=82 isotones and Z=SO isotopes. The effects of the pion-induced tensor interaction on these spectra are discussed.