Density-dependent Meson-nucleon Couplings Research Articles

Clustering in nuclei at finite temperature

We investigate the localization and clustering features in $^{20}$Ne ($N=Z$) and neutron-rich $^{32}$Ne nuclei at zero and finite temperatures. The finite temperature Hartree-Bogoliubov theory is used with the relativistic density-dependent meson-nucleon coupling functional DD-ME2. It is shown that clustering features gradually weaken with increasing temperature and disappear when the shape phase transition occurs. Considering thermal fluctuations in the density profiles, the clustering features vanish at lower temperatures, compared to the case without thermal fluctuations. The effect of the pairing correlations on the nucleon localization and the formation of cluster structures are also studied at finite temperatures. Due to the inclusion of pairing in the calculations, cluster structures are preserved until the critical temperatures for the shape phase transition are reached. Above the critical temperature of the shape phase transition, the clustering features suddenly disappear, which differs from the results without pairing.

Relativistic random-phase-approximation description of M1 excitations with the inclusion of π mesons

Based on the covariant density functional theory, the magnetic dipole ($M1$) resonance is described in the framework of relativistic random-phase approximation with density-dependent meson-nucleon coupling. The isovector-pseudovector interaction channel, represented by the exchange of $\ensuremath{\pi}$ meson, is included in the residual interaction to describe unnatural parity transitions. The strength distributions of $M1$ resonances are studied in doubly magic nuclei $^{48}\mathrm{Ca}$, $^{90}\mathrm{Zr}$, and $^{208}\mathrm{Pb}$, in comparison with their analog Gamow-Teller (GT) excitations. It is found that the $\ensuremath{\pi}$ meson and its zero-range counterterm are responsible for almost all of the energy shift caused by residual interaction, which is similar to the case of GT excitation. However, the strength of the counterterm suggested by the GT study is not suitable to simultaneously reproduce the experimental $M1$ peak energies from $^{48}\mathrm{Ca}$ to $^{208}\mathrm{Pb}$. To improve the descriptions of $M1$, effects caused by adjusting the strength of pionic counterterm and introducing the density dependence of the $\ensuremath{\pi}$ meson channel are explored. Finally, from the analyses of dominant transition configurations of GT and $M1$ resonance, we find that the proper spin-orbit splitting is the key to simultaneously reproduce the $M1$ strength distributions from light to heavy nuclei.

Relativistic Hartree-Fock model for axially deformed nuclei

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.

Novel relativistic mean field Lagrangian guided by pseudo-spin symmetry restoration * * Supported by National Natural Science Foundation of China (11675065, 11875152, 11905088), Fundamental Research Funds for the central universities (lzujbky-2019-11), and the Supercompuer Center of HIRFL

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.

Relativistic Mean-Field Models with Different Parametrizations of Density Dependent Couplings

Relativistic mean-field models are successfully used for the description of finite nuclei and nuclear matter. Approaches with density-dependent meson-nucleon couplings assume specific functional forms and a dependence on vector densities in most cases. In this work, parametrizations with a larger sample of functions and dependencies on vector and scalar densities are investigated. They are obtained from fitting properties of finite nuclei. The quality of the description of nuclei and the obtained equations of state of symmetric nuclear matter and neutron matter below saturation are very similar. However, characteristic nuclear matter parameters, the equations of state and the symmetry energy at suprasaturation densities show some correlations with the choice of the density dependence and functional form of the couplings. Conditions are identified that can lead to problems for some of the parametrizations.

Covariance analysis for energy density functionals and instabilities

We present the covariance analysis of two successful nuclear energy density functionals (EDFs), (i) a non-relativistic Skyrme functional built from a zero-range effective interaction, and (ii) a relativistic nuclear EDF based on density dependent meson–nucleon couplings. The covariance analysis is a useful tool for understanding the limitations of a model, the correlations between observables and the statistical errors. We show, for our selected test nucleus Pb, that when the constraint on a property A included in the fit is relaxed, correlations with other observables B become larger; on the other hand, when a strong constraint is imposed on A, the correlations with other properties become very small. We also provide a brief review, partly connected with the covariance analysis, of some instabilities displayed by several EDFs currently used in nuclear physics.

The symmetry energy, neutron skin thickness and isovector dipole response of neutron-rich nuclei

The isotopic evolution of the relationship between the symmetry energy at saturation density of nuclear matter (J ), neutron skin thickness (ΔR ) and relevant observables related to isovector dipole excitations in neutron rich 116−136 Sn isotopes has been investigated in the framework of relativistic nuclear energy density functional theory. The description employs a family of effective interactions with density dependent meson-nucleon couplings (DDME) spanning the range of values J = 30 − 38 MeV.

Description of carbon isotopes within relativistic Hartree-Fock-Bogoliubov theory

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.

Density-dependent deformed relativistic Hartree-Bogoliubov theory in continuum

The deformed relativistic Hartree-Bogoliubov theory in continuum with the density-dependent meson-nucleon couplings is developed. The formulism is briefly presented with the emphasis on handling the density-dependent couplings, meson fields, and potentials in axially deformed system with partial wave method. Taking the neutron-rich nucleus $^{38}$Mg as an example, the newly developed code is verified by the spherical relativistic continuum Hartree-Bogoliubov calculations, where only the spherical components of the densities are considered. When the deformation is included self-consistently, it is shown that the spherical components of density-dependent coupling strengths are dominant, while the contributions from low-order deformed components are not negligible.

Relativistic mean-field interaction with density-dependent meson-nucleon vertices based on microscopical calculations

Although ab-initio calculations of relativistic Brueckner theory lead to large scalar isovector fields in nuclear matter, at present, successful versions of covariant density functional theory neglect the interactions in this channel. A new high precision density functional DD-ME$\delta$ is presented which includes four mesons $\sigma$, $\omega$, $\delta$, and $\rho$ with density dependent meson-nucleon couplings. It is based to a large extent on microscopic ab-initio calculations in nuclear matter. Only four of its parameters are determined by adjusting to binding energies and charge radii of finite nuclei. The other parameters, in particular the density dependence of the meson-nucleon vertices, are adjusted to non-relativistic and relativistic Brueckner calculations of symmetric and asymmetric nuclear matter. The isovector effective mass $m_{p}^{\ast}-m_{n}^{\ast}$ derived from relativistic Brueckner theory is used to determine the coupling strength of the $\delta$-meson and its density dependence.

Finite temperature effects on monopole and dipole excitations

The relativistic random phase approximation based on effective Lagrangian with density dependent meson-nucleon couplings has been extended to finite temperature and employed in studies of multipole excitations within the temperature range T = 1 − 2 MeV. The model calculations showed that isoscalar giant monopole and isovector giant dipole resonances are only slightly modified with temperature, but additional transition strength appears at low energies because of thermal unblocking of single-particle orbitals close to the Fermi level. The analysis of low-lying states shows that isoscalar monopole response in 132Sn results from single particle transitions, while the isovector dipole strength for 60Ni, located around 10 MeV, is composed of several single particle transitions, accumulating a small degree of collectivity.

Description of the ground state of axially deformed nuclei within the Relativistic Hartree–Fock–Bogoliubov model

The Relativistic Hartree–Fock–Bogoliubov model for axially deformed nuclei (RHFBz) is presented. The model involves a phenomenological Lagrangian with density-dependent meson–nucleon couplings in the particle-hole channel and the central part of the Gogny force in the particle–particle channel. The RHFBz equations are solved by expansion in the basis of a deformed harmonic oscillator. Illustrative RHFBz calculations are performed for Neon isotopes.

Hadron-quark phase coexistence in a hybrid MIT-Bag model

The phase transition of hadronic to quark matter and the boundaries of the hadron-quark coexistence phase are studied within the two Equation of State (EoS) models. The relativistic effective mean-field approach with constant and density-dependent meson-nucleon couplings is used to describe hadronic matter, and the MIT-Bag model is adopted to describe quark matter. The boundaries of the mixed phase for different Bag constants are obtained solving the Gibbs equations. We notice that the dependence on the Bag parameter of the critical temperatures (at zero chemical potential) can be well reproduced by a fermion ultrarelativistic quark gas model, without contribution from the hadron part. At variance, the critical chemical potentials (at zero temperature) are very sensitive to the EoS of the hadron sector. Hence, the contribution of the hadronic interaction is much more relevant for the determination of the transition to the quark-gluon plasma at finite baryon density and low T . Moreover, in the low-temperature and finite chemical potential region no solutions of the Gibbs conditions are existing for small Bag-constant values, B < (135 MeV)4 . Isospin effects in asymmetric matter appear important in the high chemical-potential regions at lower temperatures, of interest for the inner-core properties of neutron stars and for heavy-ion collisions at intermediate energies.

Relativistic Hartree-Fock-Bogoliubov model for deformed nuclei

The Relativistic Hartree-Fock-Bogoliubov model for axially deformed nuclei (RHFBz) is introduced. The model is based on an effective Lagrangian with density-dependent meson-nucleon couplings in the particle-hole channel, and the pairing part of the Gogny force is used in the pairing channel. The RHFBz quasiparticle equations are solved by expansion in the basis of a deformed harmonic oscillator. Illustrative RHFBz calculations are performed for Carbon, Neon and Magnesium isotopes. The effect of the explicitly including the pion field is investigated for binding energies, deformation parameters, and charge radii.

Relativistic Hartree-Fock-Bogoliubov theory with density dependent meson-nucleon couplings

Relativistic Hartree-Fock-Bogoliubov (RHFB) theory with density-dependent meson-nucleon couplings is presented. The integro-differential RHFB equations are solved by expanding the different components of the quasi-particle spinors in the complete set of eigen-solutions of the Dirac equations with Woods-Saxon potentials. Using the finite-range Gogny force D1S as an effective interaction in the pairing channel, systematic RHFB calculations are performed for Sn isotopes and N=82 isotones. It is demonstrated that an appropriate description of both mean field and pairing effects can be obtained within RHFB theory with finite range Gogny pairing forces. Better systematics are also found in the regions from the stable to the neutron-rich side with the inclusion of Fock terms, especially in the presence of $\rho$-tensor couplings.

Finite- to zero-range relativistic mean-field interactions

We study the relation between the finite-range (meson-exchange) and zero-range (point-coupling) representations of effective nuclear interactions in the relativistic mean-field framework. Starting from the phenomenological interaction DD-ME2 with density-dependent meson-nucleon couplings, we construct a family of point-coupling effective interactions for different values of the strength parameter of the isoscalar-scalar derivative term. In the meson-exchange picture this corresponds to different values of the σ-meson mass. The parameters of the isoscalar-scalar and isovector-vector channels of the point-coupling interactions are adjusted to nuclear matter and ground-state properties of finite nuclei. By comparing results for infinite and semi-infinite nuclear matter, ground-state masses, charge radii, and collective excitations, we discuss constraints on the parameters of phenomenological point-coupling relativistic effective interaction.

Isospin-dependent properties of asymmetric nuclear matter in relativistic mean field models

Using various relativistic mean-field models, including nonlinear ones with meson field self-interactions, models with density-dependent meson-nucleon couplings, and point-coupling models without meson fields, we have studied the isospin-dependent bulk and single-particle properties of asymmetric nuclear matter. In particular, we have determined the density dependence of nuclear symmetry energy from these different relativistic mean-field models and compared the results with the constraints recently extracted from analyses of experimental data on isospin diffusion and isotopic scaling in intermediate energy heavy-ion collisions as well as from measured isotopic dependence of the giant monopole resonances in even-$A$ Sn isotopes. Among the 23 parameter sets in the relativistic mean-field model that are commonly used for nuclear structure studies, only a few are found to give symmetry energies that are consistent with the empirical constraints. We have also studied the nuclear symmetry potential and the isospin splitting of the nucleon effective mass in isospin asymmetric nuclear matter. We find that both the momentum dependence of the nuclear symmetry potential at fixed baryon density and the isospin splitting of the nucleon effective mass in neutron-rich nuclear matter depend not only on the nuclear interactions but also on the definition of the nucleon optical potential.

Structure of nuclei far from the stability in relativistic approach

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 sigma,omega,rho and pi meson-nucleon couplings for finite nuclei and nuclear matter, will be highlighted.

Calculation of β-decay rates in a relativistic model with momentum-dependent self-energies

The relativistic proton-neutron quasiparticle random phase approximation (PN-RQRPA) is applied in the calculation of \ensuremath{\beta}-decay half-lives of neutron-rich nuclei in the $Z\ensuremath{\approx}28$ and $Z\ensuremath{\approx}50$ regions. The study is based on the relativistic Hartree-Bogoliubov calculation of nuclear ground states, using effective Lagrangians with density-dependent meson-nucleon couplings, and also extended by the inclusion of couplings between the isoscalar meson fields and the derivatives of the nucleon fields. This leads to a linear momentum dependence of the scalar and vector nucleon self-energies. The residual QRPA interaction in the particle-hole channel includes the $\ensuremath{\pi}+\ensuremath{\rho}$ exchange plus a Landau-Migdal term. The finite-range Gogny interaction is employed in the $T=1$ pairing channel, and the model also includes a proton-neutron particle-particle interaction. The results are compared with available data, and it is shown that an extension of the standard relativistic mean-field framework to include momentum-dependent nucleon self-energies naturally leads to an enhancement of the effective (Landau) nucleon mass, and thus to an improved PN-QRPA description of ${\ensuremath{\beta}}^{\ensuremath{-}}$-decay rates.

Relativistic Hartree–Bogoliubov theory and the isospin dependence of the effective nuclear force

The role of the isospin dependence of the effective Lagrangian of the Relativistic Mean Field Theory (RMF) is investigated. The standard RMF density functional based on non-linear meson-exchange terms is extended to include density dependent meson–nucleon coupling constants. The new variation of the RMF, in which the isospin dependence enters in both isoscalar and isovector channels, provides improved description of the equation of state of neutron matter, better isovector properties of finite nuclei such as neutron skin thickness, more accurate nuclear masses and a consistent description of both isovector and isoscalar giant resonances.