Relativistic Effective Interaction Research Articles

Implementation of the quasiparticle finite amplitude method within the relativistic self-consistent mean-field framework (II): The program DIRQFAM v2.0.0

We describe the new version 2.0.0 of the code DIRQFAM that calculates the multipole response of even-even axially symmetric deformed nuclei using the framework of relativistic self-consistent mean-field models. The response is calculated by implementing the finite amplitude method for relativistic quasiparticle random phase approximation. In the new version, we have implemented the following features: (i) meson-exchange interactions, (ii) low-rank method for calculating induced densities and currents, (iii) generalized minimal residual method (GMRES), (iv) evaluation of the nucleon localization function, (v) extraction of the QRPA transition matrix elements and eigenfrequencies, (vi) evaluation of the H11 part of the induced Hamiltonian, (vii) multipole excitation operators up to J≤5 are now included. Program summaryProgram title:DIRQFAM v2.0.0CPC Library link to program files:https://doi.org/10.17632/6gv8nxg4ns.2Licensing provisions: GPLv3Programming language: Fortran 90.External routines/libraries: BLAS/LAPACK, version 3.1. or higher.Journal reference of previous version: A. Bjelčić, T. Nikšić, Comp. Phys. Comm. 253, 107184 (2020).Does the new version supersede the previous version?: YesNature of problem: Multipole response of deformed even-even open-shell nuclei can be calculated using the quasiparticle finite amplitude method (QFAM), based on the relativistic self-consistent mean-field models. The particle-hole channel is described by a zero-range relativistic effective interaction or interaction based on meson exchange, while the particle-particle channel of the effective inter-nucleon interaction is described by a separable finite-range pairing force. The method can be applied to perform systematic studies of collective modes even in heavy deformed nuclei.Solution method: The current implementation computes the multipole response by solving the QFAM equations in a self-consistent iteration scheme. At each iteration the QFAM solutions are updated using the GMRES method. The QFAM amplitudes are expanded in the simplex-y harmonic oscillator basis.Summary of revisions:1.meson-exchange interaction are included in the code;2.calculation of the nucleon localization function;3.extraction of the QRPA transition matrix elements and eigenfrequencies;4.evaluation of the H11 part of the induced Hamiltonian;5.multipoles excitation operators up to J≤5 are included;6.low-rank method for calculating induced densities and currents;7.generalized minimal residual method;8.dynamic memory allocation;9.reduced memory requirements;Additional comments including restrictions and unusual features: Open-shell even-even nuclei with parity conserved axially symmetric ground states are considered. An electric multipole operator with J≤5 is used to calculate the response function.

Exploring effects of tensor force and its strength via neutron drops * *Supported by National Natural Science Foundation of China (11905088, 11675065, 12075104), the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34000000), JSPS Grant-in-Aid for Early-Career Scientists (18K13549), JSPS Grant-in-Aid for JSPS Fellows (19J20543), and JSPS Grant-in-Aid for Scientific Research (S) (20H05648)

The tensor-force effects on the evolution of spin-orbit splittings in neutron drops are investigated within the framework of the relativistic Hartree-Fock theory. For a fair comparison 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 -pseudovector ( -PV) coupling affects the evolutionary trend through the embedded tensor force. The strength of the tensor force is explored by enlarging the strength of the -PV coupling. It is found that weakening the density dependence of is slightly better than enlarging it with a factor. We thus provide a semiquantitative support for the renormalization persistency of the tensor force within the framework of density functional theory. This will serve as important guidance for further development of relativistic effective interactions with particular focus on the tensor force.

Implementation of the quasiparticle finite amplitude method within the relativistic self-consistent mean-field framework: The program DIRQFAM

The DIRQFAM code calculates the multipole response of even–even axially symmetric deformed nuclei using the framework of relativistic self-consistent mean-field models. The response is calculated by implementing the finite amplitude method for relativistic quasiparticle random phase approximation. Program summaryProgram Title:DIRQFAMProgram Files doi:http://dx.doi.org/10.17632/6gv8nxg4ns.1Licensing provisions: GPLv3Programming language: Fortran 90/95, easily downgradable to FORTRAN 77.External routines/libraries: BLAS/LAPACK, version 3.6.0. or higher.Nature of problem: Multipole response of deformed even–even open-shell nuclei can be calculated using the quasiparticle finite amplitude method (QFAM), based on the relativistic self-consistent mean-field models. The particle–hole channel is described by a zero-range relativistic effective interaction, while the particle–particle channel of the effective inter-nucleon interaction is described by a separable finite-range pairing force. The method can be applied to perform systematic studies of collective modes even in heavy deformed nuclei.Solution method: The current implementation computes the multipole response by solving the QFAM equations in a self-consistent iteration scheme. At each iteration the QFAM solutions are updated using the modified Broyden’s method. The QFAM amplitudes are expanded in the simplex-y harmonic oscillator basis.Restrictions: Open-shell even–even nuclei with axially symmetric ground states are considered. An electric multipole operator with J≤3 is used to calculate the response function.Unusual features: The code should be recompiled before running it with different values of one of the following input parameters: number of oscillator shells in the expansion of nucleon spinors (n0f), number of Gauss–Hermite (NGH) or Gauss–Laguerre nodes (NGL), the multipolarity values that define the external perturbation operator (J_multipole, K_multipole).

New relativistic effective interaction for finite nuclei, infinite nuclear matter, and neutron stars

We carry out the study of finite nuclei, infinite nuclear matter, and neutron star properties with the newly developed relativistic force, the Institute of Physics Bhubaneswar-I (IOPB-I). Using this force, we calculate the binding energies, charge radii, and neutron-skin thickness for some selected nuclei. From the ground-state properties of superheavy nuclei ($Z=120$), it is noticed that considerable shell gaps appear at neutron numbers $N=172$, 184, and 198, manifesting the magicity at these numbers. The low-density behavior of the equation of state for pure neutron matter is compatible with other microscopic models. Along with the nuclear symmetry energy, its slope and curvature parameters at the saturation density are consistent with those extracted from various experimental data. We calculate the neutron star properties with the equation of state composed of nucleons and leptons in $\ensuremath{\beta}$-equilibrium, which are in good agreement with the x-ray observations by Steiner [Astrophys. J. 722, 33 (2010)] and N\"attil\"a [Astron. Astrophys. 591, A25 (2016)]. Based on the recent observation of GW170817 with a quasi-universal relation, Rezzolla et al. [Astrophys. J. Lett. 852, L25 (2018)] have set a limit for the maximum mass that can be supported against gravity by a nonrotating neutron star in the range $2.01\ifmmode\pm\else\textpm\fi{}0.04\ensuremath{\lesssim}M({M}_{\ensuremath{\bigodot}})\ensuremath{\lesssim}2.16\ifmmode\pm\else\textpm\fi{}0.03$. We find that the maximum mass of the neutron star for the IOPB-I parametrization is $2.15{M}_{\ensuremath{\bigodot}}$. The radius and tidal deformability of a canonical neutron star of mass $1.4{M}_{\ensuremath{\bigodot}}$ are 13.2 km and $3.9\ifmmode\times\else\texttimes\fi{}{10}^{36}\phantom{\rule{0.16em}{0ex}}\mathrm{g}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{2}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{2}$, respectively.

Spin-orbit interaction in relativistic nuclear structure models

Relativistic self-consistent mean-field (SCMF) models naturally account for the coupling of the nucleon spin to its orbital motion, whereas non-relativistic SCMF methods necessitate a phenomenological ansatz for the effective spin-orbit potential. Recent experimental studies aim to explore the isospin properties of the effective spin-orbit interaction in nuclei. SCMF models are very useful in the interpretation of the corresponding data, however standard relativistic mean-field and non-relativistic Hartree-Fock models use effective spin-orbit potentials with different isovector properties, mainly because exchange contributions are not treated explicitly in the former. The impact of exchange terms on the effective spin-orbit potential in relativistic mean-field models is analysed, and it is shown that it leads to an isovector structure similar to the one used in standard non-relativistic Hartree-Fock. Data on the isospin dependence of spin-orbit splittings in spherical nuclei could be used to constrain the isovector-scalar channel of relativistic mean-field models. The reproduction of the empirical kink in the isotope shifts of even Pb nuclei by relativistic effective interactions points to the occurrence of pseudospin symmetry in the single-neutron spectra in these nuclei.

Three-body model for an isoscalar spin-triplet neutron-proton pair inSb102

We discuss the isoscalar $T=0, S=1$ pairing correlation in the low-lying states of $^{102}{\rm Sb}={}^{100}{\rm Sn}+p+n$ nucleus. To this end, we employ ${\rm core}+p+n$ three-body model with the model space constructed by self-consistent mean-field calculations. The model is developed with both non-relativistic and relativistic effective interactions, the latter of which are found to be more realistic for the present case due to the pseudo-spin symmetry. It turns out that the $(L,S,T)=(0,1,0)$ pairing scheme is strongly hindered in $^{102}$Sb with the relativistic model because of the near degeneracy of the $g_{7/2}$ and $d_{5/2}$ orbitals in the valence space. This pair-breaking effect is clearly seen in the charge-exchange Gamow-Teller-type transitions rather than in the binding energies of $T=0$ and $T=1$ states.

Information and statistics: a new paradigm in theoretical nuclear physics

Theoretical predictions of physical observables often involve extrapolations to regions that are poorly constrained by laboratory experiments and astrophysical observations. Without properly quantified theoretical errors, such model predictions are of very limited utility. In this contribution we use maximum-likelihood estimation to compute theoretical errors and assess correlations between physical observables. We illustrate the power and elegance of these methods using examples of both pedagogical and realistic interest. In particular, we implement a Gaussian approximation to the likelihood function to develop a new relativistic effective interaction constrained by ground-state properties of finite nuclei, their monopole response, and masses of neutron stars.

Massive neutron stars with a hyperonic core: A case study with the IUFSU relativistic effective interaction

The recent discoveries of massive neutron stars, such as PSR J$0348+0432$ and PSR J$1614--2230$, have raised questions about the existence of exotic matter such as hyperons in the neutron star core. The validity of many established equations of states (EoSs) like GM1 and FSUGold are also questioned. We investigate the existence of hyperonic matter in the central regions of massive neutron stars by using relativistic mean field (RMF) theory with the recently proposed Indiana University Florida State University (IUFSU) model. The IUFSU model is extended by including hyperons to study the neutron star in $\ensuremath{\beta}$ equilibrium. The effect of different hyperonic potentials, namely $\ensuremath{\Sigma}$ and $\ensuremath{\Xi}$ potentials, on the EoS and hence the maximum mass of neutron stars has been studied. We have also considered the effect of stellar rotation since the observed massive stars are pulsars. It has been found that a maximum mass of $1.93{M}_{\ensuremath{\bigodot}}$, which is within the $3\ensuremath{\sigma}$ limit of the observed mass of PSR J$0348+0432$, can be obtained for rotating stars, with certain choices of the hyperonic potentials. The said star contains a fair amount of hyperons near the core.

DIRHB—A relativistic self-consistent mean-field framework for atomic nuclei

The DIRHB package consists of three Fortran computer codes for the calculation of the ground-state properties of even–even atomic nuclei using the framework of relativistic self-consistent mean-field models. Each code corresponds to a particular choice of spatial symmetry: the DIRHBS, DIRHBZ and DIRHBT codes are used to calculate nuclei with spherical symmetry, axially symmetric quadrupole deformation, and triaxial quadrupole shapes, respectively. Reflection symmetry is assumed in all three cases. The latest relativistic nuclear energy density functionals are implemented in the codes, thus enabling efficient and accurate calculations over the entire nuclide chart. Program summaryProgram title: DIRHB package (codes DIRHBS, DIRHBZ and DIRHBT)Catalogue identifier: AESN_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AESN_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: noneNo. of lines in distributed program, including test data, etc.: 44516No. of bytes in distributed program, including test data, etc.: 317161Distribution format: tar.gzProgramming language: Fortran 77.Computer: All computers.Operating system: All operating systems. The Makefiles are specific for a Unix OS and have to be modified for Windows.RAM: Depends on the imposed symmetry and number of oscillator shells. For the triaxial test case it takes 300 MB.Classification: 17.22.Nature of problem:Ground-state properties of even–even open-shell nuclei can be calculated using the framework of self-consistent mean-field models based on relativistic energy density functionals. The structure of arbitrary heavy nuclei with spherical symmetry, axially symmetric quadrupole deformation, and triaxial quadrupole shapes, is modeled using the latest zero- and finite-range relativistic effective interactions. The particle–particle channel of the effective inter-nucleon interaction is described by a separable finite-range pairing force.Solution method:The current implementation of the model computes the mean-field solution of the nuclear many-body problem for even–even open-shell spherical and quadrupole deformed nuclei. The codes are used to solve the stationary relativistic Hartree–Bogoliubov equations in a self-consistent iteration scheme. At each iteration the matrix elements of the equations are updated using the modified Broyden method or the linear mixing method. The single-nucleon wave functions are expanded in a basis of spherical, axially symmetric or triaxial harmonic oscillator, depending on the assumed symmetry of the nuclear shape. For calculations that constrain the shape to specific values of the deformation parameters, the augmented Lagrangian method is used.Restrictions:Time-reversal and reflection symmetries are assumed. Open-shell even–even spherical and quadrupole deformed nuclei are considered.Running time:Depends on the imposed symmetry and number of oscillator shells. For the test cases it runs from few seconds (spherical) up to few hours (triaxial).

Low-energy isovector and isoscalar dipole response in neutron-rich nuclei

The self-consistent random phase approximation (RPA), based on the framework of relativistic energy density functionals, is employed in the study of isovector and isoscalar dipole response in $^{68}$Ni, $^{132}$Sn, and $^{208}$Pb. The evolution of pygmy dipole states (PDS) in the region of low excitation energies is analyzed as a function of the density-dependence of the symmetry energy for a set of relativistic effective interactions. The occurrence of PDS is predicted in the response to both the isovector and isoscalar dipole operators, and its strength is enhanced with the increase of the symmetry energy at saturation and the slope of the symmetry energy. In both channels the PDS exhausts a relatively small fraction of the energy-weighted sum rule but a much larger percentage of the inverse energy-weighted sum rule. For the isovector dipole operator the reduced transition probability $B(E1)$ of the PDS is generally small because of pronounced cancellation of neutron and proton partial contributions. The isoscalar reduced transition amplitude is predominantly determined by neutron particle-hole configurations, most of which add coherently, and this results in a collective response of the PDS to the isoscalar dipole operator.

Relativistic effective interaction for nuclei, giant resonances, and neutron stars

Nuclear effective interactions are useful tools in astrophysical applications especially if one can guide the extrapolations to the extremes regions of isospin and density that are required to simulate dense, neutron-rich systems. Isospin extrapolations may be constrained in the laboratory by measuring the neutron skin thickness of a heavy nucleus, such as 208Pb. Similarly, future observations of massive neutron stars will constrain the extrapolations to the high-density domain. In this contribution we introduce a new relativistic effective interaction that is simultaneously constrained by the properties of finite nuclei, their collective excitations, and neutron-star properties. By adjusting two of the empirical parameters of the theory, one can efficiently tune the neutron skin thickness of 208Pb and the maximum neutron star mass. We illustrate this procedure in response to the recent interpretation of X-ray observations by Steiner, Lattimer, and Brown that suggests that the FSUGold effective interaction predicts neutron star radii that are too large and a maximum stellar mass that is too small. The new effective interaction is fitted to a neutron skin thickness in 208Pb of only R_n - R_p = 0.16 fm and a moderately large maximum neutron star mass of 1.94 Msun.

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.

Relativistic transport approach to collective nuclear dynamics

The isoscalar giant monopole resonance (ISGMR) and isovector giant dipole resonance (IVGDR) in finite nuclei are studied within the framework of a relativistic transport approach. Small-amplitude oscillations are analyzed with the relativistic Vlasov equation, i.e., neglecting nucleon collision terms. The excitation energies of ISGMR and IVGDR are obtained for spherical nuclei with various sets of Lagrangian parameters. In the case of $^{208}\mathrm{Pb}$ we study in detail the dependence of the monopole response on the effective mass and symmetry energy at saturation ${a}_{4}$ given by the used covariant effective interaction. We show that a reduced ${m}^{*}$ and a larger ${a}_{4}$ can compensate for the effect on the ISGMR energy centroid of a much larger compressibility modulus ${K}_{\mathit{nm}}$. The role of the symmetry energy is confirmed by the observation of reduced corrections for the more symmetric $^{90}\mathrm{Zr}$. This result is important for overcoming the conflicting determination of nuclear compressibility between nonrelativistic and relativistic effective interactions. For symmetry-energy dynamical effects, we analyze the influence of the inclusion of an effective isovector-scalar channel, \ensuremath{\delta}-meson field, with constant- and density-dependent couplings. We show that the \ensuremath{\delta}-meson contribution, keeping fixed the equilibrium ${a}_{4}$ value, leads to a reduction in the centroid energy of the ISGMR and IVGDR for $^{208}\mathrm{Pb}$. The same mechanism can account for the apparent paradox of a decrease of the frequency of a IVGDR mode in heavy nuclei (of volume type) even in presence of a larger ${a}_{4}$. All that in fact reveals the sensitivity of the ISGMR and IVGDR collective motions for neutron-rich systems on the slope (or pressure) of the symmetry energy at saturation. Density-dependent vertices do not much affect our conclusions. Following as a guidance the dispersion relations in nuclear matter, we see two main reasons for that: The smoothness of the density dependences around saturation and the presence of compensation effects coming from rearrangement terms.

Reaction Dynamics with Exotic Nuclei

AbstractWe review the new possibilities offered by the reaction dynamics of asymmetricheavy ion collisions, using stable and unstable beams. We show that it represents arather unique tool to probe regions of highly Asymmetric Nuclear Matter (ANM) incompressed as well as dilute phases, and to test the in-medium isovector interactionfor high momentum nucleons. The focus is on a detailed study of the symmetryterm of the nuclear Equation of State (EOS) in regions far away from saturationconditions but always under laboratory controlled conditions.Thermodynamic properties of ANM are surveyed starting from nonrelativisticand relativistic effective interactions. In the relativistic case the role of the isovectorscalar δ-meson is stressed. The qualitative new features of the liquid-gas phase tran-sition, ”diffusive” instability and isospin distillation, are discussed. The results ofab-initio simulations of n-rich, n-poor, heavy ion collisions, using stochastic isospindependent transport equations, are analysed as a function of beam energy and cen-trality. The isospin dynamics plays an important role in all steps of the reaction,from prompt nucleon emissions to the final fragments. The isospin diffusion is alsoof large interest, due to the interplay of asymmetry and density gradients. In rela-tivistic collisions, the possibility of a direct study of the covariant structure of theeffective nucleon interaction is shown. Results are discussed for particle production,collective flows and iso-transparency.Perspectives of further developments of the field, in theory as well as in experi-ment, are presented.

Asymmetry effects on nuclear fragmentation

We review the new possibilities offered by the reaction dynamics of asymmetric heavy-ion collisions, using stable and unstable beams. We show that it represents a rather unique tool to probe regions of highly asymmetric nuclear matter (ANM) in compressed as well as dilute phases, and to test the in-medium isovector interaction for high-momentum nucleons. The focus is on a detailed study of the symmetry term of the nuclear equation of state (EOS) in regions far away from saturation conditions but always under laboratory controlled conditions.Thermodynamic properties of ANM are surveyed starting from non-relativistic and relativistic effective interactions. In the relativistic case, the role of the isovector–scalar δ-meson is stressed. The qualitative new features of the liquid–gas phase transition, “diffusive” instability and isospin distillation, are discussed. The results of ab initio simulations of n-rich, n-poor, heavy-ion collisions, using stochastic isospin-dependent transport equations, are analyzed as a function of beam energy and centrality. The isospin dynamics plays an important role in all steps of the reaction, from prompt nucleon emissions to the final fragments. The isospin diffusion is also of large interest, due to the interplay of asymmetry and density gradients. In relativistic collisions, the possibility of a direct study of the covariant structure of the effective nucleon interaction is shown. Results are discussed for particle production, collective flows and isotransparency.Perspectives of further developments of the field, in theory as well as in experiment, are presented.

Nuclear effective forces and isotope shifts

Abstract Presently available relativistic and nonrelativistic effective interactions do not predict the same behavior for the isotope shifts in the Pb region. We analyze this difference and find that it is related to the characteristics of the spin-orbit term used in the parametrizations. We show that a simple modification of the spin-orbit contribution to the nonrelativistic Skyrme functional solves this problem.

Finite - Nuclei Properties in Relativistic Density Dependent Hartree - Fock Approach

Finite nucleus properties are studied in a relativistic effective interaction approach. Density dependent coupling constants of the meson-nucleon interactions are adopted to incorporate the relativistic Brueckner-Hartree-Fock results in the relativistic mean field (RMF) or relativistic Hartree-Fock (RHF) approach. It is desired to remedy the deficiencies of RMF and RHF without losing the features of the relativistic G matrix and at the same time retain the simplicity. The calculated ground state properties with the density dependent coupling constants are in a good agreement with experiment. The contribution of isovector mesons in RHF is discussed.

Isovector meson contribution in the relativistic Hartree-Fock approach for finite nuclei.

The properties of finite nuclei are studied in a relativistic effective interaction approach. Density dependent coupling constants of the meson-nucleon interactions are adopted to incorporate the Dirac Brueckner-Hartree-Fock (DBHF) results in the relativistic mean field (RMF) or relativistic Hartree-Fock (RHF) approach. It is desired to remedy the deficiencies of the RMF and RHF without losing the features of the relativistic G matrix and at the same time retain the simplicity. The importance of the nucleon correlations, which are expressed by density-dependent coupling constants, is studied and the contribution of isovector mesons is discussed. It is shown that the calculated ground state properties with the density-dependent coupling constants are in good agreement with experiment.

Comparison between relativistic and nonrelativistic models of the nucleon-nucleon effective interaction. I. Normal-parity isoscalar transitions

Relativistic density-dependent effective interactions for nucleon-nucleus scattering based upon a complete set of Lorentz-invariant NN amplitudes are used in calculations of elastic and inelastic scattering to normal-parity states of self-conjugate targets. Owing to distortion of Dirac spinors by the relativistic mean fields, the effective interaction appropriate for use in a Schr\odinger formalism incorporates relativistic density dependence, which is stronger for inelastic than elastic scattering. The dominant effect for normal-parity transitions is equivalent to a short-ranged repulsive contribution to the real central interaction that is proportional to density and nearly independent of energy. Pauli blocking of occupied intermediate states is included and gives results similar to the familiar Clementel-Villi damping of the absorptive potential. The relativistic effective interaction is compared with nonrelativistic G-matrix calculations and with empirical effective interactions fitted to data for proton elastic and inelastic scattering. Calculations for elastic and inelastic scattering are compared with data for 200, 318, and 500 MeV and we find that the agreement with data improves as the energy increases. The density dependence of the relativistic model is much stronger at low energies than either the G matrix or the empirical interaction; its repulsive contribution to the central interaction is too strong to give a good description of the data for 200 MeV. Near 500 MeV the relativistic interaction is closer to the empirical interaction and better agreement with the data is obtained, whereas the density dependence of nonrelativistic effective interactions is too small.

Relativistic Effective Interaction11The project supported by National Natural Science Foundation of China

In analogy with the idea of the effective interaction commonly used in the nonrelativistic approach, the relativistic effective interactions are adopted to incorporate the relativistic Brueckner-Hartree-Fock (RBHF) results in the relativistic mean field approach (RMF) or relativistic Hartree-Fock approach (RHF). It is desired to remedy the deficiencies of RMF and RHF without losing the features of the relativistic G matrix and at the same time retain the simplicity. The relativistic effective interactions are used to describe the ground state properties of nuclei and medium-energy nucleon-nucleus scattering in this paper.