Properties of collective flow and pion production in intermediate-energy heavy-ion collisions with a relativistic quantum molecular dynamics model

The relativistic mean-field approach was implemented in the Lanzhou quantum molecular dynamics transport model(LQMD.RMF). Using the LQMD.RMF, the properties of collective flow and pion production were investigated systematically for nuclear reactions with various isospin asymmetries. The directed and elliptic flows of the LQMD.RMF are able to describe the experimental data of STAR Collaboration. The directed flow difference between free neutrons and protons was associated with the stiffness of the symmetry energy, that is, a softer symmetry energy led to a larger flow difference. For various collision energies, the ratio between the π^(-) and π^(+) yields increased with a decrease in the slope parameter of the symmetry energy. When the collision energy was 270 MeV/nucleon, the single ratio of the pion transverse momentum spectra also increased with decreasing slope parameter of the symmetry energy in both nearly symmetric and neutron-rich systems.However, it is difficult to constrain the stiffness of the symmetry energy with the double ratio because of the lack of threshold energy correction on the pion production.

Study of the Alpha-Decay Chain for ^(194)Rn with Relativistic Mean-Field Theory

The structures of the nuclei on the alpha-decay chain of ^194Rn are investigated in the deformed relativistic mean-field theory with the effective interaction TMA. We put an emphasis on the ground state properties of ^194Rn. The calculated alpha-decay energies and lifetimes are both very close to the experimental data for ^186Pb and ^190Po. For ^194Rn, the deviations are a little large on both the alpha-decay energy and the lifetime. We also calculate the alpha-decay energies for the isotopes 192～208^Rn. The tendency for the change of the alpha-decay energies with neutron number is correctly reproduced in the relativistic mean-field theory （RMF）. In general, the RMF theory can give a good description of the alpha decay chain of ^194Rn.

Relativistic Consistent Angular-Momentum Projected Shell-Model： Relativistic Mean Field

We develop a relativistic nuclear structure model, relativistic consistent angular-momentum projected shell-model (RECAPS), which combines the relativistic mean-field theory with the angular-momentum projection method. In this new model, nuclear ground-state properties are first calculated consistently using relativistic mean-field (RMF) theory. Then angular momentum projection method is used to project out states with good angular momentum from a few important configurations. By diagonalizing the hamiltonian, the energy levels and wave functions are obtained. This model is a new attempt for the understanding of nuclear structure of normal nuclei and for the prediction of nuclear properties of nuclei far from stability. In this paper, we will describe the treatment of the relativistic mean field. A computer code, RECAPS-RMF, is developed. It solves the relativistic mean field with axial-symmetric deformation in the spherical harmonic oscillator basis. Comparisons between our calculations and existing relativistic mean-field calculations are made to test the model. These include the ground-state properties of spherical nuclei 16O and 208Pb, the deformed nucleus 20Ne. Good agreement is obtained.

Quantum Corrections on Relativistic Mean Field Theory for Nuclear Matter

We propose a quantization procedure for the nucleon-scMar meson system, in which an arbitrary mean scalar meson field Ф is introduced. The equivalence of this procedure with the usual one is proven for any given value of qS. By use of this procedure, the scalar meson field in the Walecka＇s MFA and in Chin＇s RHA are quantized around the mean field, Its corrections on these theories are considered by perturbation up to the second order. The arbitrariness of Ф makes us free to fix it at any stage in the calculation. When we fix it in the way of Walecka＇s MFA, the quantum corrections are big, and the result does not converge. When we fix it in the way of Chin＇s RHA, the quantum correction is negligibly small, and the convergence is excellent. It shows that RHA covers the leading part of quantum field theory for nuclear systems and is an excellent zeroth order approximation for further quantum corrections, while the Walecka＇s MFA does not. We suggest to fix the parameter Ф at the end of the whole calculation by minimizing the total energy per-nucleon for the nuclear matter or the total energy for the finite nucleus, to make the quantized relativistic mean field theory （QRMFT） a variational method.

Investigations on Nuclei near Z = 82 in Relativistic Mean Field Theory with FSUGold

In this work, the ground-state properties of Pt, Hg, Pb, and Po isotopes have been systematically investigated in the deformed relativistic mean field （RMF） theory with the new parameter set FSUGold. The calculated results show that FSUGold is as successful as NL3 in reproducing the ground-state binding energies of the nuclei in this region. The calculated two- neutron separation energies, quadrupole deformations, and root-mean-square charge radii are in agreement with the experimental data. The parameter set FSUGold can successfully describe the shell effect of the neutron magic number N = 126 and give smaller neutron skin thicknesses than NL3 for all the nuclei considered.

Determining Nuclear Form factor for Detection of Dark Matter in Relativistic Mean Field Theory

In this work, we derive the nuclear form factor for the spin-independent collision between the WIMPs and nucleus in terms of the relativistic mean field （RMF） theory. Comparison with the traditional form factors which are commonly used in literature is given and it is found that our results are slightly above that of the 2PF model by 4% to 8%, but deviate from the Helm form factor by 15% to 25% for the whole recoil energy spectrum of 0 -100 keV. Moreover, taking Xe and Ge as examples, we show the dependence of the form Factor on the recoil energy.

Octupole Deformations of Even-Even Rn, Th, and U Nuclei in Relativistic Mean Field Theory

The octupole deformations and other ground state properties of even-even Rn, Th and U isotopes are investigated systematically within the framework of the reflection asymmetric relativistic mean field （RAS-RMF） model. The calculation results reproduce the binding energies and the quadrupole deformations well. The calculation results indicate these nuclei at ground states evolve from neaxly-spherical （N = 130） shape to quadrupole deformation shape with the increase of the neutron number. It is also found that among the Rn isotopes, only^222,224 Rn axe oetupole deformed and the octupole deformations for them are small. However, more nuclei （N ≌ 134 148） in Th and U isotopes are octupole deformed and the octupole deformations for some of them are significant （｜β3｜- 0.1 or even larger）.

Exploration of the ground state properties of neutron-rich sodium isotopes using the deformed relativistic mean field theory in complex momentumrepresentations with BCS pairings

This study explores the ground-state characteristics of neutron-rich sodium isotopes,encompassing two-neutron separation energies,root-mean-square radii,quadrupole moments of proton and neutron distributions,single-particle levels of bound and resonant states,and neutron density distributions and shapes.Simultaneously,special attention is paid to the distinctive physical phenomena associated with these isotopes.The deformed relativistic mean field theory in complex momentum representations with BCS pairings(DRMF-CMR-BCS)employed in our research provides resonant states with real physics,offering insights into deformed halo nuclei.Four effective interactions(NL3,NL3^(*),PK1,and NLSH)were considered to assess the influence of continuum and deformation effects on halo structures.Calculations for odd-even nuclei ^(35–43)Na revealed the dependence on the chosen effective interaction and number of considered resonant states.Neutron occupation patterns near the Fermi surface,particularly in orbitals 1/2^(−)_(3) and 3/2^(−)_(2),were determined to be crucial in halo formation.The study provided detailed insights into the density distributions,shape evolution,and structure of neutron-rich sodium isotopes,contributing valuably to the field of nuclear physics.

Mean-field effects on matter and antimatter elliptic flow

We report our recent work on mean-field potential effects on the elliptic flows of matters and antimatters in heavy ion collisions leading to the production of a baryon-rich matter.Within the framework of a multiphase transport(AMPT) model that includes both initial partonic and final hadronic interactions,we have found that including mean-field potentials in the hadronic phase leads to a splitting of the elliptic flows of particles and their antiparticles,providing thus a plausible explanation of the different elliptic flows between p and anti-p,K+and K-,and π+ and π- observed by the STAR Collaboration in the Beam Energy Scan(BES) program at the Relativistic Heavy Ion Collider(RHIC).Using a partonic transport model based on the Nambu-Jona-Lasinio(NJL) model,we have also studied the effect of scalar and vector mean fields on the elliptic flows of quarks and antiquarks in these collisions.Converting quarks and antiquarks at hadronization to hadrons via the quark coalescence model,we have found that the elliptic flow differences between particles and antiparticles also depend on the strength of the quark vector coupling in baryon-rich quark-gluon plasma,providing thus the possibility of extracting information on the latter's properties from the BES program at RHIC.

Scalar-isovector δ-meson mean-field and mixed phase structure in compact stars

The deconfinement phase transition from ha-dronic matter to quark matter in the interior of compact stars is investigated. The hadronic phase is described in the framework of relativistic mean-field (RMF) theory, when also the scalar-isovector δ-meson effective field is taken into account. The MIT bag model for describing a quark phase is used. The changes of the pa-rameters of phase transition caused by the pre- sence of δ-meson field are investigated. Finally, alterations in the integral and structure para-meters of hybrid stars due to deconfinement phase transitions are discussed.

Density-dependent relativistic mean field approach and its application to single-Λhypernuclei in oxygen hyperisotopes

The in-medium feature of nuclear force, which includes both nucleon-nucleon( NN) and hyperon-nucleon( ΛN) interactions, impacts the description of single-Λ hypernuclei. With the alternated mass number or isospin of hypernuclei, such effects may be unveiled by analyzing the systematic evolution of the bulk and single-particle properties. From a density-dependent meson-nucleon/hyperon coupling perspective, a new ΛN effective interaction in the covariant density functional(CDF) theory, namely, DD-LZ1-Λ1, is obtained by fitting the experimental data ofΛ separation energies for several single-Λ hypernuclei. It is then used to study the structure and transition properties of single-Λ hypernuclei in oxygen hyperisotopes, in comparison with those determined using several selected CDF Lagrangians. A discrepancy is explicitly observed in the isospin evolution of Λ1p spin-orbit splitting with various effective interactions, which is attributed to the divergence of the meson-hyperon coupling strengths with increasing density. In particular, the density-dependent CDFs introduce an extra contribution to reduce the value but enhance the isospin dependence of the splitting, which originates from the rearrangement terms of Λ self-energies. In addition, the characteristics of hypernuclear radii are studied along the isotopic chain. Owing to the impurity effect of theΛ hyperon, a size shrinkage is observed in the matter radii of hypernuclei compared with the cores of normal nuclei,and its magnitude is further elucidated to correlate with the incompressibility of nuclear matter. Moreover, there is a sizable model-dependent trend in which the Λ hyperon radii evolve with neutron number, which is decided partly by the in-medium NN interactions and core polarization effects.

Deformation constrained relativistic mean-field approach with fixed configuration and time-odd component

Deformation constrained relativistic mean-field (RMF) approach with fixed configuration and timeodd component has been developed and applied to investigate magnetic moments of light nuclei near doublyclosed shells. Taking 17O as an example, the results and discussion are given in detail.

Octupole deformation for Ba isotopes in a reflection-asymmetric relativistic mean-field approach

The potential energy surfaces of even-even 142-156Ba are investigated in the constrained reflectionasymmetric relativistic mean-field approach with parameter set PK1. It is shown that for the ground states, 142Ba is near spherical,156Ba well quadrupole-deformed, and in between 144-154Ba octupole deformed. In particular, the nuclei 148,150Ba with N=92, 94 have the largest octupole deformations. By including the octupole degree of freedom, energy gaps N = 88, N = 94 and Z = 56 near Fermi surfaces for the singleparticle levels in 148Ba with β2 ～ 0.26 and β3 ～ 0.17 are found. Furthermore, the performance of the octupole deformation driving pairs （ν2f7/2, ν1i13/2） and （π2d5/2, π1h11/2） is demonstrated by analyzing the singleparticle levels near Fermi surfaces in 148Ba.

Antimagnetic rotation in ^(108,110)In with tilted axis cranking relativistic mean-field approach

Based on tilted axis cranking relativistic mean-field theory within point-coupling interaction PC-PK1, the rotational structure and the characteristic features of antimagnetic rotation for AI = 2 bands in 108,110In are studied. Tilted axis cranking relativistic mean-field calculations reproduce the experimental energy spectrum well and are in agreement with the experimental I -w plot, although the calculated spin overestimates the experimental values. In addition, the two-shears-like mechanism in candidate antimagnetic rotation bands is clearly illustrated and the contributions from two-shears-like orbits, neutron （gd） orbits above Z = 50 shell and Z = 50, N = 50 core are investigated microscopically. The predicted B（E2）, dynamic moment of inertia ■ （2）, deformation parametersβ and γ, and ■ （2）/B（E2） ratios in tilted axis cranking relativistic mean-field calculations are discussed and the characteristic features of antimagnetic rotation for the bands before and after alignment are shown.

Constraining the relativistic mean-field models from PREX-2 data:effective forces revisited

Based on the current measurement of the neutron distribution radius(R_(n))of ^(208)Pb from the PREX-2 data,we revisited the recently developed G3 and IOPB-I force parameters by fine-tuning some specific couplings within the relativistic mean-field(RMF)model.Theω-ρ-mesons coupling and theρ-meson coupling are constrained to the experimental neutron radius of^(208)Pb without compromising the bulk properties of finite nuclei and infinite nuclear matter observables.The modified parameter sets are applied to calculate the gross properties of finite nuclei such as binding energies,charge distributions,nuclear radii,pairing gaps,and single-particle energies.The root-mean-square deviations in binding energy and charge radius are estimated with respect to the available experimental data for 195 even-even nuclei,and the results compare favourably with the well-calibrated effective interactions of Skyrme,Gogny and other relativistic mean-field parametrizations.The pairing gap estimations for modified G3 and IOPB-I for Sn isotopes are also compared with the Hartree-Fock-Bogoliubov calculation with the Gogny(D1S)interaction.The isotopic shift and single-particle energy spacing are also calculated and compared with the experimental data for both original and modified versions of the G3 and IOPB-I parameter sets.Subsequently,both the modified parameter sets are used to obtain the various infinite nuclear matter observables at saturation.In addition to these,the force parameters are adopted to calculate the properties of a high isospin asymmetry dense system such as neutron star matter and tested for validation using the constraint from GW170817 binary neutron star merger events.The tuned forces predict relatively good results for finite and infinite nuclear matter systems and the current limitation on the neutron radius from PREX-2.A systematic analysis using these two refitted parameter sets over the nuclear chart will be communicated shortly.

Radius studies of ^8Li and ^8B using the optical-limit Glauber model in conjunction with relativistic mean-field theory

We study the reaction cross sections （σR） and root-mean-square （RMS） radii of ^8Li and ^8B, the halo-like nuclei, with stable target ^12C, ^27Al and ^9Be within the standard optical-limit Glauber model, using densities obtained from relativistic mean-field （RMF） formalisms and other types of distributions. It is found that the experimental σR can be reproduced well at high energy. The RMS radius and Ar extracted by RMF- theory and harmonic oscillator distribution are compared. larger than those of SLi. In addition, we analyze in detail the We find that the RMS radius and Ar of SB are relationship between σR and density distribution.

The symmetry energy γ parameter of relativistic mean-field models

The relativistic mean-field models tested in previous works against nuclear matter experimental values,critical parameters and macroscopic stellar properties are revisited and used in the evaluation of the symmetry energyγ parameter obtained in three different ways. We have checked that, independent of the choice made to calculate theγ values, a trend of linear correlation is observed between γ and the symmetry energy（S0） and a more clear linear relationship is established between γ and the slope of the symmetry energy（L0）. These results directly contribute to the arising of other linear correlations between γ and the neutron star radii of R（1.0） and R（1.4）, in agreement with recent findings. Finally, we have found that short-range correlations induce two specific parametrizations, namely,IU-FSU and DD-MEδ, simultaneously compatible with the neutron star mass constraint of 1.93≤M（max）/M☉≤2.05 and with the overlap band for the L0 ×S0 region, to present γ in the range of γ=0.25±0.05.

Magnetic moments of ^(33)Mg in the time-odd relativistic mean field approach

The configuration-fixed deformation constrained relativistic mean field approach with time-odd component has been applied to investigate the ground state properties of 33Mg with effective interaction PK1.The ground state of 33Mg has been found to be prolate deformed,β2=0.23,with the odd neutron in 1/2[330] orbital and the energy -251.85 MeV which is close to the data -252.06 MeV.The magnetic moment -0.9134 μN is obtained with the effective electromagnetic current which well reproduces the data -0.7456 μN self-consistently without introducing any parameter.The energy splittings of time reversal conjugate states,the neutron current,the energy contribution from the nuclear magnetic potential,and the effect of core polarization are discussed in detail.

Ground state properties of La isotopes in reflection asymmetric relativistic mean field theory

The ground state properties of La isotopes are investigated with the reflection asymmetric relativistic mean field(RAS-RMF) model.The calculation results of binding energies and the quadrupole moments are in good agreements with the experiment.The calculation results indicate the change of the quadrupole deformation with the nuclear mass number.The "kink" on the isotope shifts is observed at A = 139 where the neutron number is the magic number N = 82.It is also found that the octupole deformations may exist in the La isotopes with mass number A ～ 145-155.

A Global Weizsacker mass model with relativistic mean field shell correction

A relativistic Weizsacker mass model is proposed based on the single-particle levels and ground state deformations obtained in axial deformed relativistic mean field theory.The density functional of relativistic mean field theory is chosen as DD-LZ1,which can partially remove spurious shell closures.Compared with the fourth Weizsacker-Skyrme mass model,the proposed model provides shell correction energies that exhibit wide spreading,and the root-mean-square mass deviation is 1.353 MeV.Further improvement is in progress.