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.

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.

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.

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.

Shell evolution at N=20 in the constrained relativistic mean field approach

The shell evolution at N = 20, a disappearing neutron magic number observed experimentally in very neutron-rich nuclides, is investigated in the constrained relativistic mean field （RMF） theory. The trend of the shell closure observed experimentally towards the neutron drip-line can be reproduced. The predicted two-neutron separation energies, neutron shell gap energies and deformation parameters of ground states are shown as well. These results are compared with the recent Hartree-Fock-Bogliubov （HFB-14） model and the available experimental data. The perspective towards a better understanding of the shell evolution is discussed.

Investigation of the Mg isotopes using the shell-model-like approach in relativistic mean field theory

Ground state properties for Mg isotopes, including binding energies, one- and two-neutron separation energies, pairing energies, nuclear matter radii and quadrupole deformation parameters, are obtained from the self- consistent relativistic mean field （RMF） model with the pairing correlations treated by a shell-mode-like approach （SLAP）, in which the particle-number is conserved and the blocking effects are treated exactly. The experimental data, including the binding energies and the one- and two-neutron separation energies, which are sensitive to the treatment of pairing correlations and block effects, are well reproduced by the RMF＋SLAP calculations.

Particle number conserving BCS approach in the relativistic mean field model and its application to ^32-74Ca

A fixed particle number BCS （FBCS） approach is formulated in the relativistic mean field （RMF） model. It is shown that the RMF＋FBCS model obtained can describe the weak pairing limit. We calculate the ground-state properties of the calcium isotopes ＆32-74Ca and compare the results with those obtained from the usual RMF＋BCS model. Although the results are quite similar to each other, we observe the interesting phenomenon that for ^54Ca, the FBCS approach can enhance the occupation probability of the 2p1/2 single particle level and slightly increases its radius, compared with the RMF＋BCS model. This leads to the unusual scenario that although ^54Ca is more bound with a spherical configuration, the corresponding size is not the most compact. We anticipate that such a phenomenon might happen for other neutron-rich nuclei and should be checked by further more systematic studies.

A systematic study of the superdeformation of Pb isotopes with relativistic mean field theory

The microscopically constrained relativistic mean field theory is used to investigate the superdeformation for Pb isotopes. The calculations have been performed with the four different interactions NL3, PK1, TM1 and NLSH, and show that there exists a clear superdeformed minimum in the potential energy surfaces. The excitation energy, deformation and depth of the well in the superdef.ormed minimum are comparable for the four different interactions. Furthermore the trend for the change of the superdeformed excitation energy with neutron number is correctly reproduced. The calculated two-neutron separation energy in the ground state and superdeformed minimum together with their differences are in agreement with the available data. The larger energy difference appearing in the superdeformed minimum reflects a lower average level density at superdeformations for Pb isotopes.

Shears mechanism in two-dimensional cranking relativistic mean field approach

Using the new two-dimensional cranking relativistic mean field (RMF) approach, the shears mechanism of magnetic rotation based on configuration πh121/2νh-211/2 in 142Gd is microscopically and self-consistently examined by investigating the aligning angular momenta of the valence nucleons.

Towards Lambda-nucleon coupling constants in relativistic mean field theory

New parameter sets for Λ-nucleon coupling in relativistic mean field theory are proposed based on nucleon-nucleon effective interaction PK1. Hypernuclear properties are described well through a systematical study. Effects of hyperon tensor coupling term on spin-orbit splitting are also investigated self-consistently.

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.

Nuclear structure and decay modes of Ra isotopes within an axially deformed relativistic mean field model

We examine the structural properties and half-life decay of Ra isotopes within the axially deformed Relativistic Mean-Field（RMF）theory with NL3 force parameters.We work out the binding energy（BE）,RMS radii,two-neutron separation energies（S（2n））,and some other observables.The results are in good agreement with the finite-range droplet model（FRDM）and experimental results.Considering the possibility of neutron magic number,theα-decay and cluster decay half-lives of Ra isotopes are calculated systematically using the Q-values obtained from the RMF formalism.These decay half-life calculations are carried out by taking three different empirical formulae.The calculated decay half-lives are found to be highly sensitive to the choice of Q-values.Possible shell or sub-shell closures are found at daughter nuclei with N=128 and N=126 when alpha and 8Be,12C,18O respectively are emitted from Ra isotopes.Though the cluster radioactivity is affected by the shell closure of parent and daughter,a long half-life indicates the stability of the parent,and a small parent half-life indicates that the shell stability of the daughter against decay.

Massive neutron stars and A-hypernuclei in relativistic mean field models

Based on relativistic mean field（RMF） models, we study finite A-hypernuclei and massive neutron stars. The effective N-N interactions PK1 and TM1 are adopted, while the N-A interactions are constrained by reproducing the binding energy of A-hyperon at 1 s orbit of Λ^40Ca. It is found that the A-meson couplings follow a simple relation, indicating a fixed A potential well for symmetric nuclear matter at saturation densities, i.e., around VΛ=-29.786 MeV. With those interactions, a large mass range of Λ-hypernuclei can be described well. Furthermore,the masses of PSR J1614-2230 and PSR J0348＋0432 can be attained adopting the Λ-meson couplings gσΛ/gσN≥0.73,gωΛ/gωN≥0.80 for PK1 and gσΛ/gσN≥0.81,gωΛ/gωN≥0.90 for TM1, respectively. This resolves the hyperon puzzle without introducing any additional degrees of freedom.

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.

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.

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.

Effects of σ* and Φ mesons on the surface redshift of a neutron star

The effects of σ^＊ and Ф mesons on the surface redshift of a neutron star have been investigated within the framework of relativistic mean field theory for the baryon octet {n, p, ∧, ∑-,∑0, ∑＋, -, 0} system. It is found that compared with those without considering the contributions of σ^＊ and Ф mesons, the surface redshift decreases and that corresponding to the maximum value of the mass also decreases from 0.2540 to 0.2236, about by 12%. Meanwhile, it is also found that including σ^＊ and Ф mesons, the M/R and that corresponding to the maximum mass decrease.

A study of U-isotope ground state properties with covariant energy density functional

In this study,we systematically analyzed the ground state of uranium isotopes from 225 to 240.In our calculations,we used the covariant energy density functional of density-dependent meson exchange interaction(DDME2)with separable pairing interaction(TMR).Using the multiple deformation constraint,we calculated the potential energy surface(PES)of the uranium isotopes for both even-even and even-odd nuclei with quadrupole and octupole deformation.Based on our calculation and upon comparing the experimental data and Hartree-Fock-Bogoliubov calculations with Gogny D1S calculation data,the ground state of uranium isotopes with reflection-asymmetric deformation was found to be preferred.

Quasielastic electron scattering in a derivative coupling model with relativistic random phase approximation

We apply the derivative coupling model with ZM and ZM3 parameters to investigate the longitudinal response function in quasielastic electron scattering in the relativistic random phase approximation. The non-spectral method is chosen to describe the nucleon Green＇s function in a finite nucleus. Some remarks have been made in conclusion.

Preformation probability and kinematics of cluster emission yielding Pb-daughters

In the present study,the newly established preformation formula is applied for the first time to study the kinematics of the cluster emission from various radioactive nuclei,especially those that decay to the double shell closure^(208)Pb nucleus and its neighbors as daughters.The recently proposed universal cluster preformation formula has been established based on the concepts that underscore the influence of mass and charge asymmetry(η_(A)andη_(Z)),cluster mass A_(c),and the Q-value,paving the way to quantify the energy contribution during preformation as well as during the tunneling process separately.The cluster-daughter interaction potential is obtained by folding the relativistic mean-field(RMF)densities with the recently developed microscopic R3Y using the NL 3^(*)and the phenomenological M3Y NN potentials to compare their adaptability.The penetration probabilities are calculated from the WKB approximation.With the inclusion of the new preformation probability P_(0),the predicted half-lives of the R3Y and M3Y interactions are in good agreement with the experimental data.Furthermore,a careful inspection reflects slight differences in the decay half-lives,which arise from their respective barrier properties.The P_(0)for systems with double magic shell closure^(208)Pb daughter are found to be an order of≈10^(2)higher than those with neighboring Pb daughter nuclei.By exploring the contributions of the decay energy,the recoil effect of the daughter nucleus is evaluated,in contrast to several other conjectures.Thus,the centrality of the Q-value in the decay process is demonstrated and redefined within the preformed cluster-decay model.Additionally,we have introduced a simple and intuitive set of criteria that governs the estimation of recoil energy in the cluster radioactivity.