Relativistic Mean Field Approach Research Articles

Electromagnetic properties of Λ hypernuclei with a beyond relativistic mean-field approach

We present a microscopic study of electromagnetic properties of the low-lying states of single-Λ hypernucleus Λ9Be using a quantum-number projected generator coordinate method (HyperGCM) based on covariant density functional theory. All the configurations are restricted to have axial symmetry, with the Λ hyperon in the lowest-energy state. The results are compared to the predictions of a simple particle-rotor model (PRM), for which analytic expressions are available. We show that the electromagnetic properties of Λ9Be from the HyperGCM calculation are close to those by the PRM. In particular, it is found that the magnetic moments and M1 transition strengths are less sensitive to the coupling strengths of the ΛN interaction than the electric quadrupole transition strengths. The latter may provide additional constraints on the ΛN interaction.

Density-dependent relativistic mean field approach and its application to single-Λ hypernuclei in oxygen hyperisotopes* *Supported by the Fundamental Research Funds for the Central Universities, Lanzhou University (lzujbky-2022-sp02, lzujbky-2023-stlt01), the National Natural Science Foundation of China (11875152, 12275111), and the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34000000)

The in-medium feature of nuclear force, which includes both nucleon-nucleon () and hyperon-nucleon () 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 effective interaction in the covariant density functional (CDF) theory, namely, DD-LZ1-, is obtained by fitting the experimental data of Λ 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 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 the Λ 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 interactions and core polarization effects.

New bound-state energy of double magic number plus one nucleon nuclei with a relativistic and non-relativistic mean-field approach in 3D-RNCQS and 3D-NRNCQS symmetries

New bound-state energy of double magic number plus one nucleon nuclei with a relativistic and non-relativistic mean-field approach in 3D-RNCQS and 3D-NRNCQS symmetries

Correlation between the nuclear structure and reaction dynamics of Ar-isotopes as projectile using the relativistic mean-field approach

This theoretical study is devoted to bridging the gap between the nuclear structure and reaction dynamics and unravelling their impact on each other, considering the neutron-rich light mass 30−60Ar isotopes. Using the relativistic mean-field with the NL3⁎ parameter set, several bulk properties such as binding energies, charge radii, quadrupole deformation parameter, two neutron separation energy, and differential two neutron separation energy with the shell closure parameter are probed for the mentioned isotopic chain. For validation, the RMF (NL3⁎) results are compared with those obtained from the finite range droplet model (FRDM), Weizsäcker-Skyrme model with WS3, WS⁎ parameters, and the available experimental data. Most of the participating isotopes are found to be prolate in structure, and neutron shell closures are conspicuously revealed at N=14,20,40 but weakly shown at N=24,28,34. From our analysis, a central depletion in the nucleonic density is identified in 32 Ar and 42−58 Ar, indicating that they are possible candidates for a semi-bubble-like structure. Interestingly, these results are consistent with recent theoretical and experimentally measured data. Furthermore, using the Glauber model, the reaction cross-sections are determined by taking 26−48Ar as projectiles and stable targets such as 12C, 16O, 40Ca, 90Zr, 124,132Sn, 208Pb and 304120. Although there is no experimental evidence for the stability of 304120, it was predicted by Bhuyan and Patra (2012) [115] as a stable nucleus. A relatively higher cross-section value is noticed between 30 Ar and 32 Ar, which infers that 32Ar is the most stable isotope among the considered chain. Moreover, we noticed that the profile of the differential cross-sections and scattering angle are highly influenced by the mass of the target nuclei and the magnitude of the incident energy of the projectile nucleus.

Deformation dependence of 2p-radioactivity half-lives: probe with a new formula across the mass region with Z < 82

Effect of deformation on half-life of two-proton (2p) radioactivity is investigated across the periodic chart for nuclei with Z < 82. 2p-decay half-lives are estimated by employing our newly proposed semi-empirical formula wherein the nuclear deformation has been incorporated in a phenomenological way. Robustness of the formula is demonstrated as it estimates the measured values quite accurately and, hence, reliably applied to predict the other possible 2p-emitters. For many proton rich nuclei for which experimental data on the decay energies are not available, we have used the theoretical values obtained from our calculations using the relativistic mean-field approach. The uncertainties in the theoretical decay energy values are minimised by machine learning technique. Correlation of 2p-radioactivity with 2p-halo and deformation is probed. Our calculations show the phenomenon of shape coexistence in several 2p-emitters, wherein the prolate shape is found to be more predominant for the ground state.

Extracting nuclear matter properties from the neutron star matter equation of state using deep neural networks

The extraction of the nuclear matter properties from neutron star (NS) observations is nowadays an important issue, in particular, the properties that characterize the symmetry energy which are essential to describe correctly asymmetric nuclear matter. We use deep neural networks (DNNs) to map the relation between cold $\beta$-equilibrium NS matter and the nuclear matter properties. Assuming a quadratic dependence on the isospin asymmetry for the energy per particle of homogeneous nuclear matter and using a Taylor expansion up to fourth order in the iso-scalar and iso-vector contributions, we generate a dataset of different realizations of $\beta$-equilibrium NS matter and the corresponding nuclear matter properties. The DNN model was successfully trained, attaining great accuracy in the test set. Finally, a real case scenario was used to test the DNN model, where a set of 33 nuclear models, obtained within a relativistic mean field approach or a Skyrme force description, were fed into the DNN model and the corresponding nuclear matter parameters recovered with considerable accuracy, in particular, the standard deviations $\sigma(L_{\text{sym}})= 12.85$ MeV and $\sigma(K_{\text{sat}})= 41.02$ MeV were obtained, respectively, for the slope of the symmetry energy and the nuclear matter incompressibility at saturation.

Quenched Λ spin-orbit splitting by a relativistic Fock diagram in single- Λ hypernuclei

We extend the relativistic Hartree-Fock (RHF) theory to study the structure of single-$\Lambda$ hypernuclei. The density dependence is taken in both meson-nucleon and meson-hyperon coupling strengths, and the induced $\Lambda$-nucleon ($\Lambda N$) effective interactions are determined by fitting $\Lambda$ separation energies to the experimental data for several single-$\Lambda$ hypernuclei. The equilibrium of nuclear dynamics described by the RHF model in normal atomic nuclei, namely, the balance between nuclear attractive and repulsive interactions, is then found to be drastically changed in single-$\Lambda$ hypernuclei, revealing a different role of Fock terms via $\Lambda$ hyperon from the nucleon exchange. Since only one hyperon exists in a single-$\Lambda$ hypernucleus, the overwhelmed $\Lambda N$ and $\Lambda\Lambda$ attractions via the Hartree than the $\Lambda\Lambda$ repulsion from the Fock terms require an alternation of meson-hyperon coupling strengths in RHF to rebalance the effective nuclear force with the strangeness degree of freedom, leading to an improved description of $\Lambda$ Dirac mass and correspondingly a systematically reduced $\sigma$-$\Lambda$ coupling strength $g_{\sigma\Lambda}$ in current models as compared to those relativistic mean-field (RMF) approaches without Fock terms. As a result, the effective $\Lambda$ spin-orbit coupling potential in the ground state of hypernuclei is suppressed, and these RHF models predict correspondingly a quenching effect in $\Lambda$ spin-orbit splitting in comparison with the RMF cases. Furthermore, the $\Lambda$ spin-orbit splitting could decrease efficiently by evolving the hyperon-relevant couplings $g_{\sigma\Lambda}$ and $g_{\omega\Lambda}$ simultaneously, where to reconcile with the empirical value the RHF models address a larger parameter space of meson-hyperon couplings.

Isotopic Shift in Hg-Isotopes within Brückner versus Relativistic Energy Density Functional

The present study is focused on revealing a characteristic kink of the neutron shell closure N = 126 across the Hg-isotopic chain within the relativistic mean-field (RMF) approach with the IOPB-I, DD-ME2, DD-PC1 and NL3 parameter sets. The RMF densities are converted to their spherical equivalence via the Wood–Saxon approximation and used as input within the parametrization procedure of the coherent density fluctuation model (CDFM). The nuclear matter symmetry energy is calculated using the Brückner energy density functional, and its surface, as well as volume components, are evaluated within Danielwicz’s liquid drop prescription. In addition, a comparison between Brückner and relativistic energy density functionals using the NL3 parameter set is shown as a representative case. The binding energy, charge distribution radius and symmetry energy are used as indicators of the isotopic shift in both ground and isomeric states. We have found the presence of a kink at the shell/sub-shell closure at N = 126 for neutron-rich 206Hg. The formation of the kink is traceable to the early filling of the 1i11/2 orbitals rather than 2g9/2, due to the large spin-orbit splitting. As such, the link between the occupational probability and the magicity of nuclei over the Hg-isotopic chain is established.

Medium-dependent relativistic NN potential: Application to fusion dynamics

In-medium effects are introduced in the microscopic description of the effective nucleon-nucleon (NN) interaction potential entitled DDR3Y in terms of the density-dependent nucleon-meson couplings within the Relativistic-Hartree-Bogoliubov (RHB) approach. The nuclear densities of the interacting target and projectile nuclei and NN potentials are obtained for non-linear NL3$^*$ and TM1 parameter sets within the relativistic mean-field approach and density-dependent DDME1 and DDME2 parameter sets within the Relativistic-Hartree-Bogoliubov (RHB) formalism. The DDR3Y NN potential and the densities are used to obtain the nuclear potential by adopting the double folding approach. This nuclear potential is further used to probe the fusion dynamics within the $\ell-$summed Wong model for a few {\it even-even} systems leading to the formation of light, heavy and superheavy nuclei. The calculations are also performed for the relativistic R3Y, density-dependent and independent M3Y interaction potentials for the comparison. We observed that the DDR3Y NN potential gives a better overlap with the experimental data as compared to non-relativistic M3Y and DDM3Y NN potentials. From the comparison of R3Y and DDR3Y interactions, it is manifested that the inclusion of in-medium effects in terms of density-dependent nucleon-meson couplings raises the fusion barrier and consequently decreases the fusion and/or capture cross-section. Moreover, the nuclear densities, as well as the relativistic R3Y NN potential obtained for the NL3$^*$ parameter set, are observed to give a comparatively better fit to the experimental data.

Structure and decay chain of fermium isotopes using relativistic mean-field approach

In this paper, we have analyzed the ground state structural properties of fermium-isotopes in the mass range [Formula: see text] within the relativistic mean-field with NL3[Formula: see text] and Relativistic Hartree–Bogoliubov approach with DD-ME2 parameter sets. The bulk properties, such as binding energy, root mean-square charge radius, quadruple deformation parameter, chemical potentials, two-neutron separation energy and differential two- neutron separation energy, are estimated for the above Fm- isotopic chain. All the calculated observables are compared with finite range droplet model (FRDM) predictions and experimental data wherever available. The analysis predicts the existence of shell closure in the neutron-rich region of the isotopic chain at [Formula: see text]. The decay properties such as the [Formula: see text]-decay energy and corresponding half-life for three decay chains i.e. [Formula: see text]Fm, [Formula: see text]Fm and [Formula: see text]Fm are studied. Six different empirical formulae, namely; Viola-Seaborg, Royer, modified B. Alex Brown, Parkhomenko–Sobiczewski, Universal decay law and modified universal decay law are employed to ascertain the numerical dependency of the half-life for each decay energy. A comparative study of [Formula: see text]-values and half-lives for these decay chains gives a good signature of the calculated results. The half-life calculations of three decay chains suggest that [Formula: see text]Pu, [Formula: see text]Pu, [Formula: see text]Pu are shell closure nuclei having maximum half-lives, whereas [Formula: see text]Fm, [Formula: see text]Fm and [Formula: see text]Fm are shell stabilized with lower half-lives.

Theoretical Investigation of α-decay Chains of Fm-isotopes

Background: The theoretical and experimental investigations of decay properties of heavy and superheavy nuclei are crucial to explore the nuclear structure and reaction dynamics.&#x0D; Purpose: The aim of this study is to probe the α-decay properties of 243Fm and 245Fm isotopic chains using relativistic mean-field (RMF) approach within the framework of preformed cluster-decay model (PCM).&#x0D; Methods: The RMF densities are folded with the relativistic R3Y NN potential to deduce the nuclear interaction potential between the α particle and daughter nucleus. The penetration probability is calculated within the WKB approximation.&#x0D; Results: The α-decay half-lives of even-odd 243Fm and 245Fm isotopes and their daughter nuclei are obtained from the preformed cluster-decay model. These theoretically calculated half-lives are found to be in good agreement with the recent experimental measurements.&#x0D; Conclusions: The novel result here is the applicability of the scaling factor within the PCM as a signature for shell/sub-shell closures in α-decay studies. As such, we have also demonstrated that N=137, 139 and Z=94 corresponding to 231,233Pu could be shell/sub-shell closures. The least T1/2 is found at 243,245Fm which indicate their individual stability and α-decay as their most probable decay mode.

Systematic Analysis for Neck-Length and Q-Values on Cluster Decay from Ba Isotopes

The present study provides a detailed investigation of the neck-configuration and Q-values on the cluster decay of proton-rich even-even 124-128Ba isotopes using the relativistic mean-field (RMF) formalism with the NL3* parameter set. The densities of the interacting nuclei from the RMF approach are folded with the R3Y and M3Y interactions to obtain the nuclear potential via the double-folding technique. The preformed cluster model (PCM) based on the quantum mechanical fragmentation theory is employed for the calculation of the decay half-lives. The preformation probability P0 and the penetration probabilities are estimated by the phenomenological scaling factor of Blendowske &amp; Walliser and the WKB approximation respectively. The present investigation reveals that the M3Y and R3Y are associated with different barrier characteristics which are significantly modified with a little variation in the neck-length parameter ΔR. From the Q-value analysis, we have demonstrated that α-decay may not be a favourable decay mode for proton-rich barium isotopes with A &gt; 122.

Fusion cross section of α -induced reactions for heavy target nuclei

The fusion reactions induced by $^{4}\mathrm{He}$ projectiles on heavy target nuclei provide the reference to study the reaction dynamics of exotic halo nuclei. The present analysis aims to probe the effects of different nuclear density distributions and the effective nucleon-nucleon ($NN$) interaction potentials on the fusion cross section of $^{4}\mathrm{He}$-induced reactions for heavy target nuclei. The nuclear densities for the heavy nuclei are obtained within the well-known Skyrme-Hartree-Fock model and the relativistic mean-field (RMF) approach for the $\mathrm{NL}{3}^{*}$ parameter set. These densities are integrated with the density-dependent M3Y and the relativistic R3Y nucleon-nucleon ($NN$) potentials to obtain the nuclear interaction potential. The fusion cross section and the astrophysical $S$ factor are obtained for $^{4}\mathrm{He}+^{208}\mathrm{Pb}, ^{4}\mathrm{He}+^{209}\mathrm{Bi}, ^{4}\mathrm{He}+^{235}\mathrm{U}$, and $^{4}\mathrm{He}+^{238}\mathrm{U}$ systems within the $\ensuremath{\ell}$-summed Wong model. The relativistic R3Y $NN$ potential folded with RMF densities are observed to give a better fit to the available experimental data. Furthermore, a comparison is made for the results obtained using Hill-Wheeler and Wentzel-Kramers-Brillouin transmission coefficients for $^{4}\mathrm{He}+^{208}\mathrm{Pb}$ system. We found a reasonable fit in the cross section at around the Coulomb-barrier energies for both the approximations and also similar predictions can be drawn for all considered systems.

Systematic application of the M3Y NN forces for describing the capture process in heavy-ion collisions involving deformed target nuclei

We present results of a systematic study of the capture process through the barrier penetration model. The nucleus-nucleus interaction potential is calculated using the double-folding model (DFM) with the M3Y Paris $\mathit{NN}$ forces. The nucleon densities entering the model are generated from the experimental three-parameter Fermi charge densities. The DFM has been extended to the case of deformed target nuclei. It is shown that the density-dependent M3Y $\mathit{NN}$ forces with the finite range exchange part can be mimicked successfully by the zero-range density-independent forces. The latter option significantly reduces the required computer time. For the nucleon densities and target nuclei deformations, we employ the values from the commonly used data bases. Thus, we do not vary any parameters to reach a better agreement with the data. The resulting cross sections are compared with data for 20 reactions with the product of the charge numbers ${Z}_{P}{Z}_{T}$ ranging from 216 up to 2576. We discuss the opinion met in the literature that the M3Y $\mathit{NN}$ forces provide a poorer description of the capture cross sections in heavy-ion collisions in comparison to the $\mathit{NN}$ forces coming from the relativistic mean-field approach. Our calculations show that the M3Y $\mathit{NN}$ forces give an agreement with the data which is not perfect yet is not worse than the one resulting from the relativistic mean-field approach $\mathit{NN}$ forces.

Structural evolution and shape transition in even-even Hf-isotopes within the relativistic mean-field approach

In this theoretical study, we calculate the ground state parameters like binding energy, charge radii, neutron skin-thickness, chemical potentials, quadrupole deformation parameter, neutron separation energy, and single-particle energy for Hf isotopes of mass 170 ⩽ A ⩽ 220. The potential energy surface in parallel with the Fermi energy as a function of the quadrupole deformation parameter is estimated to determine the ground state configuration. The Relativistic Hartree-Bogoliubov approach with density-dependent DD-ME2 and the relativistic mean-field formalism with the popular NL3 and NL3⁎ parameter sets are used for the present analysis. The study involves a constant gap BCS approach within NL3, & NL3⁎ and Bogoliubov transformation within DD-ME2 parameter sets to examine the effect of pairing correlations. The calculated bulk quantities are reasonably good agreement with available experimental data, the finite range droplet model predictions, and the Weizsäcker-Skyrme mass formula. We find the signature of shell/sub-shell closure at N = 126 for all the parameter sets, which indicates the stability of 198Hf in the neutron drip-line region of the Hf-isotopes.

Hyperonic equation of state at finite temperature for neutron stars

We review the composition and the equation of state of the hyperonic core of neutron stars at finite temperature within a relativistic mean-field approach. We make use of the new FSU2H∗ model, which is built upon the FSU2H scheme by improving on the Ξ potential according to the recent analysis on the Ξ atoms, and we extend it to include finite temperature corrections. The calculations are done for a wide range of densities, temperatures and charge fractions, thus exploring the different conditions that can be found in protoneutron stars, binary mergers remnants and supernovae explosions. The inclusion of hyperons has a strong effect on the composition and the equation of state at finite temperature, which consequently would lead to significant changes in the properties and evolution of hot neutron stars.

Pairing strength in the relativistic mean-field theory determined from the fission barrier heights of actinide nuclei and verified by pairing rotation and binding energies

Abstract We have studied the strength of the Bardeen–Cooper–Schrieffer (BCS) pairing force, used as a residual interaction to the relativistic mean-field approach, to reproduce the height of the inner fission barriers for actinide nuclei. It was found that increasing the pairing strength by about $13\%$ makes the reproduction of the inner fission barriers better over a wide range of actinide nuclei. This result was verified by using the moment of inertia of the pairing rotational energy, which was introduced to avoid mean-field and odd-mass effects in the pairing interaction, to deduce purely the pairing strength. The pairing interaction thus determined could also improve the description of the binding energy of heavy nuclei. As a result, a consistent picture among inner fission barrier, binding energy, and pairing moment of inertia could be obtained in terms of the relativistic mean-field + BCS theory for a broad region of the actinide nuclei.

Comparative studies on nuclear elastic magnetic form factors between the relativistic and non-relativistic mean-field approaches * *Supported by the National Natural Science Foundation of China (11505292, 11605105, 11822503, 11975167, 12035011), the Shandong Provincial Natural Science Foundation, China (ZR2020MA096), the Fundamental Research Funds for the Central Universities (20CX05013A, 22120210138), and the Graduate Innovative Research Funds of China University of Petroleum (East

It is known that elastic magnetic electron scattering can be used to study the magnetic properties of nuclei and determine the outermost-shell single-particle orbitals. In this study, the magnetic form factors of odd-A nuclei calculated with relativistic and non-relativistic models are systematically compared. We use the relativistic mean-field (RMF) and Skyrme Hartree-Fock (SHF) models to generate single-particle wave functions and calculate the values of selected nuclei under relativistic and non-relativistic frameworks, respectively. Geometric factors are introduced through the spherical limit method to consider the influences of deformation, which improves the agreement between the theoretical results and experimental data. It is shown that both the models have the capability to describe the magnetic form factors in the spherical and deformed cases, and the discrepancies in reflect the differences in the descriptions of the single-particle orbital between the two models.

Collapse of N = 28 magicity in exotic 40Mg—probe of deformed halo and 2n-radioactivity at Mg neutron drip-line

The exotic phenomenon of two-neutron halos and 2n-radioactivity are explored in the neutron-rich 40,42,44Mg by employing various variants of the relativistic mean-field approach. The extended tail of spatial density distributions including the enhanced neutron radii and skin thickness, pairing correlations, single-particle spectrum and wave functions predict 40,42,44Mg to be strong candidates for deformed neutron halos. Weakening of magicity at N = 28 plays a significant role in the existence of a weakly bound halo in 40Mg which is currently the heaviest isotope of Mg accessible experimentally. Large deformation, mixing of f–p shell Nilsson orbitals and the valence neutron occupancy of p-states leads to a reduced centrifugal barrier and broader spatial density distributions that favour 2n-radioactivity in 42,44Mg.

Neutron star deformability with hyperonization in density-dependent relativistic mean-field models

Neutron star tidal deformability extracted from gravitational wave data provides a novel probe to the interior neutron star structures and the associated nuclear equation of state (EOS). Instead of the popular composition of nucleons and leptons in neutron stars, we include hyperons and examine the role of hyperons in the tidal deformability and its impact on the symmetry energy in a relativistic mean-field approach with the density-dependent parametrizations. The hyperons are found to have a significant impact on the deformability, correlated sensitively with the onset density and fraction of hyperons in neutron star matter. A moderately lower onset density of hyperons can yield considerable modification to the tidal deformability and shift its inference on the nuclear EOS. The future measurements of the tidal deformability at multifiducial star masses are anticipated to lift the degeneracy between the contributions from the hyperon component and symmetry energy.