Relativistic Mean Field Formalism Research Articles

Cluster decay dynamics of actinides yielding non-Pb-daughter within relativistic mean field formalism

Cluster decay dynamics of actinides yielding non-Pb-daughter within relativistic mean field formalism

Probing the impact of delta-baryons on nuclear matter and non-radial oscillations in neutron stars

Non-radial oscillations of Neutron Stars (NSs) provide a means to learn important details regarding their interior composition and equation of state. We consider the effects of Δ-baryons on non-radial f-mode oscillations and other NS properties within the Density-Dependent Relativistic Mean Field formalism. Calculations are performed for Δ-admixed NS matter with and without hyperons. Our study of the non-radial f-mode oscillations revealed a distinct increase in frequency due to the addition of the Δ-baryons with upto 20% increase in frequency being seen for canonical NSs. Other bulk properties of NSs, including mass, radii, and dimensionless tidal deformability (Λ) were also affected by these additional baryons. Comparing our results with available observational data from pulsars (NICER) and gravitational waves (LIGO-VIRGO collaboration), we found strong agreement, particularly concerning Λ.

Influence of the tetraneutron on the EoS under core-collapse supernova and heavy-ion collision conditions

Context. Recently, a resonant state of four neutrons (tetraneutron) with an energy of E4n = 2.37 ± 0.38(stat) ± 0.44(sys) MeV and a width of Γ = 1.75 ± 0.22(stat) ± 0.30(sys) MeV was reported. Aims. In this work, we analyze the effect of including such an exotic state on the yields of other light clusters; these clusters not only form in astrophysical sites, such as core-collapse supernovae and neutron star (NS) mergers, but also in heavy-ion collisions. Methods. To this aim, we used a relativistic mean-field (RMF) formalism, where we consider in-medium effects in a two-fold way – that is, via the couplings of the clusters to the mesons, and via a binding energy shift – to compute the low-density equation of state (EoS) for nuclear matter at finite temperature and fixed proton fraction. We consider five light clusters – namely deuterons, tritons, helions, α-particles, and 6He – immersed in a gas of protons and neutrons, and we calculate their abundances and chemical equilibrium constants with and without the tetraneutron. We also analyze how the associated energy of the tetraneutron would influence such results. Results. We find that the low-temperature, neutron-rich systems are the ones most affected by the presence of the tetraneutron, making NSs excellent environments for their formation. Moreover, its presence in strongly asymmetric matter may increase the proton and α-particle fractions considerably. This may have an influence on the dissolution of the accretion disk of the merger of two NSs.

Constraining Nuclear Parameters Using Gravitational Waves from f-mode Oscillations in Neutron Stars

Gravitational waves (GWs) emanating from unstable quasi-normal modes in neutron stars (NSs) could be accessible with the improved sensitivity of the current GW detectors or with the next-generation GW detectors and, therefore, can be employed to study the NS interior. Assuming f-mode excitation in isolated pulsars with typical energy of pulsar glitches and considering potential f-mode GW candidates for A+ (upgraded LIGO detectors operating at fifth observing run design sensitivity) and Einstein Telescope (ET), we demonstrate the inverse problem of NS asteroseismology within a Bayesian formalism to constrain the nuclear parameters and NS equation of state (EOS). We describe the NS interior within relativistic mean-field formalism. Taking the example of glitching pulsars, we find that for a single event in A+ and ET, among the nuclear parameters, the nucleon effective mass (m*) within 90% credible interval can be restricted within 10% and 5%, respectively. At the same time, the incompressibility (K) and the slope of the symmetry energy (L) are only loosely constrained. Considering multiple (10) events in A+ and ET, all the nuclear parameters are well constrained, especially m*, which can be constrained to 3% and 2% in A+ and ET, respectively. Uncertainty in the observables of a 1.4 M ⊙ NS such as radius (), f-mode frequency (), damping time (), and a few EOS properties including squared speed of sound (c s 2) are also estimated.

Probing the impact of WIMP dark matter on universal relations, GW170817 posterior, and radial oscillations

ABSTRACT In this study, we investigate the impact of weakly interacting massive particles (WIMPs) dark matter (DM) on C–Λ universal relations, GW170817 posterior, and radial oscillations of neutron stars (NSs) by considering the interactions of uniformly trapped neutralinos as a DM candidate with the hadronic matter through the exchange of the Higgs boson within the framework of the Next-to-Minimal Supersymmetric Standard Model (NMSSM). The hadronic equation of state (EOS) is modelled using the relativistic mean-field (RMF) formalism with IOPB-I, G3, and quark–meson coupling (QMC)-RMF series parameter sets. The presence of DM softens the EOS at both the background and the perturbation levels that implies a small shift to the left in the posterior accompanied by a much larger jump in the left of the mass–radius curves with increasing DM mass. It is observed that EOSs with DM also satisfy the C–Λ universality relations among themselves but get slightly shifted to the right in comparison to that without considering DM. Additionally, we find that the inclusion of DM allows the mass–radius (M–R) curves to remain consistent with observational constraints for HESS J1731−347, indicating the possibility of classifying it as a dark matter-admixed neutron star (DMANS). Moreover, we explore the impact of DM on the radial oscillations of pulsating stars and investigate the stability of NSs. The results demonstrate a positive correlation between the mass of DM and the frequencies of radial oscillation modes.

Structure and reaction studies of $$Z=120$$ isotopes using non-relativistic and relativistic mean-field formalisms

Structure and reaction studies of $$Z=120$$ isotopes using non-relativistic and relativistic mean-field formalisms

Comment on “Effect of density and nucleon-nucleon potential on the fusion cross section within the relativistic mean field formalism”

We discuss critical approximations making the calculated results of the article by Bhuyan et al. [Phys. Rev. C 101, 044603 (2020)] unreliable. Namely, all target nuclei used for the calculations are strongly deformed, whereas, in the article they are considered to be spherical. In addition, we indicate other misleading points and missing/incorrect references.

Structure and Decay Properties of Th Isotopes Using E-RMFT Formalism

In the present scenario, the search for the thermally fissile nuclei is crucial and also important not only for the research background of nuclear physics but also for the great social and economic impact on the country. Many theoretical works have been performed to analyze a series of Th and U-isotopes and found that some of these isotopes are stable against α-decays and spontaneous fission. Here, we have chosen the isotopic chain of Th-nuclei for the present analysis using relativistic mean-field formalism. The work also explores a few stable isotopes in this region of the nuclear landscape, which is crucial for understanding the exotic region of the nuclear landscape. The objective of this work is to study the bulk properties such as binding energies, root mean square charge radii, neutron-proton radii, neutron skin-thickness as well as intrinsic properties such as excitation energy and specific heat for the 216-238 Th-isotopic chain. Furthermore, the stability of these isotopes is investigated through their possible decay chain analysis. The relativistic mean-field theory was used to obtain the nuclear bulk properties, namely, binding energies, root-mean-square charge radii, neutron skin-thickness, and excitation energy. The steady solution of the temperature-dependent effective relativistic mean-field equations was obtained self-consistently by taking different inputs of the initial deformations. All the calculations were done for NL3, FSUGarnet and IOPB-I parameter sets for 216-238 Th-isotopes. The decay energy of α (Q α ) and β-decay (Q β ) were calculated from the binding energies and were further used to obtain the corresponding half-lives. We have analyzed the structural and decay properties of 216-238 Th isotopes. The excitation energy and specific heat are also estimated for these considered nuclei by using the temperature-dependent effective relativistic mean-field (E-RMFT) formalism for NL3, FSUGarnet and IOPB-I parameters sets. The calculated results are compared with the available experimental data and found similar observations for all the parameter sets at a given temperature. The excitation energy study signifies the shell melting point where maybe the shape transition occurs. Three phenomenological formulae such as Viola-Seaborg, Royer and modified universal decay law are adopted for the calculation of α-decay half-lives. We found lower values of α-decay half-lives indicating a higher rate of β-decay for the isotopic chain.

Isospin dependent properties of the isotopic chains of Scandium and Titanium nuclei within the relativistic mean-field formalism * *Supported by Science and Engineering Research Board (SERB) (CRG/2021/001229), FOSTECT (FOSTECT. 2019B.04), FAPESP (2017/05660-0)

Density-dependent nuclear symmetry energy is directly related to isospin asymmetry for finite and infinite nuclear systems. It is critical to determine the coefficients of symmetry energy and their related observables because they hold great importance in different areas of nuclear physics, such as the analysis of the structure of ground state exotic nuclei and neutron star studies. The ground state bulk properties of Scandium (Z = 21) and Titanium (Z = 22) nuclei are calculated, such as their nuclear binding energy ( ), quadrupole deformation ( ), two-neutron separation energy ( ), differential variation in the two-neutron separation energy ( ), and root-mean-square charge radius ( ). The isospin properties, namely the coefficient of nuclear symmetry energy and its components, such as the surface and volume symmetry energy of a finite isotopic chain, from the corresponding quantities of infinite nuclear matter, are also estimated. Finally, we correlate the neutron-skin thickness with the coefficient of symmetry energy and the related observables corresponding to the isotopic chains of these nuclei. The coherent density fluctuation model (CDFM) is used to estimate the isospin-dependent properties of finite nuclei, such as symmetry energy, surface symmetry energy, and volume symmetry energy, from their corresponding component in infinite nuclear matter. The relativistic mean-field (RMF) formalism with non-linear NL3 and relativistic-Hartree-Bogoliubov theory with density-dependent DD-ME2 interaction parameters are employed in the analysis. The weight function is estimated using the total density of each nucleus, which in turn is used with the nuclear matter quantities to obtain the effective symmetry energy and its components in finite nuclei. We calculate the ground state bulk properties, such as nuclear binding energy, quadrupole deformation, two-neutron separation energy, differential variation in the two-neutron separation energy, and root-mean-square charge radius, for the Sc- and Ti- isotopic chains using the non-linear NL3 and density-dependent DD-ME2 parameter sets. Furthermore, the ground state density distributions are used within the CDFM to obtain the effective surface properties, such as symmetry energy and its components, namely volume and surface symmetry energy, for both the parameter sets. The calculated quantities are used to understand the isospin dependent structural properties of finite nuclei near and beyond the drip line, which broadens the scope of discovering new magicity along the isotopic chains. A shape transition is observed from spherical to prolate near 44 and 40 for the Sc- and Ti- isotopic chains, respectively. Notable signatures of shell and/or sub-shell closures are found for the magic neutron numbers N = 20 and 28 for both isotopic chains using the nuclear bulk and isospin quantities. In addition to these, a few shell/sub-shell closure signatures are observed near the drip-line region at N = 34 and 50 by following the surface/isospin dependent observables, namely symmetry energy and its component, for both the isotopic chain of odd-A Sc- and even-even Ti- nuclei.

Systematic study of fusion barrier characteristics within the relativistic mean-field formalism

Background: The nuclear interaction potential and hence the fusion barrier formed between the interacting nuclei are the keys to understanding the complex fusion process dynamics. Purpose: This work intends to explore the fusion barrier characteristics of different target-projectile combinations within the relativistic mean-field (RMF) formalism. Methods: The density distributions of interacting nuclei and the microscopic R3Y NN interaction are obtained from relativistic mean-field (RMF) formalism for non-linear NL1, NL3, TM1, and relativistic-Hartree-Bogoliubov (RHB) approach for DDME2 parameter sets. The fusion and/or capture cross-section for the different reaction systems is calculated using the well-known $\ell$-summed Wong model. Results: The barrier height and position of 24 heavy-ion reaction systems are obtained for different nuclear density distributions and effective NN interaction potentials. The comparison of fusion and/or capture cross-section obtained from the $\ell$-summed Wong model is made with the available experimental data. Conclusions: The phenomenological M3Y NN potential is observed to give higher barrier heights than the relativistic R3Y NN potential for all the reaction systems. The comparison of results obtained from different relativistic parameter sets shows that the densities from NL1 and TM1 parameter sets give the lowest and highest barrier heights for all the systems under study. We observed higher barrier heights and lower cross-sections for DDR3Y NN potential as compared to density-independent R3Y NN potentials obtained for considered non-linear NL1, NL3 and TM1 parameter sets. According to the present analysis, it is concluded that the NL1 and NL3 parameter sets provide comparatively better overlap with the experimental fusion and/or capture cross-section than the TM1 and DDME2 parameter sets.

Cluster decay half-lives of Ba112–122 isotopes from the ground state and intrinsic excited state using the relativistic mean-field formalism within the preformed-cluster-decay model

Background: The cluster radioactivity from the neutron-deficient trans-tin region of the nuclear landscape has given immediate attention in the nuclear structure studies. Recent prediction of the emitting clusters from the ground and intrinsic excited states of proton-rich Ba isotopes opens the direction to explore the corresponding decay characteristics. A theoretical probe is necessary for understanding the cluster decays of Ba isotopes.Purpose: In the present study, cluster-decay half-lives are calculated and their decay characteristics are investigated for even-even $^{112--122}\mathrm{Ba}$ isotopes in both ground and intrinsic excited states along the proton drip line.Method: The preformed-cluster-decay model (PCM) is employed for estimating the decay half-lives. The preformation probability $({P}_{0})$ of the cluster decay from the parent nuclei is calculated by using the well-known phenomenological formula of Blendowske and Walliser [Phys. Rev. Lett. 61, 1930 (1988)], supplemented with the newly proposed $Q$-value-based preformation factor for the cluster with mass ${A}_{c}>28$. The penetration probability is calculated from the interaction potential using the Wentzel-Kramers-Brillouin (WKB) approximation. The nucleon-nucleon ($NN$) potential and individual binding energy (BE) of the cluster and daughter nuclei are estimated from the microscopic relativistic mean-field formalism (RMF) and compared with those from experiments and the finite-range-droplet model for the estimation of the $Q$ values of the cluster decays. The nonlinear RMF Lagrangian from which the effective relativistic R3Y $NN$ potential is derived using the $\mathrm{NL}{3}^{*}$ parameter set is employed for the calculation of the nuclear matter densities. The R3Y and well-known M3Y potential are employed to obtain the cluster-daughter interaction potential using the double-folding procedure along with their corresponding RMF densities. The total potential along with their respective cluster decay $Q$ values are used as input in the PCM to obtain the half-lives (${T}_{1/2}$) of $^{112--122}\mathrm{Ba}$ isotopes in their ground and intrinsic excited states.Results: The calculated half-lives (${T}_{1/2}$) for relativistic R3Y $NN$ potential and $Q$ values are found to deviate slightly compared to the ones from the M3Y due to the difference in their barrier characteristics. We notice that at elongated neck configuration a minimum neck-length parameter $\mathrm{\ensuremath{\Delta}}R=1.0\phantom{\rule{4.pt}{0ex}}\text{fm}$ is required for R3Y potential due to its repulsive nature, whereas the value is $0.5\phantom{\rule{4.pt}{0ex}}\text{fm}$ is suitable for the M3Y case. However, the estimated decay half-lives for both the potentials are in reasonably good agreement with the experimental lower limit of $^{114}\mathrm{Ba}$. In contrast with the ground-state decays, the inclusion of intrinsic excitation reduces the corresponding half-life values considerably but does not rule out the role of magicity.Conclusions: The sensitivity of the decay half-lives to $Q$ values and neck-length parameter has also been demonstrated. The decay half-lives are predicted for various cluster decays from neutron-deficient Ba isotopes. Since none of the experimental half-lives for the examined clusters is precisely known yet, further studies with available observed half-lives will be needed to substantiate our findings.

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 & 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 > 122.

Investigation of Astrophysical S-Factor for 12C + 16O and 16O + 16O Reactions Within the Relativistic Mean-Field Approach

The fusion dynamics of 12C + 16O and 16O + 16O astrophysical reactions is investigated using the relativistic mean-field (RMF) formalism for the non-linear NL3* parameter set. The RMF densities, along with the widely adopted M3Y and relativistic R3Y nucleon-nucleon (NN) interaction potentials, are used to obtain the nuclear potential within the double folding approach. The ℓ-summed Wong model is used to obtain the fusion cross-section. The ℓmax values are extracted from the sharp cut-off model. The fusion cross-section is also represented in terms of the astrophysical S-factor, and the results are compared with the available experimental data. The microscopic R3Y NN potential is observed to give a reasonable fit to the experimental cross-section.

Systematic study for the surface properties of neutron stars

[Background] In our earlier work {\bf [Phys. Rev. C 104, 055804 (2021)]}, we studied the surface properties of a neutron star, assuming it as a huge finite nucleus containing protons, neutrons, electrons, and muons. For the first time, we reported these results of a neutron star for a few representative masses. In the present paper, we give a detailed study of these quantities to draw definite conclusions. [Method]To carry forward our earlier idea, the energy density functional of the momentum space of neutron star matter is converted to the coordinate space in a local density approximation. This functional is again used to derive the neutron star surface properties within the coherent density fluctuation model using the weight function obtained from the density profile of the neutron star using the recently developed G3 and widely used NL3 and IU-FSU parameter sets in the context of relativistic mean-field formalism. [Results] The systematic surface properties of the neutron star, such as incompressibility, symmetry energy, slope parameter, and curvature coefficient, is calculated. The volume and surface components of the total symmetry energy are decomposed with the help of the $\kappa$ factor obtained from the volume to surface ratio of the symmetry energies in the liquid drop limit of Danielewicz. The magnitude of the computed surface quantities increases with the neutron star's mass. [Conclusion] The incompressibility $K^{\rm star}$, symmetry energy $S^{\rm star}$, slope parameter $L_{\rm sym}^{\rm star}$ and curvature coefficient $K_{\rm sym}^{\rm star}$ of the neutron stars with different mass are analyzed and found to be model dependent. NL3 is the stiffest equation of state endue us with the higher magnitude of surface quantities as compared to the G3 and IU-FSU forces.

Thermal relaxation of dark matter admixed neutron star

ABSTRACT Motivated by the various theoretical studies regarding the efficient capturing of dark matter by neutron stars, we explore the possible indirect effects of captured dark matter on the cooling mechanism of a neutron star. The equation of states for different configurations of dark matter admixed star at finite temperature is obtained using the relativistic mean-field formalism with the IOPB-I parameter set. We show that the variation in the dark matter momentum vastly modifies the neutrino emissivity through specific neutrino generating processes of the star. The specific heat and the thermal conductivity of a dark matter admixed star have also been investigated to explore the propagation of cooling waves in the interior of the star. The dependence of theoretical surface temperature cooling curves on the equation of state and chemical composition of the stellar matter has also been discussed along with the observational data of thermal radiation from various sources. We observed that the dark matter admixed canonical stars with $k_{f}^{\rm DM} \gt 0.04$ comply with the fast cooling scenario. Further, the metric for internal thermal relaxation epoch has also been calculated with different dark matter momentum and we deduced that increment of dark matter segment amplify the cooling and internal relaxation rates of the star.

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.

Divergence in the Relativistic Mean Field Formalism: A Case Study of the Ground State Properties of the Decay Chain of 214,216,218U Isotopes

A new α-emitting 214U has been recently observed experimentally. This opens the window to theoretically investigate the ground-state properties of the lightest known even–even neutron deficient 214,216,218U isotopes and to examine α-particle clustering around the shell closure. The decay half-lives are calculated within the preformed cluster-decay model (PCM). To obtain the α-daughter interaction potential, the RMF densities are folded with the newly developed R3Y and the well-known M3Y NN potentials for comparison. The alpha preformation probability (Pα) is calculated from the analytic formula of Deng and Zhang. The WKB approximation is employed for the calculation of the transmission probability. The individual binding energies (BE) for the participating nuclei are estimated from the relativistic mean-field (RMF) formalism and those from the finite range droplet model (FRDM) as well as WS3 mass tables. In addition to Z=84, the so-called abnormal enhancement region, i.e., 84≤Z≤90 and N<126, is normalised by an appropriately fitted neck-parameter ΔR. On the other hand, the discrepancy sets in due to the shell effect at (and around) the proton magic number Z=82 and 84, and thus a higher scaling factor ranging from 10−8–10−5 is required. Additionally, in contrast with the experimental binding energy data, large deviations of about 5–10 MeV are evident in the RMF formalism despite the use of different parameter sets. An accurate prediction of α-decay half-lives requires a Q-value that is in proximity with the experimental data. In addition, other microscopic frameworks besides RMF could be more reliable for the mass region under study. α-particle clustering is largely influenced by the shell effect.

Structural and decay properties of Z = 124 isotopes using RMF densities

We investigate various ground state characteristics of Z = 124 super-heavy nuclei in the region 296 ⩽ A ⩽322 using the relativistic mean field (RMF) formalism with NL3∗ parametrization. First, the calculation was carried out for the binding energy per nucleon, root-mean-square charge (rms) radii, quadrupole deformation parameter, two-neutron separation energies and other observables.The outcomes are comparable to the macro–microscopic predictions made by the Finite Range Droplet Model (FRDM) and the Weizsȧcker-Skyrme (WS) mass model. The binding energies of the parent and daughter nuclei are used to estimate the α-decay energies. Then, the Viola-Seaborg (VSS) formula and the universal decay law (UDL) have been used to explore the α-decay half-lives of two isotopes 124304,305, and the comparison is made with FRDM and WS predictions. The maximum half-lives of 124292,297 isotopes indicate the signature of shell closure.

Erratum: Effect of density and nucleon-nucleon potential on the fusion cross section within the relativistic mean field formalism [Phys. Rev. C 101 , 044603 (2020)

Received 3 May 2021DOI:https://doi.org/10.1103/PhysRevC.104.059901©2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasLow & intermediate energy heavy-ion reactionsNuclear fusionNucleon-nucleon interactionsPropertiesA ≥ 220Nuclear Physics

Isotopic shift in magic nuclei within relativistic mean-field formalism

The ground-state properties such as binding energy, root-mean-square radius, pairing energy, nucleons density distribution, symmetry energy, and single-particle energies are calculated for the isotopic chain of Ca, Sn, Pb, and Z = 120 nuclei. The recently developed G3 and IOPB-I forces along with the DD-ME1 and DD-ME2 sets are used in the analysis employing the relativistic mean-field approximation. To locate the magic numbers in the superheavy region and to explain the observed kink at neutron number N = 82 for Sn isotopes, a three-point formula is used to see the shift of the observable and other nuclear properties in the isotopic chain. Unlike the electronic configuration, due to strong spin-orbit interaction, the higher spin orbitals are occupied earlier than the lower spin, causing the possible kink at the neutron magic numbers. We find peaks at the known neutron magic number with the confirmation of sub-shell, shell closure respectively at N = 40, 184 for Ca and 304120.