Relativistic Mean-field Model Research Articles

Linkage among the neutron-skin thickness of 208Pb and nuclear symmetry energy using heavy particle radioactivity

The nuclear symmetry energy (NSE) is a linchpin in deciphering the behavior of matter in a wider domain extending from the characteristics of exotic nuclei to those of neutron stars in the cosmos. Therefore, it is crucial to utilize potential probes to constrain the NSE and its slope parameter L(ρ 0). In this work, we put forth the heavy particle radioactivity (HPR) as a probable bridge among the slope of NSE (L(ρ 0)) and neutron-skin thickness of 208Pb (R skin 208), which serves to put constrain on the L(ρ 0) value. The NSE and its slope parameter are determined from the single nucleon potential of asymmetric nuclear matter exploiting the analytical relationship between these quantities. The isovector/symmetry potential component of the single nucleon potential is derived through HPR for varying R skin 208 by employing the heavy particle/cluster densities and core densities from the relativistic mean field model in conjunction with M3Y nucleon–nucleon interaction. It facilitates in constraining the L(ρ 0) value and neutron skin of finite nuclei using HPR as a linkage, where heavy cluster and core densities of standard Fermi form are considered. The constrained value of L(ρ o ) is 45 ± 8 MeV, which aligns with other estimations derived from nuclear mass measurements, dipole polarizability measurements, and astrophysical data.

Cost of Inferred Nuclear Parameters toward the f-mode Dynamical Tide in Binary Neutron Stars

Gravitational-wave (GW) observations from neutron stars (NSs) in a binary system provide an excellent scenario to constrain the nuclear parameters. The investigation of Pratten et al. has shown that the ignorance of f-mode dynamical tidal correction in the GW waveform model of the binary NS system can lead to substantial bias in the measurement of NS properties and NS equations of state. In this work, we investigate the bias in the nuclear parameters resulting from the ignorance of dynamical tidal correction. In addition, this work demonstrates the sensitivity of the nuclear parameters and the estimated constraints on nuclear parameters and NS properties from future GW observations. We infer the nuclear parameters from GW observations by describing the NS matter within the relativistic mean field model. For a population of GW events, we notice that the ignorance of dynamical tide predicts a lower median for nucleon effective mass (m*) by ∼6% compared to the scenario when dynamical tidal correction is considered. Whereas, at a 90% credible interval, m* gets constrained up to ∼5% and ∼3% in A+ (the LIGO-Virgo detectors with a sensitivity of the fifth observing run) and Cosmic Explorer, respectively. We also discuss the resulting constraints on all other nuclear parameters, including compressibility, symmetry energy, and slope of symmetry energy, considering an ensemble of GW events. We do not notice any significant impact in analyzing nuclear parameters other than m* due to the ignorance of f-mode dynamical tides.

Relativistic energy density functional from momentum space to coordinate space within a coherent density fluctuation model

In this theoretical study, we have derived a simplified analytical expression for the binding energy per nucleon as a function of density and isospin asymmetry within the relativistic mean-field model. We have generated a new parameterization for the density-dependent DD-ME2 parameter set using the Relativistic-Hartree-Bogoliubov approach. Moreover, this work attempts to revisit the prior polynomial fitting in Kumar A. et al. Phys. Rev. C, 103 (2021) 024305 for the non-linear NL3 force parameter to provide a simplified set of equations for the energy density functional which is used for calculating the surface properties of finite nuclei. The current study improves the existing fitting procedure by effectively proposing a simpler model that provides comparably precise results while lowering the computational expense. To study the surface properties of finite nuclei with these parameterizations, we have adopted the coherent density fluctuation model, which effectively translates the quantities of nuclear matter from momentum space to coordinate space at local density. The isospin properties, such as symmetry energy and its surface and volume components, slope parameter, finite nuclear incompressibility, and surface incompressibility for even-even nuclei, are calculated for different mass regions. Moreover, we have studied the effect of density, weight function, and choice of relativistic force parameters on the surface properties. The significance of this work will help to determine the properties of nuclei along the nuclear landscape and can facilitate an improved understanding of the island of stability, heavy-ion collision, and nucleosynthesis, among others.

Constraining the Onset Density for the QCD Phase Transition with the Neutrino Signal from Core-collapse Supernovae

The occurrence of a first-order hadron–quark matter phase transition at high baryon densities is investigated in astrophysical simulations of core-collapse supernovae, to decipher yet incompletely understood properties of the dense matter equation of state (EOS) using neutrinos from such cosmic events. It is found that the emission of a nonstandard second neutrino burst, dominated by electron antineutrinos, is not only a measurable signal for the appearance of deconfined quark matter but also reveals information about the state of matter at extreme conditions encountered at the supernova (SN) interior. To this end, a large set of spherically symmetric SN models is investigated, studying the dependence on the EOS and the stellar progenitor. General relativistic neutrino-radiation hydrodynamics is employed featuring three-flavor Boltzmann neutrino transport and a microscopic hadron-quark hybrid matter EOS class. Therefore, the DD2 relativistic mean-field hadronic model is employed, and several variations of it, and the string-flip model for the description of deconfined quark matter. The resulting hybrid model covers a representative range of onset densities for the phase transition and latent heats. This facilitates the direct connection between intrinsic signatures of the neutrino signal and properties of the EOS. In particular, a set of linear relations has been found empirically. These potentially provide a constraint for the onset density of a possible QCD phase transition from the future neutrino observation of the next galactic core-collapse SN, if a millisecond electron anti-neutrino burst is present around or less than 1 s.

Constraining a relativistic mean field model using neutron star mass–radius measurements I: nucleonic models

ABSTRACT Measurements of neutron star mass and radius or tidal deformability deliver unique insight into the equation of state (EOS) of cold dense matter. EOS inference is very often done using generalized parametric or non-parametric models, which deliver no information on composition. In this paper, we consider a microscopic nuclear EOS model based on a field theoretical approach. We show that current measurements from NICER and gravitational wave observations constrain primarily the symmetric nuclear matter EOS. We then explore what could be delivered by measurements of mass and radius at the level anticipated for future large-area X-ray timing telescopes. These should be able to place very strong limits on the symmetric nuclear matter EOS, in addition to constraining the nuclear symmetry energy that determines the proton fraction inside the neutron star.

Extracting the hyperon-nucleon interaction via collective flows in heavy-ion collisions

The 2-body hyperon-nucleon interaction softens the equation of state of neutron star matter and leads to the maximum mass of neutron star to be 1.3-1.6M⊙, which deviates from the recent observation with the masses of PSR J0348+0432 (2.01±0.04M⊙) and J0740+6620 (2.14−0.09+0.10M⊙). One attempt is to introduce the more repulsive hyperon-nucleon interaction above the saturation density. A phenomenological Λ potential by fitting the 3-body ΛNN results of chiral effective field theory is implemented into the quantum molecular dynamics transport model to solve the ‘hyperon puzzle’ in neutron stars. It is found that the directed and elliptic flows are sensitive to the high-density hyperon-nucleon potentials in collisions of 197Au + 197Au and 124Sn + 124Sn. The influence of the phenomenological potential on the Λ yields, rapidity distributions and transverse momentum spectra is negligible in comparison with the ones calculated by the well-known relativistic mean-field model. The inclusion of the ΛN, ΣN and ΞN potentials leads to the reduction of hyperon production in the midrapidity region. The Λ directed flows and the slope in the midrapidity region are enhanced with the phenomenological potential and more consistent with the STAR data in collisions of 197Au + 197Au at sNN=3 GeV.

Correlation between the shape coexistence and stability in Mo and Ru isotopes

In a rapidly changing shape phase region, the presence of shape coexistence and its possible impact on the decay modes and half-lives, has been explored in astrophysically interesting Mo and Ru isotopes, in an extensive study within the microscopic theoretical framework using Nilsson Strutinsky Method and Relativistic Mean Field Model. The isotopic chains of Mo and Ru exhibit rapid shape phase transitions, triaxial γ softness, shape instability along with many coexisting states mostly with oblate and triaxial shapes. Proton and neutron separation energies have been calculated and compared with the available data. Results obtained from both the formalisms are in good agreement with each other as well as the available experimental data. Our computed β-decay half-lives and separation energy for nuclei exhibiting shape coexistence were examined for the decay mode from second minima state of the parent nuclei to the ground or excited state of the daughter nuclei. The second minima state of the coexisting shapes in Mo and Ru isotopes, were seen to impact the structural properties, β-decay half-lives, separation energy and hence the stability of the nuclei.

Exploring Semi-Inclusive Two-Nucleon Emission in Neutrino Scattering: A Factorized Approximation Approach

The semi-inclusive cross-section of two-nucleon emission induced by neutrinos and antineutrinos is computed by employing the relativistic mean field model of nuclear matter and the dynamics of meson-exchange currents. Within this model, we explore a factorization approximation based on the product of an integrated two-hole spectral function and a two-nucleon cross-section averaged over hole pairs. We demonstrate that the integrated spectral function of the uncorrelated Fermi gas can be analytically computed, and we derive a simple, fully relativistic formula for this function, showcasing its dependency solely on both missing momentum and missing energy. A prescription for the average momenta of the two holes in the factorized two-nucleon cross-section is provided, assuming that these momenta are perpendicular to the missing momentum in the center-of-mass system. The validity of the factorized approach is assessed by comparing it with the unfactorized calculation. Our investigation includes the study of the semi-inclusive cross-section integrated over the energy of one of the emitted nucleons and the cross-section integrated over the emission angles of the two nucleons and the outgoing muon kinematics. A comparison is made with the pure phase-space model and other models from the literature. The results of this analysis offer valuable insights into the influence of the semi-inclusive hadronic tensor on the cross-section, providing a deeper understanding of the underlying nuclear processes.

Impact of Fermi-surface distortion in a relativistic mean-field model on the moment of inertia and tidal deformability of neutron stars

Impact of Fermi-surface distortion in a relativistic mean-field model on the moment of inertia and tidal deformability of neutron stars

Constraining equations of state for massive neutron star within relativistic mean field models

Constraining equations of state for massive neutron star within relativistic mean field models

Equation of state and anisotropy of pressure of magnetars

AbstractMagnetars are the neutron stars with the highest magnetic fields up to 1015–1016 G. It has been proposed that they are also responsible for a variety of extra‐galactic phenomena, ranging from giant flares in nearby galaxies to fast radio bursts. Utilizing a relativistic mean field model and a variable magnetic field configuration, we investigate the effects of strong magnetic fields on the equation of state and anisotropy of pressure of magnetars. It is found that the mass and radius of low‐mass magnetars are weakly enhanced under the action of the strong magnetic field, and the anisotropy of pressure can be ignored. Unlike other previous investigations, the magnetic field is unable to violate the mass limit of the neutron stars.

Re-analysis of the Gamow-Teller distributions for [formula omitted] nuclei, 24Mg, 28Si, and 32S

The Gamow-Teller (GT) strength distributions of sd-shell N=Z nuclei (24Mg, 28Si, and 32S) are investigated within the framework of proton–neutron quasi-particle random phase approximation (pn-QRPA) using a deformed basis. The nuclear properties of these special nuclei were investigated by the Relativistic Mean Field (RMF) model. The RMF framework with density-dependent interactions (DD-PC1 and DD-ME2) was employed to compute ground-state deformation parameters (β2) using potential energy curves. The β2 values computed from the RMF and the finite range droplet model (FRDM) were employed as a free parameter in the pn-QRPA calculation to investigate the resulting GT strength distributions. The present model-based analyses compare well with the observed data.

Bayesian model averaging for nuclear symmetry energy from effective proton-neutron chemical potential difference of neutron-rich nuclei

The data-driven Bayesian model averaging is a rigorous statistical approach to combining multiple models for a unified prediction. Compared with the individual model, it provides more reliable information, especially for problems involving apparent model dependence. In this work, within both the non-relativistic Skyrme energy density functional and the nonlinear relativistic mean field model, the effective proton-neutron chemical potential difference Δμpn⁎ of neutron-rich nuclei is found to be strongly sensitive to the symmetry energy Esym(ρ) around 2ρ0/3, with ρ0 being the nuclear saturation density. Given discrepancies on the Δμpn⁎-Esym(2ρ0/3) correlations between the two models, we carried out a Bayesian model averaging analysis based on Gaussian process emulators to extract the symmetry energy around 2ρ0/3 from the measured Δμpn⁎ of 5 doubly magic nuclei 48Ca, 68Ni, 88Sr, 132Sn and 208Pb. Specifically, the Esym(2ρ0/3) is inferred to be Esym(2ρ0/3)=25.6−1.3+1.4MeV at 1σ confidence level. The obtained constraints on the Esym(ρ) around 2ρ0/3 agree well with microscopic predictions and results from other isovector indicators.

Relativistic Hartree-Fock model of nuclear single-particle resonances based on real stabilization method

With the development of radioactive ion beam devices along with associated nuclear experimental detection technologies, the research areas in atomic nuclei have been further expanded, illustrating many new aspects of nuclear excitation as well as the physics of exotic nuclei far from the <i>β</i>-stability line. For weakly bound nuclei, the Fermi surface may lie near the continuum, which facilitates the easy scattering of valence nucleons into the continuum to occupy the resonance state. These continuum effects are of crucial importance in explaining the unusual structure of unstable nuclei. In this work, with the real stabilization method in coordinate space, nuclear structure model for single-particle resonances is developed within the framework of the relativistic Hartree-Fock (RHF) theory. In order to extract potential single-particle resonance structures, we study the evolution of single-particle states with box size in the continuum. To avoid the instability of nuclear binding energy, the pairing correlations are not taken into account in the calculation. As an important motivation, the roles of Fock terms in determining the energy, widths and spin-orbit splitting are discussed for low-lying neutron resonance states of <inline-formula><tex-math id="M5">\begin{document}$^{120}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231632_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231632_M5.png"/></alternatives></inline-formula>Sn. By comparing with the relativistic mean field (RMF) model, it is found that the inclusion of exchange terms in the RHF model changes the in-medium balance of nuclear interactions and the equilibrium of nuclear dynamics, which in turn affects the description of the single-particle effective potential. For several neutron resonance states in <inline-formula><tex-math id="M6">\begin{document}$^{120}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231632_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231632_M6.png"/></alternatives></inline-formula>Sn with finite resonant width, RHF model predicts lower resonant energy and smaller widths than RMF. For the single-particle states around the continuum threshold, the featured signals of resonance can depend sensitively on the effective interactions. In addition, for the spin-partner states <inline-formula><tex-math id="M7">\begin{document}$\nu {\mathrm{i}}_{13/2}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231632_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231632_M7.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M8">\begin{document}$\nu {\mathrm{i}}_{11/2}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231632_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231632_M8.png"/></alternatives></inline-formula> in resonance states, the effect of Fock terms on their spin-orbit splitting is analyzed. In comparison with the bound states, the wave functions of resonant spin-partner states can differ remarkably from each other, changing the effective potential and single-particle energies correspondingly. Thus, additional components in the single-particle effective potential may also contribute to the spin-orbit splitting of resonance states, aside from the spin-orbit interaction. In order to elucidate the mechanism of Fock term in single-particle resonance physics, in the subsequent study more numerical techniques that have been recently developed will be incorporated into the RHF methodology.

Tensor and isovector–isoscalar terms of relativistic mean field model: Impacts on neutron-skin thickness, charge radius, and nuclear matter

The origin of the neutron skin thickness, measured by the CREX and PREX collaborations as thin for 40Ca and thick for 28Pb, remains a mystery. We investigate the effects of tensor and nonlinear isovector–isoscalar terms in a relativistic mean-field model (RMF) on the properties of finite nuclei and nuclear matter. Tensor couplings are crucial for better quality binding energies of finite nuclei and charge radii for relatively heavy nuclei. However, for light nuclei, the tensor terms cannot improve the compatibility of charge radius predictions by the RMF model with experimental data. We find that parameter sets with a larger nonlinear isovector–isoscalar parameter, particularly η2ρ = 0.028, agree better with experimental data for Δrnp across light, medium, and heavy isotope chains. Using PT28, we calculate Δrnp for 208Pb as 0.214 fm, J as 33.078, and L as 58.426. Δrnp for 208Pb obtained using PT28 is consistent with the PREX-II data. Moreover, the corresponding values of J and L agree with the low L constraints. Meanwhile, the canonical mass radius predicted by PT28 aligns with the mass and radius data from the NICER collaboration. The combination of tensor and nonlinear isovector–isoscalar couplings in the RMF model provides accurate predictions for finite nuclei binding energies and relatively heavy nuclei charge radii, resulting in relatively thick Δrnp values for 208Pb without substantial L values.

Relativistic mean-field model for the ultracompact low-mass neutron star HESS J1731-347

Relativistic mean-field model for the ultracompact low-mass neutron star HESS J1731-347

Quarkyonic matter and quarkyonic stars in an extended relativistic mean field model

Quarkyonic matter and quarkyonic stars in an extended relativistic mean field model

Meson-Exchange Currents in Quasielastic Electron Scattering in a Generalized Superscaling Approach

We introduce a method for consistently incorporating meson-exchange currents (MEC) within the superscaling analysis with relativistic effective mass, featuring a new scaling variable, ψ*, and single-nucleon cross-sections derived from the relativistic mean field (RMF) model of nuclear matter. The single-nucleon prefactor is obtained from the 1p1h matrix element of the one-body current, combined with the two-body current, averaged over a momentum distribution of Fermi kind. The approach is applied to selected quasielastic cross-sectional data on 12C. The results reveal a departure from scaling behavior, yet, intriguingly, the data collapse into a discernible band that is parametrized using a simple function of ψ*. This calculation, as developed, is not intended to provide pinpoint precision in extracting nuclear responses. Instead, it offers a global description of the quasielastic data with a considerable level of uncertainty. However, this approach effectively captures the overall trends of the quasielastic data beyond the Fermi gas model with a minimal number of parameters. The model incorporates partially transverse enhancement of the response, as embedded within the relativistic mean field framework. However, it does not account for enhancements attributed to the combined effects of tensor correlations and MEC, given that the initial RMF model lacks these correlations. A potential avenue for improvement involves starting with a correlated Fermi gas model to incorporate additional enhancements into single-nucleon responses. This study serves as a practical demonstration of implementing such corrections.

Classical and Bayesian error analysis of the relativistic mean-field model for doubly magic nuclei

Classical and Bayesian error analysis of the relativistic mean-field model for doubly magic nuclei

Bayesian analysis of a relativistic hadronic model constrained by recent astrophysical observations

ABSTRACTWe use Bayesian analysis in order to constrain the equation of state for nuclear matter from astrophysical data related to the recent measurements from the NICER mission, LIGO/Virgo collaboration, and probability distributions of mass and radius from other 12 sources, including thermonuclear busters, and quiescent low-mass X-ray binaries. For this purpose, we base our study on a relativistic hadronic mean field model including an ω − ρ interaction. Our results indicate optimal ranges for some bulk parameters at the saturation density, namely, effective mass, incompressibility, and symmetry energy slope (L0). For instance, we find $L_0 = 50.79^{+15.16}_{-9.24}$ MeV (Case 1) and $L_0 = 75.06^{+8.43}_{-4.43}$ MeV (Case 2) in a 68 per cent confidence interval for the two cases analysed (different input ranges for L0 related to the PREX-II data). The respective parametrizations are in agreement with important nuclear matter constraints, as well as observational neutron star data, such as the dimensionless tidal deformability of the GW170817 event. From the mass–radius curves obtained from these best parametrizations, we also find the ranges of 11.97 km ≤ R1.4 ≤ 12.73 km (Case 1) and 12.34 km ≤ R1.4 ≤ 13.06 km (Case 2) for the radius of the $1.4\, \mathrm{M}_\odot$ neutron star.