Bulk Properties Of Nuclear Matter Research Articles

Bulk properties of nuclear matter in a modified relativistic dirac formalism

In this study, we employ a phenomenologically modified relativistic Dirac framework coupled with the σ - ω quark-meson coupling model to look into the properties of nuclear matter. By combining scalar and vector linear potential forms and incorporating perturbative adjustments for various factors such as centre-of-mass motion, gluonic, and pionic effects, we aim to find the nucleon’s mass in a vacuum. Then, we consider nucleon-nucleon interactions are constructed within a mean-field approximation. Our methodology systematically explores key characteristics of nuclear matter, including equations of state, compressibility, binding energy, and pressure. Furthermore, we compute essential parameters such as the nucleon charge radius, axial-vector coupling constant, pion coupling constant, nuclear sigma term, sensitivity, and potential strengths. And also, we calculate symmetry energy, density slop (L) and incompressibility ( K0 ). In addition, we compute the mass and radius of a neutron star and provide a graphical representation illustrating the relationship between mass and radius. To validate our results, we comprehensively compare them with other theoretical models and quark-meson coupling approaches, confirming the precision and reliability of our theoretical paradigm. Overall, our study enhances our understanding of the fundamental properties of nuclear matter and underscores their relevance in elucidating complex astrophysical phenomena.

Relativistic description of dense matter equation of state and neutron star observables constrained by recent astrophysical observations

In the present work, we investigate the bulk properties of nuclear matter and neutron stars with the newly proposed relativistic interaction NL-RS which provides an opportunity to readjust the coupling constants keeping in view the properties of finite nuclei, nuclear matter, PREX-II results for neutron skin thickness in 208Pb and astrophysical observations. The NL-RS model interaction has been proposed by fitting the ground state properties (binding energies and charge radii) of finite nuclei, bulk nuclear matter properties, and PREX-II results for neutron skin thickness of 208Pb. The relativistic interaction has been generated by including nonlinear self-interactions of σ and ω μ -mesons and mixed interactions of ω μ , and ρ μ -meson up to the quartic order. The proposed interaction harmonizes with the finite nuclei, bulk nuclear matter, and neutron star properties. A covariance analysis is performed to assess the statistical uncertainties on the model parameters and nuclear observables of interest along with correlations amongst them. The equation of state (EoS) composed of nucleons and leptons in β-equilibrium is computed with the proposed parameter set and used to study the neutron star structure. The maximum mass of the neutron star by employing the EoS computed with the NL-RS parameter set is 2.04 ± 0.03M ⊙ and the radius of a canonical mass neutron star (R 1.4) comes out to be equal to 13.06 ± 0.16 Km. The value of dimensionless tidal deformability, for canonical mass, is 602.23 ± 33.13 which satisfies the constraints of waveform models analysis of GW170817 within 90% confidence level.

Multiplicity dependence of the freezeout parameters in high energy hadron-hadron collisions* *Supported by Princess Nourah bint Abdulrahman University, Researchers Supporting Project Number PNURSP2024R106, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia. We would like to express our gratitude for the support received from Abdul Wali Khan University Mardan, Pakistan; Hubei University of Automotive Technology, Doctoral Research Fund number BK202313; University

We examined the transverse momentum ( ) spectra of various identified particles, encompassing both light-flavored and strange hadrons ( , , , ϕ, , , , and ), across different multiplicity classes in proton-proton collisions (p-p) at a center-of-mass energy of TeV. Utilizing the Tsallis and Hagedorn models, parameters relevant to the bulk properties of nuclear matter were extracted. Both models exhibit good agreement with experimental data. In our analyses, we observed a consistent decrease in the effective temperature (T) for the Tsallis model and the kinetic or thermal freeze-out temperature ( ) for the Hagedorn model, as we transitioned from higher multiplicity (class-I) to lower multiplicity (class-X). This trend is attributed to the diminished energy transfer in higher multiplicity classes. Additionally, we observed that the transverse flow velocity ( ) experiences a decline from class-I to class-X. The normalization constant, which represents the multiplicity of produced particles, was observed to decrease as we moved toward higher multiplicity classes. While the effective and kinetic freeze-out temperatures, as well as the transverse flow velocity, show a mild dependency on multiplicity for lighter particles, this dependency becomes more pronounced for heavier particles. The multiplicity parameter for heavier particles was observed to be smaller than that of lighter particles, indicating a greater abundance of lighter hadrons compared to heavier ones. Various particle species were observed to undergo decoupling from the fireball at distinct temperatures: lighter particles exhibit lower temperatures, while heavier ones show higher temperatures, thereby supporting the concept of multiple freeze-out scenarios. Moreover, we identified a positive correlation between the kinetic freeze-out temperature and transverse flow velocity, a scenario where particles experience stronger collective motion at a higher freeze-out temperature. The reason for this positive correlation is that, as the multiplicity increases, more energy is transferred into the system. This increased energy causes greater excitation and pressure within the system, leading to a quick expansion.

New equations of state for dense nuclear matter properties

In the present work, we investigate the bulk properties of nuclear matter and neutron stars with the newly proposed relativistic parametrizations HPUA, HPUB and HPUC which provides an opportunity to readjust the coupling parameters keeping in view the properties of finite nuclei, nuclear matter and astrophysical constraints. The HPUA, HPUB and HPUC are proposed by fitting both PREX-II + CREX results simultaneously, PREX-II and CREX results for neutron skin thickness of 208Pb and 48Ca respectively to assess their implications. The relativistic parameterizations have been generated by including non linear self-interactions of σ and ω- mesons and mixed interactions of ω, and ρ-meson up to the quartic order. The new equations of state (EoSs) composed of nucleons and leptons in β - equilibrium are constructed with the newly proposed parameter sets. The maximum mass of the neutron star by employing the EoSs computed with the HPU's parameter sets lies in the range 2.02±0.03 M⊙ - 2.04±0.03 M⊙ and the radius of canonical neutron star (R1.4) comes out to be equal to 12.89±0.08 Km - 13.27±0.30 Km (including BPS crust). The value of dimensionless tidal deformability, for canonical mass, is 590.83±22.58 - 631.52±78.13 which satisfies the constraints of waveform models analysis of GW170817. A covariance analysis is also performed to calculate the statistical uncertainties in the model parameters and nuclear matter observables along with their correlations.

CREX- and PREX-II-motivated relativistic interactions and their implications for the bulk properties of nuclear matter and neutron stars

We investigate the implications of parity-violating electron scattering experiment on neutron skin thickness of $^{48}\mathrm{Ca}$ [calcium radius experiment (CREX)] and $^{208}\mathrm{Pb}$ [lead radius experiment (PREX-II)] data on the bulk properties of finite nuclei, nuclear matter, and neutron stars. The neutron skin thickness from the CREX and PREX-II data is employed to constrain the parameters of relativistic mean-field models which includes different nonlinear, self- and cross-couplings among isoscalar-scalar $\ensuremath{\sigma}$, isoscalar-vector $\ensuremath{\omega}$, isovector-scalar $\ensuremath{\delta}$, and isovector-vector $\ensuremath{\rho}$ meson fields up to the quartic order. Three parametrizations of RMF model are proposed by fitting CREX, PREX-II, and both CREX as well as PREX-II data to assess their implications. A covariance analysis is performed to assess the theoretical uncertainties of model parameters and nuclear matter observables along with correlations among them. The RMF model parametrization obtained with the CREX data acquires much smaller value of symmetry energy ($J=28.97\ifmmode\pm\else\textpm\fi{}0.99$ MeV) and its slope parameter ($L=30.61\ifmmode\pm\else\textpm\fi{}6.74$ MeV) in comparison to those obtained with PREX-II data. The neutron star properties are studied by employing the equations of state composed of nucleons and leptons in $\ensuremath{\beta}$ equilibrium.

Medium modification of singly heavy baryons in a pion-mean-field approach

We investigate how the masses of singly heavy baryons undergo changes in nuclear matter. The mass spectrum of the singly heavy baryons was successfully described in a pion-mean field approach even with isospin symmetry breaking, based on which we extend the investigation to the medium modification of the singly heavy baryons. Since all dynamical parameters were determined by explaining the mass spectrum of the SU(3) light and singly heavy baryons in free space, we can directly implement the density-dependent functionals for the dynamical parameters, of which the density dependence was already fixed by reproducing the bulk properties of nuclear matter and medium modification of the SU(3) light baryons. We predict and discuss the density dependence of the masses of the singly heavy baryons.

Relativistic approach for the determination of nuclear and neutron star properties in consideration of PREX-II results

The bulk properties of nuclear matter and neutron stars with the newly generated relativisticinteraction Dev Bhoomi Himachal Pradesh (DBHP) are investigated, which provides an opportunity to modify the coupling parameters keeping in view the finite nuclei, nuclear matter, PREX-II data for neutron skin thickness in $^{208}\mathrm{Pb}$, and astrophysical constraints. The relativistic interaction has been generated by including all possible self and mixed interactions among $\ensuremath{\sigma}$, $\ensuremath{\omega}$, and $\ensuremath{\rho}$ mesons up to the quartic order satisfying the naturalness behavior of parameters. A covariance analysis is performed to assess the statistical uncertainties of the model parameters and observables of interest along with correlations amongst them. We obtained a value of neutron skin thickness for the $^{208}\mathrm{Pb}$ nucleus of $\mathrm{\ensuremath{\Delta}}{r}_{\mathrm{np}}=0.24\ifmmode\pm\else\textpm\fi{}0.02$ fm. The maximum gravitational mass of a neutron star and the radius corresponding to the canonical mass (${R}_{1.4}$) come out to be $2.03\ifmmode\pm\else\textpm\fi{}0.04$ ${M}_{\ensuremath{\bigodot}}$ and $13.39\ifmmode\pm\else\textpm\fi{}0.41$ km, respectively. The dimensionless tidal deformability $\mathrm{\ensuremath{\Lambda}}$ for a neutron star is also analyzed.

Singly heavy baryons in nuclear matter from an SU(3) chiral soliton model

We investigate how the masses of singly heavy baryons undergo changes in nuclear matter, based on a medium-modified SU(3) chiral soliton model. Having explained the bulk properties of nuclear matter, we discuss the masses of singly heavy baryons in nuclear matter. We generalize the vector-meson Lagrangian including the heavy-meson soliton interaction. The mass spectrum of singly heavy baryons are obtained with the effects of explicit SU(3) symmetry breaking considered as a perturbation. The results show that the mass of the singly heavy baryon in a nuclear medium is rather sensitive to the medium modifications of the heavy meson mass.

Universal trend of charge radii of even-even Ca–Zn nuclei

Radii of nuclear charge distributions carry information about the strong and electromagnetic forces acting inside the atomic nucleus. While the global behavior of nuclear charge radii is governed by the bulk properties of nuclear matter, their local trends are affected by quantum motion of proton and neutron nuclear constituents. The measured differential charge radii $\delta\langle r^2_c\rangle$ between neutron numbers $N=28$ and $N=40$ exhibit a universal pattern as a function of $n=N-28$ that is independent of the atomic number. Here we analyze this remarkable behavior in even-even nuclei from calcium to zinc using two state-of-the-art theories based on quantified nuclear interactions: the ab-initio coupled cluster theory and nuclear density functional theory. Both theories reproduce the smooth rise of differential charge radii and their weak dependence on the atomic number. By considering a large set of isotopic chains, we show that this trend can be captured by just two parameters: the slope and curvature of ${\delta\langle r^2_c\rangle(n)}$. We demonstrate that these parameters show appreciable model dependence, and the statistical analysis indicates that they are not correlated with any single model property, i.e., they are impacted by both bulk nuclear properties as well as shell structure.

Charge radii of exotic potassium isotopes challenge nuclear theory and the magic character of N\u2009=\u200932

Nuclear charge radii are sensitive probes of different aspects of the nucleon–nucleon interaction and the bulk properties of nuclear matter, providing a stringent test and challenge for nuclear theory. Experimental evidence suggested a new magic neutron number at N = 32 (refs. 1–3) in the calcium region, whereas the unexpectedly large increases in the charge radii4,5 open new questions about the evolution of nuclear size in neutron-rich systems. By combining the collinear resonance ionization spectroscopy method with β-decay detection, we were able to extend charge radii measurements of potassium isotopes beyond N = 32. Here we provide a charge radius measurement of 52K. It does not show a signature of magic behaviour at N = 32 in potassium. The results are interpreted with two state-of-the-art nuclear theories. The coupled cluster theory reproduces the odd–even variations in charge radii but not the notable increase beyond N = 28. This rise is well captured by Fayans nuclear density functional theory, which, however, overestimates the odd–even staggering effect in charge radii. These findings highlight our limited understanding of the nuclear size of neutron-rich systems, and expose problems that are present in some of the best current models of nuclear theory.

Isoscalar and Isovector Giant Resonances in Closed Shells Nuclei and Bulk Properties of Nuclear Matter

Centroid energies, $$E_{\textrm{CEN}}$$ , of the isoscalar ( $$T=0$$ ) and isovector ( $$T=1$$ ) giant resonances of multipolarities $$L_{m}=0$$ –3 in $${}^{\mathrm{40,48}}$$ Ca, $${}^{\mathrm{68}}$$ Ni, $${}^{\mathrm{90}}$$ Zr, $${}^{\mathrm{116}}$$ Sn, $${}^{\mathrm{144}}$$ Sm, and $${}^{\mathrm{208}}$$ Pb, were calculated within the fully self-consistent spherical Hartree–Fock (HF)-based random-phase approximation (RPA) theory, using 33 different energy density functionals associated with Skyrme-type effective nucleon–nucleon interactions of the standard form commonly employed in the literature. We also calculate the Pearson linear correlation coefficients between each $$E_{\mathrm{CEN}}$$ and each bulk property of nuclear matter (NM), associated with the Skyrme interactions used in the calculations, and determine the sensitivity of $$E_{\mathrm{CEN}}$$ to bulk properties of NM. By comparing the calculated values of $$E_{\textrm{CEN}}$$ to the experimental data, we constrain the values of the bulk NM properties. We find that interactions associated with the values of the NM effective mass, $$m^{\ast}/m=0.70$$ –0.90, incompressibility coefficient, $$K_{\textrm{NM}}=210$$ –240 MeV, and the enhancement coefficient of the energy-weighted sum rule of the isovector giant dipole resonance, $$\kappa=0.25$$ –0.70, best reproduce the experimental data.

Novel relativistic mean field Lagrangian guided by pseudo-spin symmetry restoration * * Supported by National Natural Science Foundation of China (11675065, 11875152, 11905088), Fundamental Research Funds for the central universities (lzujbky-2019-11), and the Supercompuer Center of HIRFL

The relativistic mean field (RMF) model has achieved great success in describing various nuclear phenomena. However, several serious defects are common. For instance, the pseudo-spin symmetry of high-l orbits is distinctly violated in general, leading to spurious shell closures and . This leads to problems in describing structure properties, including shell structures, nuclear masses, etc. Guided by the pseudo-spin symmetry restoration [Geng et al., Phys. Rev. C, 100: 051301 (2019)], a new RMF Lagrangian DD-LZ1 is developed by considering the density-dependent meson-nucleon coupling strengths. With the newly obtained RMF Lagrangian DD-LZ1, satisfactory descriptions can be obtained for the bulk properties of nuclear matter and finite nuclei. In particular, significant improvements on describing the single-particle spectra are achieved by DD-LZ1. In particular, the spurious shell closures and , commonly found in previous RMF calculations, are eliminated by the new effective interaction DD-LZ1, and consistently the pseudo-spin symmetry (PSS) around the Fermi levels is reasonably restored for both low-l and high-l orbits. Moreover, the description of nuclear masses is also notably improved by DD-LZ1, as compared to the other RMF Lagrangians.

Nuclear multipole excitations in the framework of self-consistent Hartree–Fock random phase approximation for Skyrme forces

In this study, the fully self-consistent Hartree–Fock (HF)-based random phase approximation (RPA) calculations were done for the $$^{40}\hbox {Ca}$$ and $$^{48}\hbox {Ca}$$ nuclei using 20 Skyrme-type interactions: KDE0, KDE0v1, SLy4, SLy5, SLy6, SK255, SKI2, SKI3, SKI5, SKM, SKMP, SKP, LNS, SGII, RAPT, SV-bas, SV-m56-O, SV-m64-O, SV-min and T6. Having a large number of Skyrme-force parameterisations requires a continuous search for the best for describing the experimental data. To examine our results, we compared the strength functions S(E), the charge density distribution and centroid energies $$E_{\mathrm{CEN}}$$ of the isoscalar giant monopole resonance (ISGMR), $$J^{\pi } = 0^{+}$$ , $$T = 0$$ , the isovector giant dipole resonance (IVGDR), $$J^{\pi } = 1^{-}$$ , $$T = 1$$ , and isoscalar giant quadrupole resonance (ISGQR), $$J^{\pi } = 2^{+}$$ , $$T = 0$$ with the available experimental data. Moreover, we discussed the sensitivities of the centroid energy $$m_{1}/m_{0}$$ and moment $$m_{1}$$ of the S(E) to the bulk properties of nuclear matter (NM), such as $$K_\mathrm{NM}$$ , the effective mass m* / m and the enhancement factor $$\kappa $$ .

Nuclear matter and neutron star properties with the extended Nambu-Jona-Lasinio model * * Supported by Hunan Provincial Natural Science Foundation of China (2015JJ2005), the Science Research Foundation of Education Department of Hunan Province (15C0029), the National Natural Science Foundation of China (11103001), and the construct program of the key discipline in Hunan province

An extended Nambu-Jona-Lasinio (eNJL) model with nucleons as the degrees of freedom is used to investigate properties of nuclear matter and neutron stars (NSs), including the binding energy and symmetry energy of the nuclear matter, the core-crust transition density, and mass-radius relation of NSs. The fourth-order symmetry energy at saturation density is also investigated. When the bulk properties of nuclear matter at saturation density are used to determine the model parameters, the double solutions of parameters are obtained for a given nuclear incompressibility. It is shown that the isovector-vector interaction has a significant influence on the nuclear matter and NS properties, and the sign of isovector-vector coupling constant is critical in the determination of the trend of the symmetry energy and equation of state. The effects of the other model parameters and symmetry energy slope at saturation density are discussed.

Effects of the equation of state on the core-crust interface of slowly rotating neutron stars

We systematically study the symmetry energy effects of the transition density $n_{\rm t}$ and the transition pressure $P_{\rm t}$ around the crust-core interface of a neutron star in the framework of the dynamical and the thermodynamical method respectively. We employ both the parabolic approximation and the full expansion, for the definition of the symmetry energy. We use various theoretical nuclear models, which are suitable for reproducing the bulk properties of nuclear matter at low densities, close to saturation density as well as the maximum observational neutron star mass. Firstly we derive and present an approximation for the transition pressure $P_{\rm t}$ and crustal mass $M_{\rm crust}$. Secondly, we explore the effects of the Equation of State (EoS) on a few astrophysical applications which are sensitive to the values of $n_{\rm t}$ and $P_{\rm t}$ including neutron star oscillation frequencies, thermal relaxation of the crust, crustal fraction of the moment of inertia and the r-mode instability window of a rotating neutron star. We found that the above quantities are sensitive mainly on the applied approximation for the symmetry energy (confirming previous results). Furthermore, an additional sensitivity also exists, depending on the used method (dynamical or thermodynamical). The above findings lead us to claim that the determination of the $n_{\rm t}$ and $P_{\rm t}$ must be reliable and accurate before they are used to constrain relevant neutron star properties.

Sensitivity of nuclear statistical equilibrium to nuclear uncertainties during stellar core collapse

I have systematically investigated the equations of state (EOSs) in nuclear statistical equilibrium under thermodynamic conditions relevant for core collapse of massive stars by varying the bulk properties of nuclear matter, the mass data for neutron-rich nuclei, and the finite-temperature modifications of the nuclear model. It is found that the temperature dependence of the nuclear free energies has a significant impact on the entropy and nuclear composition, which affect the dynamics of core-collapse supernovae. There is a little influence from the bulk properties and the mass data. For all models, common nuclei that are likely to contribute to core-deleptonization are those near $Z\approx30$ and $N\approx50$. A model with a semi-empirical expression for internal degrees of freedom, however, overestimates the number densities of magic nuclei with $N\approx50$ and $82$, while a model, in which nuclear shell effects are not considered, underestimates the number densities of heavy nuclei, and especially of the magic nuclei. Other models, which include the temperature dependence of shell effects in the internal degrees of freedom and/or in the nuclear internal free energy, indicate that the difference in population between magic nuclei and non-magic nuclei disappears as the temperature increases. The construction of complete statistical EOS will require further theoretical and experimental studies of medium-mass, neutron-rich nuclei with proton numbers 25-45 and neutron numbers 40-85.

Correlations between critical parameters and bulk properties of nuclear matter

The present work starts by providing a clear identification of correlations between critical parameters ($T_c$, $P_c$, $\rho_c$) and bulk quantities at zero temperature of relativistic mean-field models (RMF) presenting third and fourth order self-interactions in the scalar field $\sigma$. Motivated by the nonrelativistic version of this RMF model, we show that effective nucleon mass ($M^*$) and incompressibility ($K_o$), at the saturation density, are correlated with $T_c$, $P_c$, and $\rho_c$, as well as, binding energy and saturation density itself. We verify agreement of results with previous theoretical ones regarding different hadronic models. Concerning recent experimental data of the symmetric nuclear matter critical parameters, our study allows a prediction of $T_c$, $P_c$ and $\rho_c$ compatible with such values, by combining them, through the correlations found, with previous constraints related to $M^*$ and $K_o$. An improved RMF parametrization, that better agrees with experimental values for $T_c$, is also indicated.

Nuclear binding energies from a Bogomol'nyi-Prasad-Sommerfield Skyrme model

Recently, within the space of generalized Skyrme models, a submodel with a Bogomol'nyi-Prasad-Sommerfield (BPS) bound was identified that reproduces some bulk properties of nuclear matter already on a classical level and, as such, constitutes a promising field theory candidate for the detailed and reliable description of nuclei and hadrons. Here we extend and further develop these investigations by applying the model to the calculation of nuclear binding energies. Concretely, we calculate these binding energies by including the classical soliton energies, the excitation energies from the collective coordinate quantization of spin and isospin, the electrostatic Coulomb energies, and a small explicit isospin symmetry breaking, which accounts for the mass difference between proton and neutron. The integrability properties of the BPS Skyrme model allow, in fact, for an analytical calculation of all contributions, which may then be compared with the semi-empirical mass formula. We find that for heavier nuclei, where the model is expected to be more accurate on theoretical grounds, the resulting binding energies are already in excellent agreement with their physical values. This result provides further strong evidence for the viability of the BPS Skyrme model as a distinguished starting point and lowest-order approximation for the detailed quantitative investigation of nuclear and hadron physics.

THE PROPERTIES OF NUCLEAR MATTER

The microscopic and bulk properties of nuclear matter at zero and finite temperatures are studied in the frame of the Brueckner theory. The results for the symmetry energy are also obtained using different potentials. The calculations are based on realistic nucleon-nucleon interactions which reproduce the nucleon-nucleon phase shifts. These microscopic approaches are supplemented by a density-dependent contact interaction to achieve the empirical saturation property of symmetric nuclear matter. Special attention is paid to behavior of the effective mass in asymmetric nuclear matter. The nuclear symmetry potential at fixed nuclear density is also calculated and its value decreases with increasing the nucleon energy. The hot properties of nuclear matter are also calculated using T2-approximation at low temperatures. Good agreement is obtained in comparison with previous works around the saturation point.

How deep is the antinucleon optical potential at FAIR energies

The key question in the interaction of antinucleons in the nuclear medium concerns the deepness of the antinucleon–nucleus optical potential. In this work we study this task in the framework of the non-linear derivative (NLD) model which describes consistently bulk properties of nuclear matter and Dirac phenomenology of nucleon–nucleus interactions. We apply the NLD model to antinucleon interactions in nuclear matter and find a strong decrease of the vector and scalar self-energies in energy and density and thus a strong suppression of the optical potential at zero momentum and, in particular, at FAIR energies. This is in agreement with available empirical information and, therefore, resolves the issue concerning the incompatibility of G-parity arguments in relativistic mean-field (RMF) models. We conclude the relevance of our results for the future activities at FAIR.