Nuclear Statistical Equilibrium Model Research Articles

Binding energy shifts from heavy-ion experiments in a nuclear statistical equilibrium model

Chemical constants extracted from \(^{124}\)Xe+ \(^{124}\)Sn collisions at 32 AMeV are compared to the predictions of an extended nuclear statistical equilibrium model including mean-field interactions and in-medium binding energy shifts for the light (\(Z\le 2\)) clusters. The ion species and density dependence of the in-medium modification is directly extracted from the experimental data. We show that the shift increases with the mass of the cluster and the density of the medium, and we provide a simple linear fit for future use in astrophysical simulations in the framework of the CompOSE data base. The resulting mass fractions are computed in representative thermodynamic conditions relevant for supernova and neutron star mergers. A comparison to the results of a similar analysis of the same data performed in the framework of a relativistic mean-field model shows a good agreement at low density, but significant discrepancies close to the Mott dissolution of clusters in the dense medium.

New equation of state involving Bose–Einstein condensate of antikaon for supernova and neutron star merger simulations

We compute a new equation of state table including Bose-Einstein condensate of $K^{-}$ mesons for core collapse supernova and neutron star merger simulations. Nuclei and interacting nucleons in non-uniform matter is described in an extended version of the nuclear statistical equilibrium model including excluded volume effects whereas the uniform matter at higher densities is treated in the relativistic hadron field theory with density dependent couplings. The equation of state table is generated for a wide range of density ($10^{-12}$ to $\sim 1$ fm$^{-3}$), positive charge fraction (0.01 to 0.60) and temperature (0.1 to 158.48 MeV). The impact of antikaon condensate is investigated on different thermodynamic quantities for example free energy per baryon, entropy per baryon, pressure as well as compositions of matter. Furthermore, critical temperatures of antikaon condensation and the phase diagram of matter are also studied in this article.

Equation-of-state Table with Hyperon and Antikaon for Supernova and Neutron Star Merger

Abstract We develop a new equation-of-state (EOS) table involving thermal (anti)kaons, Bose–Einstein condensate of K − mesons, and Λ-hyperons for core-collapse supernova and neutron star merger simulations. This EOS table is based on a finite-temperature, density-dependent relativistic hadron field theory where baryon–baryon interaction is mediated by scalar σ, vector ω, and ρ mesons, using the parameter set DD2 for nucleons. The repulsive hyperon–hyperon interaction is mediated by an additional strange ϕ meson. The EOS for the K − condensed matter is also calculated within the framework of the relativistic mean field model, whereas the low-density, inhomogeneous matter is calculated in the extended nuclear statistical equilibrium model. The EOS table is generated for a wide range of values of three parameters—baryon density (10−12 to ∼1 fm−3), positive charge fraction (0.01–0.60), and temperature (0.1–158.48 MeV).

Light element (Z=1,2) production from spontaneous ternary fission of ^{252}Cf

The yields of light elements (Z=1,2) obtained from spontaneous ternary fission of ^{252}Cf are treated within a nonequilibrium approach, and the contribution of unstable nuclei and excited bound states is taken into account. These light cluster yields may be used to probe dense matter, and to infer in-medium corrections such as Pauli blocking which is determined by the nucleon density. Continuum correlations are calculated from scattering phase shifts using the Beth-Uhlenbeck formula, and the effect of medium modification is estimated. The relevant distribution is reconstructed from the measured yields of isotopes. This describes the state of the nucleon system at scission and cluster formation, using only three Lagrange parameters which are the nonequilibrium counterparts of the temperature and chemical potentials, as defined in thermodynamic equilibrium. We concluded that a simple nuclear statistical equilibrium model neglecting continuum correlations and medium effects is not able to describe the measured distribution of H and He isotopes. Moreover, the freeze-out concept may serve as an important ingredient to the nonequilibrium approach using the relevant statistical operator concept.

Clusterization in low and intermediate density nuclear matter in the modified nuclear statistical equilibrium model

.The formation of light and intermediate clusters in low and intermediate density nuclear matter is investigated within the modified nuclear statistical equilibrium model. We include clusters up to mass number A = 61 and densities up to 0.1 nucleons fm−3. The original nuclear statistical equilibrium model is modified by using density-dependent cluster binding energies. Whereas the light clusters are dominant at very low densities, it is found that the intermediate clusters become dominant at higher densities. As the temperature increases the dominance of the lighter clusters grows at the expense of the heavier clusters. We also evaluate the equation of state of nuclear matter within this model and determine that the critical temperature is 12.5 MeV, well below the values predicted by other equations of state. Finally we calculate the fragment multiplicity distribution within this model and find that its derivative has a maximum at a temperature (the liquid–gas transition temperature) close to that expected by other calculations.

Nuclear Statistical Equilibrium equation of state for core collapse

Extensive calculations of properties of supernova matter are presented, using the extended Nuclear Statistical Equilibrium model of Ref. [1] based on a statistical distribution of Wigner–Seitz cells modeled using realistic nuclear mass and level density tables, complemented with a non-relativistic Skyrme functional for unbound particles and beyond drip-line nuclei. Both thermodynamic quantities and matter composition are examined as a function of baryonic density, temperature, and proton fraction, within a large domain adapted for applications in supernova simulations. The results are also provided in the form of a table, with grid mesh and format compatible with the CompOSE platform [2] for direct use in supernova simulations. Detailed comparisons are also presented with other existing databases, all based on relativistic mean-field functionals, and the differences between the different models are outlined. We show that the strongest impact on the predictions is due to the different hypotheses used to define the cluster functional and its modifications due to the presence of a nuclear medium.

Light cluster production at NICA

Light cluster production at the NICA accelerator complex offers unique possibilities to use these states as "rare probes" of in-medium characteristics such as phase space occupation and early flow. In order to explain this statement, in this contribution theoretical considerations from the nuclear statistical equilibrium model and from a quantum statistical model of cluster production are supplemented with a discussion of a transport model for light cluster formation and with results from hydrodynamic simulations combined with the coalescence model.

Heat capacity of the neutron star inner crust within an extended nuclear statistical equilibrium model

Background: Superfluidity in the crust is a key ingredient for the cooling properties of proto-neutron stars. Present theoretical calculations employ the quasiparticle mean-field Hartree-Fock-Bogoliubov theory with temperature-dependent occupation numbers for the quasiparticle states.Purpose: Finite temperature stellar matter is characterized by a whole distribution of different nuclear species. We want to assess the importance of this distribution on the calculation of heat capacity in the inner crust.Method: Following a recent work, the Wigner-Seitz cell is mapped into a model with cluster degrees of freedom. The finite temperature distribution is then given by a statistical collection of Wigner-Seitz cells. We additionally introduce pairing correlations in the local density BCS approximation both in the homogeneous unbound neutron component, and in the interface region between clusters and neutrons.Results: The heat capacity is calculated in the different baryonic density conditions corresponding to the inner crust, and in a temperature range varying from 100 KeV to 2 MeV. We show that accounting for the cluster distribution has a small effect at intermediate densities, but it considerably affects the heat capacity both close to the outer crust and close to the core. We additionally show that it is very important to consider the temperature evolution of the proton fraction for a quantitatively reliable estimation of the heat capacity.Conclusions: We present the first modelization of stellar matter containing at the same time a statistical distribution of clusters at finite temperature, and pairing correlations in the unbound neutron component. The effect of the nuclear distribution on the superfluid properties can be easily added in future calculations of the neutron star cooling curves. A strong influence of resonance population on the heat capacity at high temperature is observed, which deserves to be further studied within more microscopic calculations.

NEW HYPERON EQUATIONS OF STATE FOR SUPERNOVAE AND NEUTRON STARS IN DENSITY-DEPENDENT HADRON FIELD THEORY

We develop new hyperon equation of state (EoS) tables for core-collapse supernova simulations and neutron stars. These EoS tables are based on a density-dependent relativistic hadron field theory where baryon-baryon interaction is mediated by mesons, using the parameter set DD2 from Typel et al. (2010) for nucleons. Furthermore, light and heavy nuclei along with the interacting nucleons are treated in the nuclear statistical equilibrium model of Hempel and Schaffner-Bielich which includes excluded volume effects. Of all possible hyperons, we consider only the contribution of $\Lambda$s. We have developed two variants of hyperonic EoS tables: in the np$\Lambda \phi$ case the repulsive hyperon-hyperon interaction mediated by the strange $\phi$ meson is taken into account, and in the np$\Lambda$ case it is not. The EoS tables for the two cases encompass wide range of density ($10^{-12}$ to $\sim$ 1 fm$^{-3}$), temperature (0.1 to 158.48 MeV), and proton fraction (0.01 to 0.60). The effects of $\Lambda$ hyperons on thermodynamic quantities such as free energy per baryon, pressure, or entropy per baryon are investigated and found to be significant at high densities. The cold, $\beta$-equilibrated EoS (with the crust included self-consistently) results in a 2.1 M$_{\odot}$ maximum mass neutron star for the np$\Lambda \phi$ case, whereas that for the np$\Lambda$ case is 1.95 M$_{\odot}$. The np$\Lambda \phi$ EoS represents the first supernova EoS table involving hyperons that is directly compatible with the recently measured 2 M$_{\odot}$ neutron stars.

NEW EQUATIONS OF STATE IN SIMULATIONS OF CORE-COLLAPSE SUPERNOVAE

We discuss three new equations of state (EOS) in core-collapse supernova simulations. The new EOS are based on the nuclear statistical equilibrium model of Hempel and Schaffner-Bielich (HS), which includes excluded volume effects and relativistic mean-field (RMF) interactions. We consider the RMF parameterizations TM1, TMA, and FSUgold. These EOS are implemented into our spherically symmetric core-collapse supernova model, which is based on general relativistic radiation hydrodynamics and three-flavor Boltzmann neutrino transport. The results obtained for the new EOS are compared with the widely used EOS of H. Shen et al. and Lattimer & Swesty. The systematic comparison shows that the model description of inhomogeneous nuclear matter is as important as the parameterization of the nuclear interactions for the supernova dynamics and the neutrino signal. Furthermore, several new aspects of nuclear physics are investigated: the HS EOS contains distributions of nuclei, including nuclear shell effects. The appearance of light nuclei, e.g., deuterium and tritium is also explored, which can become as abundant as alphas and free protons. In addition, we investigate the black hole formation in failed core-collapse supernovae, which is mainly determined by the high-density EOS. We find that temperature effects lead to a systematically faster collapse for the non-relativistic LS EOS in comparison to the RMF EOS. We deduce a new correlation for the time until black hole formation, which allows to determine the maximum mass of proto-neutron stars, if the neutrino signal from such a failed supernova would be measured in the future. This would give a constraint for the nuclear EOS at finite entropy, complementary to observations of cold neutron stars.

Fragmentation and clustering in star matter

The specificity of the crust-core phase transition in neutron star at zero and finite temperature will be discussed. It will be shown that, as a consequence of the presence of long range Coulomb interactions, the equivalence of statistical ensembles is violated and a clusterised phase is expected which is not accessible in the grancanonical ensemble. A specific analytical Nuclear Statistical Equilibrium model will be presented and some new quantitative results relevant for the supernova dynamics will be shown. Finally, the analogies and differences with the phenomenon of nuclear fragmentation will be highlighted.