Nuclear matter equation of state and σ-meson parameters

We try to determine phenomenologically the extent of in-medium modification of σ-meson parameters so that the saturation observables of the nuclear matter equation of state (EOS) are reproduced. To calculate the EOS we have used Brueckner-Bethe-Goldstone formalism with Bonn potential as two-body interaction. We find that it is possible to understand all the saturation observables, namely, saturation density, energy per nucleon and incompressibility, by incorporating in-medium modification of σ-meson-nucleon coupling constant and σ-meson mass by a few per cent.     

Nuclear matter equation of state with single particle correlations

Symmetrical nuclear matter at finite temperature is studied in the framework of the Brueckner-Hartree-Fock approximation extended to include single-particle correlations. A liquid-vapor phase transition is observed, wtih a critical temperature of about 20 MeV, in close similarity with Skyrme force calculations. The inclusion of single-particle correlations introduces a significant temperature dependence in the single-particle potential as well as in the nucleon effective mass. In this scheme the Hughenholtz-Van Hove theorem is well satisfied throughout the range of density and temperature considered.     

Modifications of single-particle properties in nuclear matter induced by three-body forces

Within the self-consistent Green’s function formalism, we study the effects of three-body forces on the in-medium spectral function, self-energy and effective mass of the nuclear matter constituents, analyzing the density and momentum dependence.     

Nuclear equation of state and compression modes

The nuclear matter (N = Z and no Coulomb interaction) incompressibility coefficient, K _nm , which is directly related to the curvature of the nuclear matter equation of state, is a very important physical quantity in the study of properties of nuclei, supernova collapse, neutron stars and heavy-ion collisions. We review the current status of K _nm and the experimental and theoretical methods used to determine the value of K _nm from the excitation crosssections σ(E) and the transition strength distributions S(E) of compression modes in nuclei. In particular, we will consider the isoscalar giant monopole resonance (ISGMR) and the isoscalar giant dipole resonance (ISGDR) and provide a simple explanation to the long standing problem of the conflicting results obtained for K _nm , deduced from experimental data on excitation cross sections for the ISGMR and data for the ISGDR.     

Estimating consequences of three-body forces

Classifying the strengths of three-body forces 3BFs with the condition that observables must be cut-off independent, i.e., renormalized at each order, leads to surprising results with relevance for example for thermal neutron capture on the deuteron. Details and a better bibliography in ref. [1].     

The equation of state for neutron matter

The equation of state for cold neutron matter has been derived for densities of 10¹²–10¹⁶ g/cm³. The energy density, the pressure and the velocity of sound have been calculated from nuclear forces by quantum mechanical many body techniques, which are well established in nuclear physics. It is found, that neutron matter is not bound and becomes superluminal and ultrabaric at densities of about 10¹⁵ g/cm³. In order to justify these strange results it is shown that the same physical assumptions which lead to the superluminal and ultrabaric behaviour in our calculation yield the same effects also in the lorentz invariant classical models of Zeldovich, Bludman and Ruderman.     

A phenomenological quark matter equation of state

Both the MIT bag model and potential models are able to reproduce static properties of hadrons (e.g. their mass spectrum) with reasonable accuracy. However, while the extrapolation of the MIT bag model from hadrons to dense matter is rather straightforward, it is not the same for potential models. To deal with this problem, in this paper, the methods of relativistic quantum many-body theory are applied to the study of quark matter interacting through an instantaneous potential at zero temperature. It is shown that under some conditions, the quark plasma undergoes a first order transition from a massive state at low density to a gas of particles of decreasing mass at high density—as one expects from perturbative QCD. In addition, immediately after the transition, the quarks are in a collective bound state, which might perhaps be interpreted as the fact that they just start to leave the inside of hadrons.     

PCAC and three-body forces in nuclei

Using the consistency condition on strong interactions implied by a partially conserved axial-vector current together with reasonable assumptions about the behavior of the pion-nucleon scattering amplitude under extrapolation in the pion mass, it is shown that long-range three-body forces in nuclear matter are essentially zero. This implies that they are also small in nuclei.     

Multiple scattering with three-body forces

The multiple-scattering formalism is generalized to account for simultaneous interactions of a projectile with two target particles. In the cluster expansion of multiple-scattering theory such three-body interactions combine with iterates of two-body interactions. Some comparisons of multiple scattering with the Faddeev theory are given.     

Composition and equation of state of hot dense matter

The composition and equation of state of an equilibrium mixture of non-interacting baryons, pions and leptons is computed in the density range 10¹⁴–10^15.5 g/cm³ for two values of the entropy per baryon, S=1 and 2. These parameters are chosen because of their possible importance in the supernova explosion problem. The threshold densities for the appearance of hyperons are found to be lowered compared to the zero temperature case.     

Effective nucleon-nucleon interactions and nuclear matter equation of state

Nuclear matter equations of state based on Skyrme, Myers-Swiatecki and Tondeur interactions are written as polynomials of the cubic root of density, with coefficients that are functions of the relative neutron excess δ. In the extrapolation toward states far away from the standard one, it is shown that the asymmetry dependence of the critical point ( ,) depends on the model used. However, when the equations of state are fitted to the same standard state, the value of is almost the same in Skyrme and in Myers-Swiatecki interactions, while is much lower in Tondeur interaction. Furthermore, does not depend sensitively on the choice of the parameter γ in Skyrme interaction. Received: 5 May 2000 / Accepted: 16 January 2001     

Quark matter equation of state with Hartree-Fock approximation

Both the MIT bag model and potential models are able to reproduce with reasonable accuracy static hadron properties. However while extending the MIT bag model to compute the quark matter equation of state is straightforward, this is not so for potential models. Here this is attempted, starting from a Dirac equation in the Hartree-Fock approximation.     

Nuclear matter within the relativistic-mean-field model involving free-space nucleon-nucleon forces

Masses and radii of neutron stars were calculated within the relativistic-mean-field model by using free-space nucleon-nucleon forces. Multiparticle forces and correlations were taken into account phenomenologically by introducing a nonlinearity in isoscalar channels and three-particle forces in the scalar-isovector channel.     

Charged anisotropic matter with quadratic equation of state

We extend the work of Thirukkanesh and Maharaj (Class Quantum Gravity 25:235001, 2007) by considering quadratic equation of state for the matter distribution to study the general situation of a compact relativistic body. Presence of electromagnetic field and anisotropy in the pressure are also assumed. Some new classes of static spherically symmetrical models of relativistic stars are obtained. All the results given in Thirukkanesh and Maharaj (Class Quantum Gravity 25:235001, 2007) and there in can also be recovered as a particular case of our work.     

Quark matter equation of state with Hartree-Fock approximation

Both the MIT bag model and potential models are able to reproduce with reasonable accuracy static hadron properties. However while extending the MIT bag model to compute the quark matter equation of state is straightforward, this is not so for potential models. Here this is attempted, starting from a Dirac equation in the Hartree-Fock approximation.     

Connecting neutron star observations to three-body forces in neutron matter and to the nuclear symmetry energy

Using a phenomenological form of the equation of state of neutron matter near the saturation density which has been previously demonstrated to be a good characterization of quantum Monte Carlo simulations, we show that currently available neutron star mass and radius measurements provide a significant constraint on the equation of state of neutron matter. At higher densities we model the equation of state by using polytropes and a quark matter model. We show that observations offer an important constraint on the strength of the three-body force in neutron matter, and thus some theoretical models of the three-body force may be ruled out by currently available astrophysical data. In addition, we obtain an estimate of the symmetry energy of nuclear matter and its slope that can be directly compared to the experiment and other theoretical calculations.     

Bose-Einstein correlations and the equation of state of nuclear matter

Within a relativistic hydrodynamic framework, we use four different equations of state of nuclear matter to compare to experimental spectra from CERN/SPS experiments NA44 and NA49. Freeze-out hypersurfaces and Bose-Einstein correlation functions for identical pion pairs are discussed. We find that two-pion Bose-Einstein interferometry measures the relationship between the temperature and the energy density in the equation of state during the late hadronic stage of the fireball expansion. Little sensitivity of the light-hadron data to a quark-gluon plasma phase-transition is seen. Received: 19 April 1999 / Published online: 15 July 1999     

Limiting temperatures and the equation of state of nuclear matter

From experimental observations of limiting temperatures in heavy ion collisions we derive the critical temperature of infinite nuclear matter Tc=16.6+/-0.86. Theoretical model correlations between Tc, the compressibility modulus K, the effective mass m*, and the saturation density rho s are then exploited to derive the quantity (K/m*)1/2 rho -1/3 s. This quantity together with calculations employing Skyrme and Gogny interactions indicates a value of K in moderately excited nuclei that is in excellent agreement with the value determined from giant monopole resonance data.