Nuclear matter

About: Nuclear matter is a(n) research topic. Over the lifetime, 10180 publication(s) have been published within this topic receiving 248261 citation(s).

Equation of state of nucleon matter and neutron star structure

Abstract: Properties of dense nucleon matter and the structure of neutron stars are studied using variational chain summation methods and the new Argonne ${v}_{18}$ two-nucleon interaction, which provides an excellent fit to all of the nucleon-nucleon scattering data in the Nijmegen database. The neutron star gravitational mass limit obtained with this interaction is 1.67${M}_{\ensuremath{\bigodot}}.$ Boost corrections to the two-nucleon interaction, which give the leading relativistic effect of order ${(v/c)}^{2},$ as well as three-nucleon interactions, are also included in the nuclear Hamiltonian. Their successive addition increases the mass limit to 1.80 and 2.20 ${M}_{\ensuremath{\bigodot}}.$ Hamiltonians including a three-nucleon interaction predict a transition in neutron star matter to a phase with neutral pion condensation at a baryon number density of $\ensuremath{\sim}0.2 {\mathrm{fm}}^{\ensuremath{-}3}.$ Neutron stars predicted by these Hamiltonians have a layer with a thickness on the order of tens of meters, over which the density changes rapidly from that of the normal to the condensed phase. The material in this thin layer is a mixture of the two phases. We also investigate the possibility of dense nucleon matter having an admixture of quark matter, described using the bag model equation of state. Neutron stars of 1.4${M}_{\ensuremath{\bigodot}}$ do not appear to have quark matter admixtures in their cores. However, the heaviest stars are predicted to have cores consisting of a quark and nucleon matter mixture. These admixtures reduce the maximum mass of neutron stars from 2.20 to 2.02 (1.91) ${M}_{\ensuremath{\bigodot}}$ for bag constant $B=200 (122) {\mathrm{M}\mathrm{e}\mathrm{V}/\mathrm{f}\mathrm{m}}^{3}.$ Stars with pure quark matter in their cores are found to be unstable. We also consider the possibility that matter is maximally incompressible above an assumed density, and show that realistic models of nuclear forces limit the maximum mass of neutron stars to be below 2.5${M}_{\ensuremath{\bigodot}}.$ The effects of the phase transitions on the composition of neutron star matter and its adiabatic index $\ensuremath{\Gamma}$ are discussed.

A theory of highly condensed matter

Abstract: To discuss properties of cold, condensed stellar objects such as neutron stars, it is necessary to know the stress tensor Tμν, the source in Einstein's field equations, from nuclear matter densities upwards. To overcome some of the difficulties with the conventional many-body approach to this problem, a model relativistic, many-body, quantum field theory composed of a baryon field, a neutral scalar meson field coupled to the scalar density ψ ψ , and a neutral vector meson field coupled to the conserved baryon current i Ψ γλψ is developed. For a uniform system of given baryon density ϱB, the linearized theory obtained by replacing the scalar and vector fields by their expectation pectation values, φ → φ0, Vλ → iδλ4V0 can be solved exactly. The resulting equation of state for nuclear matter exhibits nuclear saturation, and if the two dimensionless coupling constants in this theory are matched to the binding energy and density of nuclear matter, predictions are obtained for all other systems at all densities. In particular, neutron matter is unbound and the equation of state for neutron matter at all densities is presented; it extrapolates smoothly into the relativistic form P = ϵ. Comparison is made with some conventional many-body calculations. The full field theory is developed by expanding the fields about the condensed values φ0, V0, and the unperturbed hamiltonian is shown to correspond to the linearized theory. The energy shift due to these quantum fluctuations in the fields is related to the baryon Green's function. V0 is related directly to ϱB; φ0, however, must be determined through a self-consistency relation involving the baryon Green's function. The Feynman rules for this theory are developed. Expressions for the lowest-order contributions of the quantum fluctuations to the energy shift and φ0 are derived. It is shown that the terms qμqν in the vector-meson propagator do not contribute to these expressions, and a prescription involving assumptions on the limiting form of the theory as ϱB → 0 is presented which ensures that these lowest-order quantum fluctuations will yield finite results.

Modern theory of nuclear forces

Abstract: Nuclear forces can be systematically derived using effective chiral Lagrangians consistent with the symmetries of QCD. I review the status of the calculations for two- and three-nucleon forces and their applications in few-nucleon systems. I also address issues like the quark mass dependence of the nuclear forces and resonance saturation for four-nucleon operators.

Neutron Star Structure and the Equation of State

Abstract: The structure of neutron stars is considered from theoretical and observational perspectives We demonstrate an important aspect of neutron star structure: the neutron star radius is primarily determined by the behavior of the pressure of matter in the vicinity of nuclear matter equilibrium density In the event that extreme softening does not occur at these densities, the radius is virtually independent of the mass and is determined by the magnitude of the pressure For equations of state with extreme softening or those that are self-bound, the radius is more sensitive to the mass Our results show that in the absence of extreme softening, a measurement of the radius of a neutron star more accurate than about 1 km will usefully constrain the equation of state We also show that the pressure near nuclear matter density is primarily a function of the density dependence of the nuclear symmetry energy, while the nuclear incompressibility and skewness parameters play secondary roles In addition, we show that the moment of inertia and the binding energy of neutron stars, for a large class of equations of state, are nearly universal functions of the star's compactness These features can be understood by considering two analytic, yet realistic, solutions of Einstein's equations, by, respectively, Buchdahl and Tolman We deduce useful approximations for the fraction of the moment of inertia residing in the crust, which is a function of the stellar compactness and, in addition, the pressure at the core-crust interface

Hartree-Fock Calculations with Skyrme's Interaction. I. Spherical Nuclei

Abstract: Hartree-Fock calculations for spherical nuclei using Skyrme's density-dependent effective nucleon-nucleon interaction are discussed systematically. Skyrme's interaction is described and the general formula for the mean energy of a spherical nucleus derived. Hartree-Fock equations are obtained by varying the mean energy with respect to the single-particle wave functions of occupied states. Relations between the parameters of the Skyrme force and various general properties of nuclear matter and finite nuclei are analyzed. Calculations have been made for closed-shell nuclei using two rather different sets of parameters, both of which give good binding energies and radii for $^{16}\mathrm{O}$ and $^{208}\mathrm{Pb}$. Both interactions give good binding energies and charge radii for all closed-shell nuclei. Calculated electron scattering angular distributions agree qualitatively with experiment, and for one interaction there is good quantitative agreement. The single-particle energies calculated with the two interactions are somewhat different owing to a different nonlocality of the Hartree-Fock potentials, but both interactions give the correct order and density of single-particle levels near the Fermi level. They differ most strongly in their predictions for the energies of $1s$ single-particle states.