Evolution of Nuclear Spectra with Nuclear Forces

We first define a series of NN interaction models ranging from very simple to fully realistic. We then present Green's function Monte Carlo calculations of light nuclei to show how nuclear spectra evolve as the nuclear forces are made increasingly sophisticated. We find that the absence of stable five- and eight-body nuclei depends crucially on the spin, isospin, and tensor components of the nuclear force.Comment: 5 pages, 2 figures, submitted to Phys. Rev. Let

Correlations and Equilibration in Relativistic Quantum Systems

In this article we study the time evolution of an interacting field theoretical system, i.e. \phi^4-field theory in 2+1 space-time dimensions, on the basis of the Kadanoff-Baym equations for a spatially homogeneous system including the self-consistent tadpole and sunset self-energies. We find that equilibration is achieved only by inclusion of the sunset self-energy. Simultaneously, the time evolution of the scalar particle spectral function is studied for various initial states. We also compare associated solutions of the corresponding Boltzmann equation to the full Kadanoff-Baym theory. This comparison shows that a consistent inclusion of the spectral function has a significant impact on the equilibration rates only if the width of the spectral function becomes larger than 1/3 of the particle mass. Furthermore, based on these findings, the conventional transport of particles in the on-shell quasiparticle limit is extended to particles of finite life time by means of a dynamical spectral function A(X,\vec{p},M^2). The off-shell propagation is implemented in the Hadron-String-Dynamics (HSD) transport code and applied to the dynamics of nucleus-nucleus collisions.Comment: 20 pages, 7 figures to appear in "Nonequilibrium at short time scales - Formation of correlations", edited by K. Morawetz, Springer, Berlin (2003), p16

Time- and Path-Ordered Green’s Functions for Nuclei

Time dependent Green's function methods provide a basic theory for nuclear dynamics and transport-properties such as related e.g. to heavy ion collisions. In the static limit this theory is also applicable to hot as well as zero-temperature nuclei. Retarded Green's functions are introduced in the non-equilibrium case while causal Green's functions have been used extensively for calculating ground-state properties of nuclei as have the very similar Brueckner methods. The purpose of this paper is to point out and clarify differences (and similarities) between these methods. In addition to some formal differences there are those resulting from accepted methods of application. Errors caused by using free Green's functions and related spectral-functions are pointed out. Only non-relativistic theories are discussed

New Forms of Deuteron Equations and Wave Function Representations

A recently developed helicity basis for nucleon-nucleon (NN) scattering is applied to th e deuteron bound state. Here the total spin of the deuteron is treated in such a helicity representation. For the bound state, two sets of two coupled eigenvalue equations are developed, where the amplitudes depend on two and one variable, respectively. Numerical illustrations based on the realistic Bonn-B NN potential are given. In addition, an `operator form' of the deuteron wave function is presented, and several momentum dependent spin densities are derived and shown, in which the angular dependence is given analytically.Comment: 19 pages (Revtex), 9 fig

Electromagnetic Scattering from Relativistic Bound States

The quasipotential formalism for elastic scattering from relativistic bound states is formulated based on the instant constraint in the Breit frame. The quasipotential electromagnetic current is derived from Mandelstam's five-point kernel and obeys a two-body Ward identity. Breit-frame wave functions are obtained directly by solving integral equations with nonzero total three-momentum, thus accomplishing a dynamical boost. Calculations of electron-deuteron elastic form factors illustrate the importance of the dynamical boost versus kinematic boosts of the rest frame wave functions.Comment: RevTeX 3.0 manuscript, 9 pages. UU-file is a single PostScript file of the manuscript including figures. U. MD PP #93-17

Note on the single-shock solutions of the Korteweg-de Vries-Burgers equation

The well-known shock solutions of the Korteweg-de Vries-Burgers equation are revisited, together with their limitations in the context of plasma (astro)physical applications. Although available in the literature for a long time, it seems to have been forgotten in recent papers that such shocks are monotonic and unique, for a given plasma configuration, and cannot show oscillatory or bell-shaped features. This uniqueness is contrasted to solitary wave solutions of the two parent equations (Korteweg-de Vries and Burgers), which form a family of curves parameterized by the excess velocity over the linear phase speed.Comment: Accepted for publication in Astrophysics & Space Scienc

Particle production in quantum transport theories

The particle production in the intermediate energy heavy ion collisions is discussed in the framework of the nonequilibrium Green's functions formalism. The evolution equations of the Green's functions for fermions allows for the discussion of the off-shell fermion propagator and of the large momentum component in the initial state. For the case of a homogeneous system numerical calculations of the meson production rate are performed and compared with the semiclassical production rate.Comment: 45 pages, figures included, uses FEYNMAN macro

Instant Two-Body Equation in Breit Frame

A quasipotential formalism for elastic scattering from relativistic bound states is based on applying an instant constraint to both initial and final states in the Breit frame. This formalism is advantageous for the analysis of electromagnetic interactions because current conservation and four momentum conservation are realized within a three-dimensional formalism. Wave functions are required in a frame where the total momentum is nonzero, which means that the usual partial wave analysis is inapplicable. In this work, the three-dimensional equation is solved numerically, taking into account the relevant symmetries. A dynamical boost of the interaction also is needed for the instant formalism, which in general requires that the boosted interaction be defined as the solution of a four-dimensional equation. For the case of a scalar separable interaction, this equation is solved and the Lorentz invariance of the three-dimensional formulation using the boosted interaction is verified. For more realistic interactions, a simple approximation is used to characterize the boost of the interaction.Comment: 20 pages in revtex 3, 3 figures. Fixed reform/tex errors