Equilibration within a semiclassical off-shell transport approach

Equilibration times for nuclear matter configurations -- modelling intermediate and high energy nucleus-nucleus collisions -- are evaluated within the semiclassical off-shell transport approach developed recently. The transport equations are solved for a finite box in coordinate space employing periodic boundary conditions. The off-shell transport model is shown to give proper off-shell equilibrium distributions in the limit $t \to \infty$ for the nucleon and $\Delta$-resonance spectral functions. We find that equilibration times within the off-shell approach are only slightly enhanced as compared to the on-shell limit for the momentum configurations considered.Comment: 19 pages, LaTeX, including 4 postscript figures, submitted to Nucl. Phys.

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

Low-momentum effective theory for nucleons

Starting from a precise two-nucleon potential, we use the method of unitary transformations to construct an effective potential that involves only momenta less than a given maximal value. We describe this method for an S-wave potential of the Malfliet-Tjon type. It is demonstrated that the bound and scattering state spectrum calculated within the effective theory agrees exactly with the one based on the original potential. This might open an avenue for the construction of effective chiral few-nucleon forces and for a systematic treatment of relativistic effects in few-body systems.Comment: 10 pp, LaTeX file, 4 figures (uses epsf), extended version, accepted for publiaction in Phys.Lett.

New nuclear three-body clusters \phi{NN}

Binding energies of three-body systems of the type \phi+2N are estimated. Due to the strong attraction between \phi-meson and nucleon, suggested in different approaches, bound states can appear in systems like \phi+np (singlet and triplet) and \phi+pp. This indicates the principal possibility of the formation of new nuclear clusters

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

Semiclassical transport of particles with dynamical spectral functions

The conventional transport of particles in the on-shell quasiparticle limit is extended to particles of finite life time by means of a spectral function A(X,\vec{P},M^2) for a particle moving in an area of complex self-energy \Sigma^{ret}_X = Re \Sigma^{ret}_X -i \Gamma_X/2. Starting from the Kadanoff-Baym equations we derive in first order gradient expansion equations of motion for testparticles with respect to their time evolution in \vec{X}, \vec{P} and M^2. The off-shell propagation is demonstrated for a couple of model cases that simulate hadron-nucleus collisions. In case of nucleus-nucleus collisions the imaginary part of the hadron self-energy \Gamma_X is determined by the local space-time dependent collision rate dynamically. A first application is presented for A + A reactions up to 95 A MeV, where the effects from the off-shell propagation of nucleons are discussed with respect to high energy proton spectra, high energy photon production as well as kaon yields in comparison to the available data from GANIL.Comment: 34 pages, LaTeX, 11-eps figures, submitted to Nucl. Phys. A, in prin

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

Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations

A new algorithm is presented to find exact traveling wave solutions of differential-difference equations in terms of tanh functions. For systems with parameters, the algorithm determines the conditions on the parameters so that the equations might admit polynomial solutions in tanh. Examples illustrate the key steps of the algorithm. Parallels are drawn through discussion and example to the tanh-method for partial differential equations. The new algorithm is implemented in Mathematica. The package DDESpecialSolutions.m can be used to automatically compute traveling wave solutions of nonlinear polynomial differential-difference equations. Use of the package, implementation issues, scope, and limitations of the software are addressed.Comment: 19 pages submitted to Computer Physics Communications. The software can be downloaded at http://www.mines.edu/fs_home/wherema

Coherent Photoproduction of eta-mesons on Three-Nucleon Systems

A microscopic few-body description of near-threshold coherent photoproduction of the eta-meson on tritium and He3 targets is given. The photoproduction cross-section is calculated using the Finite Rank Approximation (FRA) of the nuclear Hamiltonian. The results indicate a strong final state interaction of the eta-meson with the residual nucleus. Sensitivity of the results to the choice of the eta-N T-matrix is investigated. The importance of obeying the two-body unitarity condition in the eta-N system is demonstrated.Comment: 17 pages, RevTeX, 5 eps-figures, submitted to Phys. Rev.