Transport-theoretical description of nuclear reactions

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Abstract

In this review we first outline the basics of transport theory and its recent generalization to off-shell transport. We then present in some detail the main ingredients of any transport method using in particular the Giessen Boltzmann–Uehling–Uhlenbeck (GiBUU) implementation of this theory as an example. We discuss the potentials used, the ground state initialization and the collision term, including the in-medium modifications of the latter. The central part of this review covers applications of GiBUU to a wide class of reactions, starting from pion-induced reactions over proton and antiproton reactions on nuclei to heavy-ion collisions (up to about 30AGeV). A major part concerns also the description of photon-, electron- and neutrino-induced reactions (in the energy range from a few 100MeV to a few 100GeV). For this wide class of reactions GiBUU gives an excellent description with the same physics input and the same code being used. We argue that GiBUU is an indispensable tool for any investigation of nuclear reactions in which final-state interactions play a role. Studies of pion–nucleus interactions, nuclear fragmentation, heavy-ion reactions, hypernucleus formation, hadronization, color transparency, electron–nucleus collisions and neutrino–nucleus interactions are all possible applications of GiBUU and are discussed in this article.

Section snippets

Introduction and motivation

Any reaction involving nuclear targets poses a challenge to nuclear theory. Nuclear many-body effects come into play not only in the reaction mechanism, but also in the reaction amplitude and the description of final-state interactions. These many-body effects in general evolve dynamically during the course of a reaction and thus require a time-dependent framework for their description. For the experimenters the challenge is to draw conclusions from observed asymptotic particle yields, spectra

Transport equations

The BUU equation describes the space–time evolution of a many-particle system under the influence of mean-field potentials and a collision term, or more precisely, the time evolution of the Wigner transform of the real-time one-particle Green’s function, which is a generalization of the classical phase–space density. For each particle species, within the BUU approach one obtains an additional differential equation. All these equations are coupled through the gain and loss terms, which represent

Potentials and collision terms in GiBUU

The relevant degrees of freedom in the GiBUU model are baryons, mesons, leptons, their anti-particles and the gauge bosons. The parameters for all hadrons without strangeness and charm are taken from the πN scattering phase-shift analysis of Manley and Saleski [64]; the parameters for all other particles are taken from the PDG group [65]. Besides the nucleon and the pion, also Λ, Σ, Ξ, Ω, ΛC, ΣC, Ξc, ΩC, η, J/Ψ, K, K̄, D, D̄, Ds+ and Ds are assumed to be stable because their lifetimes are much

Application to nuclear reactions

In this section we discuss applications of GiBUU to various quite different reaction types of present interest. We start out with reactions involving hadrons, i.e. pions, protons, antiprotons and heavy-ions, as projectiles. In a second subsection we discuss the applications of GiBUU to electron scattering on nuclei, covering both quasi-elastic scattering and pion production. We also discuss here studies of hadronization in high-energy electron–nucleus collisions. This subsection is followed by

Summary

In this article we have given a comprehensive, detailed discussion of transport theory and its practical implementation in the GiBUU transport model. It has been our aim to give all the essential ingredients of this model so that GiBUU is not a black box to other theorists or experimenters using it for planning or analyzing an experiment.

GiBUU is unique in the sense that it uses the same physics input for very different nuclear reactions and is not a model of many-body physics optimized for one

Acknowledgments

The authors gratefully acknowledge a very close collaboration with Luis Alvarez-Ruso (Valencia) on various aspects of resonance properties and photonuclear and electroweak processes on nuclei. We are also indebted to Stefan Leupold (Uppsala) for extremely helpful discussions over many years about various aspects of off-shell transport theory and in-medium effects. The close contact with Volker Metag (Giessen) on experiments on photoproduction of mesons and his many suggestions have always been

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    1

    Also at the National Russian Research Center “Kurchatov Institute”, Moscow, Russia.

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