Cover Pajares C., Shabelski Yu.M. Relativistic Nuclear Interactions
Id: 61934
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Relativistic Nuclear Interactions

URSS. 272 pp. (English). ISBN 978-5-484-01015-8.
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This book is devoted to the processes of elastic and inelastic hadron-nucleus interactions at moderate (  1 GeV) and high energies. After short discussion of the main properties of atomic nuclei we present the standard Glauber theory for elastic and quasielastic hadron-nucleus and nucleus-nucleus scattering. Then the inelastic shadow corrections which appear at high energies are reviewed with several methods for their calculation.

We consider... (More)

Part I. Elastic hA Scattering
1General Features of Interaction with Nuclei
 1.1.Nuclear structure, protons, neutrons, meson currents
 1.2.Elastic eA scattering and nuclear form factors
 1.3.Hofst\"adter experiments and the geometry of the nucleus
 1.4.Unitarity condition, optical model and hA cross sections
 1.5.Relativistic kinematics and Lobachevski geometry
2Elastic and Quasi-elastic hA Scattering at Intermediate Energies
 2.1.Eikonal approximation and Glauber theory
 2.2.Elastic scattering on a deuteron target
 2.3.Elastic scatterings on heavy nuclei
 2.4.Quasielastic scattering
 2.5.Experimental proton and neutron distributions in the nuclei
 2.6.Parameters of NN amplitude for bound target nucleon
3Hadron-Nucleon Collisions at High Energies
 3.1.Elastic hN scattering via Regge-pole exchange
 3.2.The change of the space-time picture of interactions at high energies
 3.3.Diffractive dissociation in hN collisions
 3.4.Inclusive reactions
 3.5.The AGK cutting rules for Reggeon diagrams
4Elastic Hadron-Nucleus Scattering at High Energies
 4.1.High energy elastic hadron-deuteron scattering
 4.2.Deuteron disintegration in AGK cutting rules
 4.3.Inelastic screening for heavy nuclei. The two-channel approach
 4.4.Different hA cross sections in the two-channel approach
 4.5.Total cross sections of unstable particles
 4.6.Multi-channel approach for high energy hA collisions
 4.7.Color transparency
5Elastic and Quasielastic Scattering in the Additive Quark Model
 5.1.Total hN cross sections
 5.2.Elastic hN scattering
 5.3.Vector meson photoproduction
 5.4.Diffraction dissociation of hadrons
 5.5.Shadowing corrections for hadron-nucleus collisions
 5.6.Coherent production from nuclei
Part II. Multiple Hadron Production on Nuclear Targets
6Production of Particles in hA Collisions at Low Energy and in the Kinematics Forbidden for hN Interactions
 6.1.Secondary production on nucleon target near threshold
 6.2.Pion production on nuclear targets at low energies
 6.3.Subthreshold production
 6.4.Cumulative effect
7Production of Secondaries in the Intranuclear Cascade Model and the Arising Problems
 7.1.General features of the model
 7.2.Multiplicities of secondaries produced on nuclear targets
 7.3.The comparison of nu A and nu N inelastic collisions
 7.4.Formation time
 7.5.Secondary production in QCD
 7.6.Hadron resonance production
 7.7.Weak absorption of low-energy antiprotons produced on nuclear target
 7.8.The possibility to account some interference contributions in the cascade model
8Parton Model and Fan Reggeon Diagram Approach
 8.1.Space-time picture of secondary production
 8.2.Inelastic hadron-nucleus interactions in the Parton Model
 8.3.Reggeon Fan Diagrams Approach for description the inclusive spectra of secondaries
9High Energy Hadron-Nucleus Collisions in Additive Quark Model
 9.1.Spectator mechanism and its consequences for secondary production on nuclear targets
 9.2.The A-dependence of the inclusive spectra in the fragmentation region
 9.3.Comparison with the data
 9.4.Hadron content of secondaries in the fragmentation region
10Multiple Scattering Theory for Secondary Production in hA Collisions
 10.1.Non-coherent elastic scattering on nuclear target
 10.2.The multiparticle absorptive parts
 10.3.Self-shadowing effects
 10.4.Energy division in multiple interaction
 10.5.The problem of planar/non-planar diagrams
11Phenomenological Predictions of the Multiple Scattering Theory
 11.1.Multiplicities and spectra of secondaries
 11.2.Cross sections of double scattering in inelastic hadron-deuteron collisions
 11.3.Multinucleon interactions of incident hadron on nuclear target
12Particle Production in the String Model
 12.1.The motion of a relativistic string
 12.2.The decay kinematics of the string
 12.3.Stochastic iterative fragmentation of the string
 12.4.The Schwinger vacuum decay mechanism
 12.5.Dipole formalism
13Quark-Gluon String Model for Multiparticle Production
 13.1.General formalism
 13.2.Quark and diquark distributions in hadrons in QGSM
 13.3.Quark and diquark fragmentation functions
 13.4.Comparison of QGSM predictions with experimental data for meson production from nucleon target
 13.5.Secondary baryon/antibaryon production
 13.6.Baryon diffusion to large distances in rapidity space
14Spectra of Secondaries on Nuclear Targets
 14.1.Inclusive spectra on nuclear target in QGSM
 14.2.Comparison with experimental data
 14.3.Heavy flavour hadron production
 14.4.Parton distributions in the bound nucleons
 14.5.A-dependence of hard processes on nuclear targets with accounting of nuclear shadowing
 14.6.Predictions for superhigh energies and violation of Feynman scaling
 14.7.Passage of cosmic rays through the atmosphere in the QGSM
 14.8.Increase of transverse momenta of secondaries and its contribution to Feynman scaling violation
15Cross Sections and Probabilities in Heavy Ion Collisions
 15.1.Amplitude of elastic nucleus-nucleus scattering
 15.2.Monte Carlo simulation of nucleus-nucleus scattering
 15.3.Integrated cross sections
 15.4.Distributions on the number of interacting nucleons
 15.5.Multiplicity distributions and dispersions
16High Density Matter
 16.1.Possibility of new physics in heavy ion collisions
 16.2.Thermalization and Collective Flow
 16.3.Parton saturation and Color Glass Condensate
 16.4.Jet quenching
 16.5.Percolation of color sources
 16.6.Charmonium supression


The subject of relativistic nuclear physics lies between classical nuclear physics and high energy physics of elementary particles. There exists a natural boundary between the classical and relativistic nuclear physics. The first one considers mainly the nuclear structure and the nuclear excitations. In the case of relativistic nuclear physics we often deal with quasi-free nucleons, and sometimes it is possible to neglect their Fermi-motion. Moreover, in many cases the internal (quark-gluon) structure of the nucleons should be taken into account. Of course, there are problems where the classical and relativistic nuclear physics overlap. In the present book we will consider mainly the problems of relativistic nuclear physics.

We will consider the energy boundary between classical and relativistic nuclear physics as the energy where the production of at least one pion in the considered hA reaction is possible.

However, the energy region of relativistic nuclear physics can also be divided into two parts. The region of "intermediate energies" is that of energies where the average multiplicity of the produced pings is rather small. The most important fact is that in secondary production processes the momenta transferred to the nucleon target are large compared to the Fermi motion momenta of nucleons. The region of "high energies" is related to "Pomeron physics", where the multiplicities of secondaries are large, and the diffractive production of secondaries with very small momentum transferred to the target nucleon is possible. In the high energy region a number of new effects appear; they will be considered later.

Relativistic nuclear physics is important in many respects in both energy regions. First of all, we have an additional variable -- the atomic weight of the target that gives new possibilities for testing the models of multiparticle production. The size of a nuclear target is rather large in comparison with QCD length scale Lambda-1QCD. Thus, we have here an interaction with an extended target, and we can change its effective length by changing the atomic weight of the target. There are also ideas about a possible new state of the matter, the quark-gluon plasma, colour glass condensate, or another type of high density parton matter, which may be produced in heavy ion collisions. High energy physics experimental data are obtained very often on nuclear targets; in these cases we have to understand the possible nuclear corrections. More examples, both fundamental and applied, can be provided.

There exist many original papers and reviews on relativistic nuclear physics which will be quoted in the course of our discussions. However, most of these papers and reviews discuss only some specific problems, and some of the considered approaches are in serious disagreement with other ones. One of the most informative book which discusses many phenomenological problems together with experimental data is [1]. This book is, however, thirty years old, so many recent questions are just not considered there. Another problem is that the main part of [1] is devoted to the cascade model and its application to the description of the data. But there exist nowadays a lot of data which are in serious contradiction with this model. These problems will be considered in detail mainly in Part 2 of our book.

The very useful book [2] considers mainly heavy ion collisions. Among other books and reviews for introducing and developing the discussed problems we can suggest [3]--[7]. Many experimental data (mainly concerning multiple secondary production on nuclear targets) can be found in [8].

The main idea of the present book is to give a more or less complete analysis of the situation in relativistic nuclear physics without the discussion of very special or purely mathematical details. So this book should be considered as an introduction to the problem. However we cannot suggest it as a textbook for students. We would like to recommend it, say, for post-graduate students and young scientists who want to have some theoretical overview on the problem. So, in many cases the results are presented without the formal detailed derivation. More details can be found in the recommended References.

Most of the discussions are based on the so-called dispersion approach which, following from the unitarity condition, allows one to consider both the processes of elastic scattering and of multiparticle production from the same point of .

We present rather simple picture which can explain a lot of experimental data concerning mainly the high energy strong interactions with nuclear targets. This picture is based on the Multiple Scattering Theory with including the inelastic screening effects, when it is necessary. Of course, the numerical predictions needs, as a rule, some additional models and assumptions, however very often all these assumptions and model parameters can be found from the interactions with nucleons.

It is necessary to note that the understanding of secondary production from nuclear targets has not only pure scientific importance. There exist several practical projects which need the calculations of such processes. Among them we can say about the neutrino exploration of the Earth for purposes of geological research [9], muon catalysis for energy production by nuclear fusion [10] and creation of high energy (14 MeV) and high intensity neutron beams (mainly for material sciences) [11].

We assume that the reader is provided with the knowledge on quantum mechanics and the basic topics of relativistic quantum theory and elementary particle physics. So we give just a very short introduction to these problems.

Let us outline the structure of this book. After discussing the general features of the interactions with nuclei at high energies, we consider in more detail the most important informations concerning elastic hadron-nucleus (hA) scatterings at intermediate and high energies; in the latter case some new contributions (e.g. inelastic screening, coherent production, etc.) appear.

One of the central topics of our discussions is multiparticle production in such processes. We consider different approaches, and show that some of them are in contradiction with each other and with the description of the experimental data. We demonstrate that the most logical way is to constrain the multiple production reactions, in close connection with elastic processes, with the help of unitarity conditions by using the technique of eigenstates and/or of dispersion integrals. Again, we consider here both the regions of intermediate and high energies.

In the last two Section of the book we discuss very shortly some well-established results for high energy heavy ion collisions coming from the Multiple Scattering Theory and the effects which appear in the high density matter. High energy heavy ion physics is developed now very fast, so, for our opinion, a manuscript on this subject will be not complete at the moment of its printing.

Hadron-nucleus collisions were a fashionable subject mainly during the seventies and eighties. So the reader should not be surprised that many references and experimental data are rather old. Another reason for this is that we wanted to recall, at least partly, the history of relativistic nuclear physics. The main results in hadron-nucleus collisions are now more or less understandable, so it is time to give a general view on the problem. Recently the most interesting results in relativistic nuclear physics come from the heavy ion collisions, due to the experimental programs at the CERN-SPS, at the BNL-RHIC and at the forthcoming CERN-LHC.

Unfortunately, mainly due to the limited volume of the book we cannot discuss many fields and ideas of the relativistic nuclear physics, for example such as interplay between soft and hard particle production, hydrodynamical, kinetic and transport equation approaches, .


We are indebted to N.Armesto and J.Nyiri for reading the manuscript and many comments.

We are grateful to V.V.Anisovich, Ya. I.Azimov, K.G.Boreskov, M.A.Braun, V.M.Braun, A.Capella, L.G.Dakhno, J.Dias de Deus, V.I.Isakov, A.B.Kaidalov, O.V.Kancheli, M.N.Kobrynsky, B.Z.Kopeliovich, E.M.Levin, L.N.Lipatov, N.N.Nikolaev, M.G.Ryskin and A.A.Vorobyov.

We would like to clime that the background of our book is based on the ideas of V.N.Gribov, V.M.Shekhter and K.A.Ter-Martirosyan.


Carlos Pajares received his PhD from Universidad Complutense de Madrid in 1971. He was researcher postdoc at Orsay and Seattle and professor at Universidad Autonoma de Barcelona. He found the Particle Physics Department of the Universidad de Santiago de Compostela where was Rector in the period 1984--1990. He has published many research papers on multiparticle production, high density matter and heavy ion collisions.

Yuliy Mechislavovich Shabelski received his PhD in 1973 from ITEP, Moscow. He first worked as a researcher and then from 1985 as a senior scientist at the Petersburg Nuclear Physics Institute (PNPI) of the USSR Academy of Science. He has published the book "Quark Model and High Energy Collisions" (World Sci., 1985 and 2004) and over 160 reseach papers on the theory and the phenomenology of multiparticle production processes, nuclear target phenomena, heavy quark production, heavy ion physics and some applied physics problems.