Introduction |

Part I. Elastic *hA* Scattering |

1 | General 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 |

2 | Elastic 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 |

3 | Hadron-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 |

4 | Elastic 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 |

5 | Elastic 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 |

6 | Production 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 |

7 | Production 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 |

8 | Parton 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 |

9 | High 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 |

10 | Multiple 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 |

11 | Phenomenological 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 |

12 | Particle 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 |

13 | Quark-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 |

14 | Spectra 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 |

15 | Cross 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 |

16 | High 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 |

Bibliography |

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*^{-1}_{QCD}. 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.