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% S. Roesler, R. Engel and J. Ranft:
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\hyphenation{DTUNUC}
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\begin{document}
%
\title*{The~Monte~Carlo~Event~Generator~DPMJET-III\footnote{SLAC-PUB-8740,
Talk given at the Conference ``Monte Carlo 2000'', Lisbon, Portugal, 
23-26 Oct. 2000}}
\toctitle{The Monte Carlo Event Generator DPMJET-III}
\titlerunning{DPMJET-III}
%
\author{Stefan Roesler\inst{1}
\and    Ralph Engel\inst{2}
\and    Johannes Ranft\inst{3} }
%
\authorrunning{Stefan Roesler et al.}
%
\institute{SLAC, P.O. Box 4349, Stanford CA 94309, USA
\and       University of Delaware, Bartol Res. Inst., Newark DE 19716, USA
\and       University of Siegen, D--57068 Siegen, Germany}
%
\maketitle              % typesets the title of the contribution
%
\begin{abstract}
A new version of the Monte Carlo event generator \textsc{Dpmjet} is presented.
It is a code system based on the Dual Parton Model and unifies all features 
of the \textsc{Dtunuc-2}, \textsc{Dpmjet}-II and \textsc{Phojet}1.12 event 
generators.
\textsc{Dpmjet-III} allows the simulation of hadron-hadron, hadron-nucleus, 
nucleus-nucleus, photon-hadron, photon-photon and photon-nucleus interactions 
from a few GeV up to the highest cosmic ray energies.
\end{abstract}
%
%-----------------------------------------------------------------------
\section{Introduction}
\vspace*{-0.1cm}
%
Hadronic collisions at high energies involve the production of
particles with low transverse momenta, the so-called \textit{soft}
multiparticle production. The theoretical tools available at present
are not sufficient to understand this feature from QCD and
phenomenological models are typically applied instead. The
Dual Parton Model (DPM) \cite{dpm-a} is such a model and its fundamental
ideas are presently the basis of many of the Monte Carlo (MC)
implementations of soft interactions in codes used for Radiation
Physics simulations.

Many of these implementations are however limited in their application by,
for example, the collision energy range which they are able to describe
or by the collision partners (hadrons, nuclei, photons) which the model can
be used for. With respect to modern \textit{multi-purpose} codes for particle
interaction and transport these limitations at high energy are clearly often a
disadvantage.

In this paper we present the \textsc{Dpmjet}-III code system, a MC event 
generator based on the DPM which is unique in its wide range of application.
%and might therefore help in overcoming many of these shortages. 
\textsc{Dpmjet}-III is capable of simulating hadron-hadron, hadron-nucleus,
nucleus-nucleus, photon-hadron, photon-photon and photon-nucleus interactions
from a few GeV up to the highest cosmic ray energies. 

%All aspects of the high-energy collisions described by \textsc{Dpmjet}-III 
%have been extensively benchmarked against experimental data.
In the present paper we give an overview over the different components and
models of \textsc{Dpmjet}-III and present a few examples for comparisons of 
model results with experimental data.
%-----------------------------------------------------------------------
\vspace*{-0.1cm}
\section{The Concept of the Program}
\vspace*{-0.1cm}
%
\textsc{Dpmjet}-III is the result of merging all features of the 
event generators \textsc{Dpmjet}-II \cite{dpmjet2-a,dpmjet2-b} and 
\textsc{Dtunuc-2} \cite{dtunuc2-a,dtunuc2-b} into one single code system.
The latter two codes are similar in their underlying concepts, however they
differ in the Monte Carlo realization of these concepts, in particular,
of the DPM.

Whereas individual nucleon-nucleon collisions in \textsc{Dpmjet}-II are
simulated based on the \textsc{Dtujet} model \cite{dtujet}, 
\textsc{Dtunuc-2} is using \textsc{Phojet}1.12 \cite{phojet-a,phojet-b}.
Since \textsc{Phojet} describes not only hadron-hadron interactions but also
hadronic interactions involving photons, \textsc{Dtunuc-2} allows also
the simulation of photoproduction off nuclei. Therefore, the strength of
\textsc{Dtunuc-2} is in the description of photoproduction and nuclear
collisions up to TeV-energies. On the other hand, \textsc{Dpmjet}-II is 
widely used to simulate cosmic-ray interactions up to 
the highest observed energies \cite{dpmjet2-b}.

However, many program modules in \textsc{Dpmjet}-II and \textsc{Dtunuc-2} 
are also identical. Examples are the Glauber-Gribov formalism for
the calculation of nuclear cross sections \cite{diagen}, the formation-zone 
intranuclear cascade \cite{fzic}, the treatment of excited 
nuclei \cite{fzic-a,fzic-b} and
the \textsc{Hadrin}-model for the description of interactions below 5 GeV
\cite{hadrin}.

The core of \textsc{Dpmjet}-III consists of \textsc{Dtunuc-2} and
\textsc{Phojet}1.12. In addition all those features of \textsc{Dpmjet}-II 
were added which were not part of \textsc{Dtunuc-2} so far.
This includes, for example, quasi-elastic neutrino interactions 
\cite{qelnu} and certain baryon-stopping diagrams~\cite{barystop-b}.
%-----------------------------------------------------------------------
\vspace*{-0.1cm}
\section{Models Implemented in DPMJET-III}
\vspace*{-0.1cm}
%
%In the following a brief description is given of the main building blocks
%of \textsc{Dpmjet}-III.
%
\vspace*{-0.1cm}
\subsection{The Realization of the Dual Parton Model}
\vspace*{-0.1cm}
%
The DPM combines predictions 
of the large $N_c,N_f$ expansion of QCD \cite{Veneziano74}
and assumptions of duality \cite{Chew78} with
Gribov's reggeon field theory \cite{Gribov67a-e}.
\textsc{Phojet}, being used for the simulation of 
elementary hadron-hadron, photon-hadron and 
photon-photon interactions
with energies greater than 5 GeV, implements the DPM as a two-component model
using Reggeon theory for soft and perturbative QCD for hard interactions.
In addition to the model features as described in detail in \cite{PhD-RE},
the version 1.12 incorporates a model for high-mass diffraction
dissociation including multiple jet production and recursive
insertions of enhanced pomeron graphs (triple-, loop- and double-pomeron
graphs). In the following only the new features are briefly discussed.

High-mass diffraction dissociation is simulated as pomeron-hadron or
pomeron-pomeron scattering, including multiple soft and hard
interactions \cite{Bopp98a}. To account for the nature of the pomeron being a
quasi-particle, the CKMT pomeron structure function \cite{Capella96a}
with a hard gluonic
component is used. These considerations refer to pomeron exchange
reactions with small pomeron-momentum transfer, $|t^2|$. For large
$|t^2|$ the rapidity gap production (e.g. jet-gap-jet events) is 
implemented on the basis the color evaporation model \cite{Eboli98a}.

Extrapolating the two-channel eikonal-unitarization of a hadron-hadron 
amplitude as used in \textsc{Phojet} to very high energies raises the
question of the treatment of enhanced graphs which become more and more
important at high energy and lead to large multiplicity fluctuations. 
A full amplitude calculation including enhanced graphs is very involved
and not suited for a Monte Carlo implementation. Therefore, based on the 
results of \cite{Kaidalov86b-e}, we use the simpler approach of 
interpreting each 
soft pomeron as the sum of a series of a bare soft pomeron and enhanced 
graphs (Froissaron). In practice, this results in the simulation of 
possibly recursive subdivisions of a single Froissaron cut into various 
other configurations such as, for example, two cut pomerons or 
a single cut pomeron and a diffractive scattering. However, the current
implementation should only be considered as a first step toward a
consistent treatment of enhanced graphs at very high energy 
because of its limitation to soft interactions. 
%
\vspace*{-0.1cm}
\subsection{Hadronic Interactions Involving Photons}
\vspace*{-0.1cm}
%
The photon is assumed to be a superposition of a \textit{bare} photon 
interacting in direct processes and a \textit{hadronic} photon interacting
in resolved processes.

The description of interactions of the hadronic photon with nuclei
is based on the Generalized Vector Dominance Model (GVDM)
\cite{GVDM}. Photons are assumed to fluctuate into quark-antiquark states $V$
of a certain mass $M$ and the interaction is described as scattering of
the hadronic fluctuation on the nucleus. Correspondingly, the scattering
amplitude $a_{VA}$ reads \cite{dtunuc2-a}
\begin{eqnarray}
a_{VA}(s,Q^2,M^2,\vec{B})=\int\prod_{j=1}^{A}d^3r_j\
\psi_A^\star\
a_{VA}(s,Q^2,M^2,\vec{B}_1,\ldots,\vec{B}_A)\
\psi_A  \\
a_{VA}(s,Q^2,M^2,\vec{B}_1,\ldots,\vec{B}_A)=
\frac{i}{2}\left(1-\prod_{\nu=1}^{A} 
\left[1+2ia_{VN}(s,Q^2,M^2,\vec{B}_\nu)\right]\right)
\end{eqnarray}
where $a_{VA}$ is expressed in terms of interactions on individual
nucleons $N$ according to the Gribov-Glauber picture (see below).
The model is limited to low photon-virtualities $Q^2$ satisfying the
relation $Q^2\ll 2m_N\nu$ ($\nu$ and $m_N$ being the photon energy and
nucleon mass).
For individual $q\bar{q}$-nucleon interactions it is sufficient to
consider only two generic $q\bar{q}$-states, the first one grouping
$\rho^0$, $\omega$ and $\phi$ and $\pi^+\pi^-$-states up to the $\phi$-mass
together and the second one including all $q\bar{q}$-states with higher
masses~\cite{phojet-a}. 

Direct photon interactions are treated as either gluon-Compton scattering
or photon-gluon fusion processes on a single nucleon. The consideration
of so-called anomalous interactions allows a steady transition between
direct and resolved interactions \cite{dtunuc2-a}.

Finally, an interface to \textsc{Lepto}6.5 \cite{lepto6} allows to
simulate deep-inelastic scattering off nuclei.
%
\vspace*{-0.1cm}
\subsection{The Gribov-Glauber Multiple Scattering Formalism}
\vspace*{-0.1cm}
%
The Monte Carlo realization of the Gribov-Glauber multiple scattering
formalism follows the algorithms of \cite{diagen} and allows the 
calculation of total, elastic, quasi-elastic and production cross
sections for any high-energy nuclear collision. 
Parameters entering the hadron-nucleon scattering amplitude (total cross
section and slope) are calculated within \textsc{Phojet}.

For photon-projectiles ideas of the GVDM have been incorporated
in order to correctly treat the mass of the hadronic fluctuation and its 
coherence length as well as pointlike photon interactions \cite{dtunuc2-a}.
Realistic nuclear densities and radii are used for light nuclei
and Woods-Saxon densities otherwise.

During the simulation of an inelastic collision the above formalism samples
the number of ``wounded'' nucleons, the impact parameter of the collision and
the interaction configurations of the wounded nucleons. Individual 
hadron(photon,nucleon)-nucleon interactions are then described by 
\textsc{Phojet} including multiple hard and soft pomeron exchanges, initial
and final state radiation as well as diffraction. 

As a new feature, \textsc{Dpmjet}-III allows the simulation of
enhanced graph cuts in non-diffractive inelastic hadron-nucleus and
nucleus-nucleus interactions. For example, in an event with two wounded
nucleons, the first nucleon might take part in a non-diffractive
interaction whereas the second one scatters diffracively producing only
very few secondaries. Such graphs are prediced by the Gribov-Glauber
theory of nuclear scattering but are usually neglected.

Finally, all color neutral
strings are hadronized according to the Lund model as implemented in
\textsc{Pythia} \cite{pythia6-a,pythia6-b}.
%
\vspace*{-0.1cm}
\subsection{The Intranuclear Cascade and Break-up of Excited Nuclei}
\vspace*{-0.1cm}
%
The treatment of intranuclear cascades in spectator prefragments and their
subsequent fragmentation is largely identical to the one described in Refs.
\cite{fzic-a,fzic-b}. 

Particles created in string fragmentation processes are
followed on straight trajectories in space and time. A certain formation time
is required before newly created particles can re-interact in the spectator
nuclei. These re-interactions are of low energy and are described by 
\textsc{Hadrin}\cite{hadrin} based on parameterized exclusive interaction channels. In 
nucleus-nucleus collisions the intranuclear cascade is calculated in both the 
projectile and target spectators.

Excitation energies of prefragments are calculated by summing up the
recoil momenta transfered to the respective prefragment by the hadrons leaving 
the nuclear potential (a constant average potential is assumed). 
The prefragments are
assumed to be in an equilibrium state and excitation energy is dissipated
by the evaporation of nucleons and light nuclei and by the emission of photons.
%-----------------------------------------------------------------------
%\section{Limits of DPMJET-III}
%%
%It is presently not advisable to use the code for very low-energy 
%nucleus-nucleus collisions (below $\approx 10-20$ GeV). This requires 
%further testing and tuning of parameters.
%Furthermore deficiencies exist in the description of some effects observed 
%in heavy ion collisions at AGS- and SPS-energies (e.g.\ strangeness 
%suppression, transverse energy flow).
%
%-----------------------------------------------------------------------
\vspace*{-0.1cm}
\section{Comparison to Experimental Data}
\vspace*{-0.1cm}
%
Since \textsc{Dpmjet}-III is the result of merging \textsc{Dpmjet}-II and
\textsc{Dtunuc-2} its predictions have to be in agreement to experimental
data where there was agreement for the two latter codes before. However, this
has to be proven again.
Here, only a few examples are given which should represent the large
amount of comparisons of \textsc{Dpmjet}-III results with experimental data
which exist.

Fig. \ref{comp1}a shows the transverse momentum distribution of negative
hadrons from p-W collisions together with data \cite{helios}. 
The rapidity distributions of negative hadrons in central S-S and S-Ag
collisions are compared to data \cite{na35} in Fig. \ref{comp1}b.
%In both cases the energy is 200 GeV/nucleon.
%\textsc{Dpmjet}-III results are compared to data of the HELIOS-Collab.
%\cite{helios} (\textbf{a}) and of the NA35-Collab. \cite{na35} (\textbf{b}).
%
\begin{figure}[htbp]
\setlength{\unitlength}{1cm}
\begin{picture}(16,4.8)
   \put(-0.8,-0.8){\scalebox{0.75}
   {\includegraphics*[bb=0 0 1027 802,height=18.5cm]{pw200_ptHELIOShm.ps}}
                  }
   \put(5.2,-0.8){\scalebox{0.75}
   {\includegraphics*[bb=0 0 1027 802,height=18.5cm]{s200c_yhm.ps}}
                  }
   \put(0.5,0.0){ {(\textbf{a})} }
   \put(6.0,0.0){ {(\textbf{b})} }
\end{picture}
\caption{
Negatively charged hadron production in nuclear collisions at 200 GeV/nucleon
%(\textbf{a}) Transverse momentum distribution in proton-tungsten interactions
%compared to data \cite{helios}.
%(\textbf{b}) Rapidity distribution in sulfur-sulfur and sulfur-silver 
%interactions compared to data~\cite{na35}
}
\label{comp1}
\vspace{-0.45cm}
\end{figure}
%
Two examples for interactions involving photons are given in Fig. \ref{comp2}.
%Hadronic interactions of muons are described by the radiation and subsequent
%interaction of a quasi-real photon off the muon. 
Hadronic interactions of muons are described by the radiation off the muon
of a quasi-real photon and the subsequent interaction of the photon.
Fig. \ref{comp2}a shows
average multiplicities of charged hadrons from $\mu$-Xe interactions at 490 GeV
compared to data \cite{e665}.
In Fig. \ref{comp2}b the calculated inclusive transverse momentum cross 
section of charged particles produced in two-photon collisions at LEP is
compared to the combined data set of the ALEPH, L3, and OPAL Collaborations 
for low-$Q^2$ deep inelastic scattering \cite{Finch99a}.
%
\begin{figure}[htbp]
\setlength{\unitlength}{1cm}
\begin{picture}(16,4.3)
   \put(-0.5,-0.8){\scalebox{0.75}
   {\includegraphics*[bb=0 0 1027 802,height=17.5cm]{mupxe490_nc.ps}}
                  }
   \put(5.0,-0.8){\scalebox{0.75}
   {\includegraphics*[bb=0 0 1027 802,height=18.5cm]{pho1.12-lowq2-pt.ps}}
                  }
   \put(0.5,0.0){ {(\textbf{a})} }
   \put(6.0,0.0){ {(\textbf{b})} }
\end{picture}
\caption{
Comparison of \textsc{Dpmjet}-III results to data on interactions involving
photons.
%(\textbf{a}) Average multiplicity of charged hadrons as function of the squared
%photon-nucleon c.m. energy in muon-xenon interactions at 490 GeV compared to
%data \cite{e665}. (\textbf{b}) Transverse momentum cross section of charged
%particles in photon-photon interactions at LEP compared to data \cite{Finch99a}
}
\label{comp2}
\end{figure}
\vspace*{-0.9cm}
%
%-----------------------------------------------------------------------
\vspace*{-0.1cm}
\section{Conclusions}
\vspace*{-0.1cm}
%
A new version of the \textsc{Dpmjet} event generator is presented. 
\textsc{Dpmjet}-III is based on \textsc{Dpmjet}-II, \textsc{Dtunuc-2} and 
\textsc{Phojet}1.12 and unifies all features of these three event generators 
in one single code system. It has been thoroughly tested and, in due time, will
largely superseed the older \textsc{Dpmjet} and \textsc{Dtunuc} versions.

It is presently not advisable to use the code for very low-energy 
nucleus-nucleus collisions (below $\approx 10-20$ GeV). This requires 
further testing and tuning of parameters.
Furthermore deficiencies exist in the description of some effects observed 
in heavy ion collisions at AGS- and SPS-energies (e.g.\ strangeness 
enhancement, transverse energy flow).

The code is available on request from the authors (Stefan.Roesler@cern.ch,
Johannes.Ranft@cern.ch) and further information can be found on the World
Wide Web (\verb?http://home.cern.ch/sroesler/dpmjet3.html?).
%-----------------------------------------------------------------------
\vspace*{-0.1cm}
\section{Acknowledgements}
\vspace*{-0.1cm}
%
The work of S.R. and R.E. is supported by the Department of Energy under 
contracts DE-AC03-76SF00515 and DE-FG02-91ER40626, respectively.
%-----------------------------------------------------------------------
\begin{thebibliography}{8.}
\addcontentsline{toc}{section}{References}

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%A.\ Capella, U.\ Sukhatme, C-I.\ Tan and J.\ Tran Thanh Van:
A.\ Capella et al.:
%\emph{Dual parton model},
Phys. Rept. \textbf{236}, 225 (1994)

\bibitem{dpmjet2-a}
J.\  Ranft:
%\emph{Dual parton model at cosmic ray energies},
Phys. Rev. D \textbf{51}, 64 (1995)

\bibitem{dpmjet2-b}
J.\  Ranft:
\emph{\textsc{Dpmjet} version II.5: Code manual},
%: Sampling of hadron-hadron, hadron-nucleus
%and nucleus-nucleus interactions at accelerator and cosmic ray
%energies according to the two-component dual parton model: Code manual},
 Preprint University of Siegen SI-99-6 (1999)

\bibitem{dtunuc2-a}
R.\ Engel, J.\  Ranft and S.\ Roesler:
%\emph{Photoproduction off nuclei and pointlike photon interactions.
%1. Cross sections and nuclear shadowing},
Phys. Rev. D \textbf{55}, 6957 (1997)

\bibitem{dtunuc2-b}
S.\ Roesler, R.\ Engel and J.\  Ranft:
%\emph{Photoproduction off nuclei: Particle and jet production},
Phys. Rev. D \textbf{57}, 2889 (1998)

\bibitem{dtujet}
P.\ Aurenche et al.:
%\emph{},
Phys. Rev. D \textbf{45}, 92 (1992)

\bibitem{phojet-a}
R.\ Engel:
%\emph{Photoproduction within the two-component dual parton model:
%Amplitudes and cross-sections},
Z. Phys. C \textbf{66}, 203 (1995)

\bibitem{phojet-b}
R.\ Engel and J.\  Ranft:
%\emph{Hadronic photon-photon interactions at high energies},
Phys. Rev. D \textbf{54}, 4244 (1996)

\bibitem{diagen}
S.Y.\ Shmakov, V.V.\ Uzhinskii and A.M.\ Zadorozhny:
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\bibitem{fzic}
J.\ Ranft:
%\emph{},
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\bibitem{fzic-a}
A.\ Ferrari, J.\ Ranft, S.\ Roesler and P.R.\ Sala:
%\emph{Cascade particles, nuclear evaporation, and residual nuclei in high
%energy hadron-nucleus interactions},
Z. Phys. C \textbf{70}, 413 (1996)

\bibitem{fzic-b}
A.\ Ferrari, J.\ Ranft, S.\ Roesler and P.R.\ Sala:
%\emph{The production of residual nuclei in peripheral high energy
%nucleus-nucleus interactions},
Z. Phys. C \textbf{71}, 75 (1996)

\bibitem{hadrin}
K.\ H\"an{\ss}gen and J.\ Ranft:
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%interactions at laboratory energies below 5 GeV},
Comput. Phys. Commun. \textbf{39}, 37 (1986)

\bibitem{qelnu}
G.\ Battistoni, P.\ Lipari, J.\ Ranft and E.\ Scapparone:
\emph{Simulation of nuclear effects in quasielastic and resonant
neutrino interactions}, 
 Preprint INFN-AE-03-98 (1998)

%\bibitem{barystop-a}
%J. Ranft:
%\emph{Baryon stopping in high energy collisions and the extrapolation
%of hadron production models to cosmic ray energies},
% (2000)

\bibitem{barystop-b}
J. Ranft, R. Engel and S. Roesler:
\emph{Baryon stopping in high energy collisions in the \textsc{Dpmjet-III} 
model},
Presented at the same meeting by J. Ranft

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G. Veneziano:
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V. N. Gribov:
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R. Engel:
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\bibitem{Bopp98a}
F. W. Bopp, R. Engel and J. Ranft:
\emph{Rapidity gaps and the PHOJET Monte Carlo},
 in Proceedings of LAFEX Int. School on High-Energy Physics
(LISHEP98), Session C: Workshop on Diffractive Physics,
Rio de Janeiro, Brazil, February 16-20, 1998

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%A. Capella, A. B. Kaidalov, C. Merino, D. Pertermann and J. Tr\^an Thanh V\^an:
A. Capella et al.:
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(Plenum Press, New York 1978)

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G.\ Ingelman, A.\ Edin and J.\ Rathsman:
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%scattering},
Comput. Phys. Commun. \textbf{101}, 108 (1997)

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\bibitem{pythia6-b}
T.\ Sj\"ostrand:
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The HELIOS Collaboration: T. {\AA}kesson et al.:
Z. Phys. C \textbf{46}, 361 (1990)

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The NA35 Collaboration: T. Alber et al.:
Eur. Phys. J. \textbf{2}, 643 (1998)

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A. J. Finch:
Nucl. Phys. B (Proc. Suppl.) \textbf{82}, 156 (2000)

\end{thebibliography}

\end{document}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% WHAT FOLLOWS IS THE REMAINDER OF THE TEMPLATE - to be removed
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Fixed-Period Problems: The Sublinear Case}
%
Of course this text has no scientific relevance but should be used
as a practical example of the Springer layout specifications for
\emph{physics books}~\cite{fhjl1}.

We begin now the search for periodic solutions to Hamiltonian systems\index{Hamiltonian
systems}. All this will be done
in the convex case; that is, we shall study the
boundary-value\index{boundary-value problem} problem
\begin{eqnarray}
  \dot{x}(0)&=&JH' (t,x)\\
  x(0) &=& x(T)
\end{eqnarray}
with $H(t,\cdot)$ a convex function of $x$, going to $+\infty$ when
$\left\|x\right\| \to \infty$.


\section{Equations}
%
Please consult the file or printout of \emph{1readme}.$^*$ to find detailed
instructions on the layout and style of mathematical elements.

The following equation is the compiled result of using the command
\verb|\vec| and using the newly defined command \verb|\umu|:
\begin{equation}
\vec{A}=\mu y = 50\; \umu {\mathrm m}\; .
\end{equation}

\subsection{Sub-equations}
As you have seen above, equations are numbered automatically
when the equations are defined with \verb|\begin{equation}|
(but not when \verb|$$| is used). Here you will find an example
for the automatic sub-numbering of equation arrays, using the style \verb|subeqnar.sty|:
\begin{subeqnarray}
a & = & c + d \; , \label{f1a}\\
e & = & f - d \;  .\label{f1b}
\end{subeqnarray}

In order to refer to the equations within the main text you must simply label your
equations (within the equation's environment) and quote the labels within the text
environment. Upon running \TeX\ you should receive the corresponding
subnumbers, e.g.
(\ref{f1a}) and (\ref{f1b}).

\subsubsection*{No Sub-numbering.}
If you want to suppress the sub-numbering of an equation
array you may use the original \verb|\begin{subeqnarray}| environment, put
\verb|\nonumber|
at the end of the line that is to have no number, and set the sub-counter to zero:
\begin{subeqnarray}
a & = & c + d \; , \nonumber \\
e & = & f - d \; .
\setcounter{eqsubcnt}{0}
\end{subeqnarray}



\section{Figures}
\begin{figure}[b]
\begin{center}
%\includegraphics[width=.3\textwidth]{figure.eps}
\end{center}
\caption[]{Example of an electronically included eps-figure}
\label{eps1}
\end{figure}

Please consult the file or printout of \emph{1readme}.$^*$ to find
detailed instructions on how to treat figures.

If your figures are available as electronic data it is advisable to
convert them to eps-format and include them directly into the text with
the help of the graphicx package (see the following example in
Fig.~\ref{eps1})


In order to mark the desired amount of space for a (centered!) figure
which has to be pasted into the manuscript manually please provide a
vertical line on the lefthand side of the figure. This
is reached by using the commands
\verb|\mpicplace{width in cm}{height in cm}|.


For further instructions
e.g. on the structure and layout of the caption see
the captions of Figs.~\ref{partfig1} and~\ref{labelfig1}.

\begin{figure}
\begin{center}
\leavevmode
\mpicplace{9 cm}{3 cm}
\end{center}
\caption{General description. (\textbf{a}) The `name' of the sub-figure should be set
boldface and in round brackets. (\textbf{b}) In general the last
sentence of a figure caption should not
end with a fullstop}
\label{partfig1}
\end{figure}

\begin{figure}
\begin{center}
\leavevmode
\mpicplace{5 cm}{3 cm}
\end{center}
\caption{This could show a figure consisting of different types of
lines to describe individual aspects. These descriptive lines ({\it
dotted line\,}) should be set italic and put into round brackets
as shown in this sample figure caption. In general the last
sentence of a figure caption ({\it straight line\,}) should not
end with a fullstop}
\label{labelfig1}
\end{figure}

\section{Tables}
If equations and figures are centered then tables should be centered as
well. Table captions should be treated in the same way as figure
legends, except that the
table captions appear {\it above} the tables. Overwide tables should
be reduced to the page width, if possible, or exceed the type area by a
maximum of 5\,mm. Please check the \TeX\ files of the following
tables
(Table~\ref{Tab1a} and ~\ref{Tab1b}) and use them as an example for
setting your own tables.

\begin{table}
\caption{Critical $N$ values}
\begin{center}
\renewcommand{\arraystretch}{1.4}
\setlength\tabcolsep{5pt}
\begin{tabular}{llllll}
\hline\noalign{\smallskip}
${\mathrm M}_\odot$ & $\beta_{0}$ & $T_{\mathrm c6}$ & $\gamma$
  & $N_{\mathrm{crit}}^{\mathrm L}$
  & $N_{\mathrm{crit}}^{\mathrm{Te}}$\\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
 30 & 0.82 & 38.4 & 35.7 & 154 & 320 \\
 60 & 0.67 & 42.1 & 34.7 & 138 & 340 \\
120 & 0.52 & 45.1 & 34.0 & 124 & 370 \\
\hline
\end{tabular}
\end{center}
\label{Tab1a}
\end{table}


\begin{table}
\caption{Please write your table caption here. Multi-line captions as
well as single-line captions automatically will be set flushleft}
\begin{center}
\renewcommand{\arraystretch}{1.4}
\setlength\tabcolsep{15pt}
\begin{tabular}{@{}llp{1.8cm}l}
\hline\noalign{\smallskip}
Nominal dimension & Angle & Tolerance & Evaluation factor \\
(mm) & & (\umu m) & \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
$10^1$ & $1^\circ$ & Untoleranced dimension& $c_1 =0$ \\
$10^{-1}$ & $1^{\prime\, {\mathrm a}}$ & 101--200 & $c_1 = 1$ \\
$10^{-2}$ & $1^{\prime\prime\, {\mathrm b}}$ & 40--100 & $c_1 = 2$ \\
$10^{-3}$ & & $< 50 $ & $c_1 = 3$ \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
\end{tabular}
\end{center}
$^{\mathrm a}$ One minute of arc. \\
$^{\mathrm b}$ One second of arc.
\label{Tab1b}
\end{table}


\section{Lists}
We have redefined the {\it itemize} environment (labelitemi) so that you
will
receive bullets instead of dashes to introduce the individual items.
We think that this way the list
\begin{itemize}
\item
is clearer
\item
looks better
\item
is more noticeable
\end{itemize}

\appendix

\section*{Appendix}
%
Of course you may use the standard \LaTeX\ command for your
appendix. But please be aware of the fact that we have modified so
that the numbering
of equations, figures and tables remains arabic, see examples below.
\begin{eqnarray}
a & = & c + d \; , \nonumber \\
e & = & f - d \; .
\setcounter{eqsubcnt}{0}
\end{eqnarray}

\begin{table}
\caption{Critical $N$ values}
\begin{center}
\renewcommand{\arraystretch}{1.4}
\setlength\tabcolsep{5pt}
\begin{tabular}{llllll}
\hline\noalign{\smallskip}
${\mathrm M}_\odot$ & $\beta_{0}$ & $T_{\mathrm c6}$ & $\gamma$
  & $N_{\mathrm{crit}}^{\mathrm L}$
  & $N_{\mathrm{crit}}^{\mathrm{Te}}$\\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
 30 & 0.82 & 38.4 & 35.7 & 154 & 320 \\
 60 & 0.67 & 42.1 & 34.7 & 138 & 340 \\
120 & 0.52 & 45.1 & 34.0 & 124 & 370 \\
\hline
\end{tabular}
\end{center}
\label{apptab1b}
\end{table}


\begin{thebibliography}{8.}
\addcontentsline{toc}{section}{References}

\bibitem{journ1} W. Frank, A. Seeger: Appl. Phys. A \textbf{3}, 66 (1988)

\bibitem{proc1} W. Greiner, D.N. Poenaru: `Cluster Preformation in
Closed- and Mid-shell Nuclei'. In:
\emph{Atomic and Nuclear Clusters, 2nd International Conference at Santorini, Greece,
June 28--July 2, 1993}, ed. by G.S. Anagnostatos, W. von Oertzen (Springer, Heidelberg 1994)
pp. 264--266

\bibitem{fhjl1} F. Holzwarth, J. Lenz  et al.: \emph{1readme.
Further Details on Layout and \LaTeX\, code}. (Springer, Berlin
Heidelberg 1999)

\bibitem{mono1} B. Jirgensons: \emph{Optical Activity for Proteins
and Other Macro-Molecules}, 2nd edn.
(Springer, New York 1984)

\bibitem{contr1} D.M. MacKay: `Visual Stability and Voluntary Eye
Movements'. In: \emph{Handbook of
Sensory Physiology VII/3}. ed. by R. Jung (Springer, Berlin, Heidelberg 1973) pp. 307--331

\bibitem{mono2} M. M\"uller, F.J. Becker: \emph{On Generalized
Hamiltonian Dynamics} (Cambridge University Press, Cambridge 1930)

\bibitem{journ2} S. Nakamura, M. Senoh, N. Iwasa, S. Nagahama: Jpn. J.
Appl. Phys. \textbf{34}, L797 (1995)
W. Frank, A. Seeger: Appl. Phys. A \textbf{3}, 66 (1988)

\bibitem{thesis1} D.W. Ross: Lysosomes and Storage Diseases. MA Thesis,
Columbia University, New York
(1977)



\end{thebibliography}


%INDEX%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Please check with the editor of your book whether he plans to
% include a "mutual" subject index - if so, please code your entries
% in the standard syntax. For your own purposes you may print your
% "personal" index by using the following commands:
%
%\clearpage
%\addcontentsline{toc}{section}{Index}
%\flushbottom
%\printindex
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\end{document}


