source: trunk/documents/UserDoc/UsersGuides/ForToolkitDeveloper/latex/GuideToExtendFunctionality/HadronicPhysics/hadronics.tex @ 1208

\chapter{Hadronic Physics}

% This is a verbatim of a paper published in a refereed journal.
% A suggestion by one of the documentation referees to re-write completely 
% seems quite inappropriate.

\section{Introduction}
Optimal exploitation of hadronic final
states played a key role in successes of all recent collider experiment in HEP,
and the ability to use hadronic final states will continue to be one of the
decisive issues during the analysis phase of the LHC experiments.
Monte Carlo programs like {\sc Geant4\cite{Geant4}} facilitate the use of 
hadronic final states, and have been developed for many years.

We give an overview of the Object Oriented frameworks for hadronic generators 
in {\sc Geant4}, and illustrate the physics models underlying hadronic shower 
simulation on examples, including the three basic types of modeling; 
data-driven, parametrisation-driven, and theory-driven modeling, and their 
possible realisations in the Object Oriented component system of {\sc Geant4}. 
We put particular focus on the level of extendibility that can and has been 
achieved by our Russian dolls approach to Object Oriented design, and the
role and importance of the frameworks in a component system.

\section{Principal Considerations}
The purpose of this section is to explain the implementation frameworks used 
in and provided by {\sc Geant4} for hadronic shower simulation as in the 1.1 
release of the program. The implementation frameworks follow the Russian dolls 
approach to implementation framework design.
A top-level, very abstracting implementation framework provides the basic
interface to the other {\sc Geant4} categories, and fulfils the most general
use-case for hadronic shower simulation. It is refined for more specific
use-cases by implementing a hierarchy of implementation frameworks, each level
implementing the common logic of a particular use-case package in a concrete 
implementation of the interface specification of one framework level above, 
this way refining the granularity of abstraction and delegation.  This defines 
the Russian dolls architectural pattern.
Abstract classes are used as the delegation
mechanism\footnote{The same can be achieved with template specialisations
with slightly improved CPU performance but at the cost of significantly more 
complex designs and, with present compilers, significantly reduced 
portability.}.
All framework functional requirements were obtained through use-case analysis. 
In the following we present for each framework level the compressed use-cases, 
requirements, designs including the flexibility provided, and illustrate the 
framework functionality with examples. All design patterns cited are to
be read as defined in \cite{Patterns}.

\section{Level 1 Framework - processes}
  There are two principal use-cases of the level 1 framework. A user will 
want to choose the processes used for his particular simulation run, and a 
physicist will want to write code for processes of his own and use these 
together with the rest of the system in a seamless manner.
 
\paragraph{Requirements}
\begin{enumerate}
\item \label{L1R1} Provide a standard interface to be used by process implementations.
\item \label{L1R2} Provide registration mechanisms for processes.
\end{enumerate}
\paragraph{Design and interfaces}
Both requirements are implemented in a sub-set of the tracking-physics 
interface in {\sc Geant4}. The class diagram is shown in figure \ref{Level1}.

\begin{figure}[htbp] % fig 1
%\includegraphics[scale=0.75]{GuideToExtendFunctionality/HadronicPhysics/Level1.ps}
\includegraphics[width=14cm]{GuideToExtendFunctionality/HadronicPhysics/Level1.eps}
%% \centerline{\epsfig{file=GuideToExtendFunctionality/HadronicPhysics/Level1.eps,scale=0.8,angle=0}}
\caption{Level 1 implementation framework of the hadronic category 
of {\sc Geant4}.}
\label{Level1}
\end{figure}

All processes have a common base-class {\tt G4VProcess}, from which a set of 
specialised classes are derived. Three of them are used as base classes for 
hadronic processes for particles at rest ({\tt G4VRestProcess}), for
interactions in flight ({\tt G4VDiscreteProcess}), and for processes like
radioactive decay where the same implementation can represent both these 
extreme cases ({\tt G4VRestDiscrete\-Process}).

Each of these classes declares two types of methods; one for calculating the
time to interaction or the physical interaction length, allowing tracking to 
request the information necessary to decide on the process responsible for 
final state production, and one to compute the final state.  These are pure 
virtual methods, and have to be implemented in each individual derived class, 
as enforced by the compiler.

\paragraph{Framework functionality}
The functionality provided is through the use of process base-class pointers 
in the tracking-physics interface, and the {\tt G4Process\-Manager}. All
functionality is implemented in abstract, and registration of derived process 
classes with the {\tt G4Process\-Manager} of an individual particle allows for
arbitrary combination of both {\sc Geant4} provided processes, and 
user-implemented processes. This registration mechanism is a modification on a 
Chain of Responsibility.  It is outside the scope of the current paper, and its
description is available from \cite{G4Manual}.

\section{Level 2 Framework - Cross Sections and Models}

At the next level of abstraction, only processes that occur for particles
in flight are considered. For these, it is easily observed that the sources 
of cross sections and final state production are rarely the same.  Also, 
different sources will come with different restrictions.  The principal 
use-cases of the framework are addressing these commonalities.  A user might 
want to combine different cross sections and final state or isotope production
models as provided by {\sc Geant4}, and a physicist might
want to implement his own model for particular situation, and add cross-section
data sets that are relevant for his particular analysis to the system in a
seamless manner.
\paragraph{Requirements}
\begin{enumerate}
\item  Flexible choice of inclusive scattering cross-sections.
\item  Ability to use different data-sets for different parts of
the simulation, depending on the conditions at the point of interaction.
\item  Ability to add user-defined data-sets in a seamless manner.
\item  Flexible, unconstrained choice of final state production models.
\item  Ability to use different final state production codes 
for different parts of the simulation, depending on the conditions at the 
point of interaction.
\item  Ability to add user-defined final state production models in
a seamless manner.
\item Flexible choice of isotope production models, to run in
parasitic mode to any kind of transport models.
\item  Ability to use different isotope production codes 
for different parts of the simulation, depending on the conditions at the 
point of interaction.
\item  Ability to add user-defined isotope production models in a 
seamless manner.
\end{enumerate}

\paragraph{Design and interfaces}
  The above requirements are implemented in three framework components, one 
for cross-sections, final state production, and isotope production each.
The class diagrams are shown in figure \ref{Level2_1} for the cross-section 
aspects, figure \ref{Level2_2} for the final state production aspects, 
and figure \ref{Level2_3} for the isotope production aspects.

\begin{figure}[htbp] % fig 2
%\includegraphics[scale=0.75]{GuideToExtendFunctionality/HadronicPhysics/Level2_1.ps}
\includegraphics[width=14cm]{GuideToExtendFunctionality/HadronicPhysics/Level2_1.eps}
%% \centerline{\epsfig{file=GuideToExtendFunctionality/HadronicPhysics/Level2_1.ps,scale=0.8,angle=0}}
\caption{Level 2 implementation framework of the hadronic category 
of {\sc Geant4}; cross-section aspect.}
\label{Level2_1}
\end{figure}

\begin{figure}[htbp] % fig 3
%\includegraphics[scale=0.75]{GuideToExtendFunctionality/HadronicPhysics/Level2_2.ps}
\includegraphics[width=14cm]{GuideToExtendFunctionality/HadronicPhysics/Level2_2.eps}
%% \centerline{\epsfig{file=GuideToExtendFunctionality/HadronicPhysics/Level2_2.ps,scale=0.8,angle=0}}
\caption{Level 2 implementation framework of the hadronic category 
of {\sc Geant4}; final state production aspect.}
\label{Level2_2}
\end{figure}

\begin{figure}[htbp] % fig 4
%\includegraphics[scale=0.75]{GuideToExtendFunctionality/HadronicPhysics/Level2_3.ps}
\includegraphics[width=14cm]{GuideToExtendFunctionality/HadronicPhysics/Level2_3.eps}
%% \centerline{\epsfig{file=GuideToExtendFunctionality/HadronicPhysics/Level2_3.ps,scale=0.8,angle=0}}
\caption{Level 2 implementation framework of the hadronic category 
of {\sc Geant4}; isotope production aspect}
\label{Level2_3}
\end{figure}
 
The three parts are integrated in the {\tt G4Hadronic\-Process} class, that 
serves as base-class for all hadronic processes of particles in flight.
\paragraph{Cross-sections}
Each hadronic process is derived from {\tt G4Hadronic\-Process}, which 
holds a list of ``cross section data sets''. 
The term ``data set'' is
representing an object that encapsulates methods and data for calculating 
total cross sections for a given process in a certain range of validity.
The implementations may take any form.  It can be a simple equation as well as 
sophisticated parameterisations, or evaluated data.
All cross section data set classes are derived from the abstract class 
{\tt G4VCrossSection\-DataSet}, which declares methods that allow
the process inquire, about the applicability of an individual data-set through
\\
{\tt IsApplicable(const G4DynamicParticle*, const G4Element*)},
\\
and to de\-le\-gate the calculation of the actual cross-section value through
\\
{\tt GetCrossSection(const G4DynamicParticle*, const G4Element*)}.
\paragraph{Final state production}
The {\tt G4HadronicInteraction} base class is provided for final state 
generation.  It declares a minimal interface of only one pure virtual method:
\\
{\tt G4VParticleChange* ApplyYourself(const G4Track \&, G4Nucleus \&)}.
\\
{\tt G4HadronicProcess} provides a registry for final state
production models inheriting from {\tt G4Hadronic\-Interaction}.  Again, final 
state production model is meant in very general terms.  This can be an 
implementation of a quark gluon string model\cite{QGSM}, a sampling code for 
ENDF/B data formats \cite{ENDFForm}, or a parametrisation describing only 
neutron elastic scattering off Silicon up to 300~MeV.
\paragraph{Isotope production}
For isotope production, a base class ({\tt G4VIsotope\-Production}) is 
provided.  It declares a method \\
{\tt G4IsoResult * GetIsotope(const G4Track \&, const G4Nucleus \&)} \\
that calculates and returns the isotope production information.  Any concrete 
isotope production model will inherit from this class, and implement the 
method.  Again, the modeling possibilities are not limited, and the 
implementation of concrete production models is not restricted in any way. 
By convention, the {\tt GetIsotope} method returns NULL, if the model
is not applicable for the current projectile target combination.
\paragraph{Framework functionality:}
\paragraph{Cross Sections}
{\tt G4HadronicProcess} provides registering possibilities for data sets.
A default is provided covering all possible conditions to some approximation.
The process stores and retrieves the data sets through a data store that acts 
like a FILO stack (a Chain of Responsibility with a 
First In Last Out decision strategy). This allows the user to map out 
the entire parameter space by overlaying cross section data sets to optimise 
the overall result.  Examples are the cross sections for low energy neutron 
transport. If these are registered last by the user, they will be used
whenever low energy neutrons are encountered. In all other conditions the 
system falls back on the default, or data sets with earlier registration dates.
 The fact that the registration is done through abstract base classes with no 
side-effects allows the user to implement and use his own cross sections. 
Examples are special reaction cross sections of $K^0$-nuclear interactions 
that might be used for $\epsilon/\epsilon '$ analysis at LHC to control the 
systematic error.
\paragraph{Final state production}
The {\tt G4HadronicProcess} class provides a registration service for classes 
deriving from {\tt G4Hadronic\-Interaction}, and delegates final state 
production to the applicable model. 
{\tt G4Hadronic\-Interaction} provides the functionality needed to define and 
enforce the applicability of a particular model.  Models inheriting from 
{\tt G4Hadronic\-Interaction} can be restricted in applicability in projectile 
type and energy, and can be activated/deactivated for individual materials and 
elements.  This allows a user to use final state production models in 
arbitrary combinations, and to write his own models for 
final state production. The design is a variant of a Chain of Responsibility.
An example would be the likely CMS scenario - the combination of low energy 
neutron transport with a quantum molecular dynamics\cite{QMD} or chiral
invariant phase space decay\cite{CHIPS} model in the case of tracker materials 
and fast parametrised models for calorimeter materials, with user defined 
modeling of interactions of spallation nucleons with the most abundant 
tracker and calorimeter materials. 
\paragraph{Isotope production}
The {\tt G4HadronicProcess} by default calculates the isotope production 
information from the final state given by the transport model. In addition, it 
provides a registering mechanism for isotope production models that run in 
parasitic mode to the transport models and inherit from 
{\tt G4VIsotope\-Production}.  The registering mechanism behaves like a FILO 
stack, again based on Chain of Responsibility.  The models will be asked for 
isotope production information in inverse order of registration. The first 
model that returns a non-NULL value will be applied.  In addition, the 
{\tt G4Hadronic\-Process} provides the basic infrastructure for accessing and
steering of isotope-production information. It allows to enable and disable 
the calculation of isotope production information globally, or for individual 
processes, and to retrieve the isotope production information through the 
\\
{\tt G4IsoParticleChange * GetIsotopeProductionInfo()} 
\\
method at the end of each step.  The {\tt G4HadronicProcess} is a finite state
machine that will ensure the {\tt GetIsotope\-ProductionInfo} returns a 
non-zero value only at the first call after isotope production occurred.  An 
example of the use of this functionality is the study of activation of a 
Germanium detector in a high precision, low background experiment.
\section{Level 3 Framework - Theoretical Models}
\begin{figure}[htbp] % fig 5
%\includegraphics[scale=0.75]{GuideToExtendFunctionality/HadronicPhysics/Level3_1.ps}
\includegraphics[width=14cm]{GuideToExtendFunctionality/HadronicPhysics/Level3_1.eps}
%% \centerline{\epsfig{file=GuideToExtendFunctionality/HadronicPhysics/Level3_1.ps,scale=1.0,angle=-90}}
\caption{Level 3 implementation framework of the hadronic category 
of {\sc Geant4}; theoretical model aspect.}
\label{Level3_1}
\end{figure}
{\sc Geant4} provides at present one implementation framework for theory 
driven models.  The main use-case is that of a user wishing to use theoretical 
models in general, and to use various intra-nuclear transport or pre-compound 
models together with models simulating the initial interactions at very high 
energies. 
\paragraph{Requirements}
\begin{enumerate}
\item Allow to use or adapt any string-parton or parton transport\cite{VNI} 
      model.
\item Allow to adapt event generators, ex. PYTHIA\cite{PYTHIA7} for final 
      state production in shower simulation.
\item Allow for combination of the above with any intra-nuclear transport 
      (INT).
\item Allow stand-alone use of intra-nuclear transport.
\item Allow for combination of the above with any pre-compound model.
\item Allow stand-alone use of any pre-compound model.
\item Allow for use of any evaporation code.
\item Allow for seamless integration of user defined components for any of the above.
\end{enumerate}
\paragraph{Design and interfaces}
To provide the above flexibility, the following abstract base classes have been
implemented:
\begin{itemize}
\item {\tt G4VHighEnergyGenerator}
\item {\tt G4VIntranuclearTransportModel}
\item {\tt G4VPreCompoundModel}
\item {\tt G4VExcitationHandler}
\end{itemize}
In addition, the class {\tt G4TheoFS\-Generator} is provided to orchestrate 
interactions between these classes.  The class diagram is shown in 
Fig. \ref{Level3_1}. 

{\tt G4VHighEnergy\-Generator} serves as base class for parton transport or 
parton string models, and for Adapters to event generators.  This class 
declares two methods, {\tt Scatter}, and {\tt GetWoundedNucleus}. 

The base class for INT inherits from {\tt G4Hadronic\-Interaction}, making any 
concrete implementation usable as a stand-alone model.  In doing so, it 
re-declares the {\tt ApplyYourself} interface of {\tt G4Hadronic\-Interaction},
and adds a second interface, {\tt Propagate}, for further propagation
after high energy interactions. {\tt Propagate}  takes as arguments a 
three-dimensional model of a wounded nucleus, and a set of secondaries with 
energies and positions.

The base class for pre-equilibrium decay models, {\tt G4VPre\-CompoundModel},
inherits from {\tt G4Hadronic\-Interaction}, again making any concrete 
implementation usable as stand-alone model. It adds a pure virtual  
{\tt DeExcite} method for further evolution of the system when intra-nuclear 
transport assumptions break down. {\tt DeExcite} takes a {\tt G4Fragment}, 
the {\sc Geant4} representation of an excited nucleus, as argument.

The base class for evaporation phases, {\tt G4VExcitation\-Handler}, declares 
an abstract method, {\tt BreakItUP()}, for compound decay.

\paragraph{Framework functionality}
The {\tt G4TheoFSGenerator} class inherits from {\tt G4Hadronic\-Interaction}, 
and hence can be registered as a model for final state production with a 
hadronic process.  It allows a concrete implementation of 
{\tt G4VIntranuclear\-TransportModel} and {\tt G4VHighEnergy\-Generator} to be 
registered, and delegates initial interactions, and intra-nuclear transport
of the corresponding secondaries to the respective classes. The design is a 
complex variant of a Strategy.  The most spectacular application of this 
pattern is the use of parton-string models for string excitation, quark 
molecular dynamics for correlated string decay, and quantum molecular dynamics 
for transport, a combination which promises to result in a coherent 
description of quark gluon plasma in high energy nucleus-nucleus interactions. 

The class {\tt G4VIntranuclearTransportModel} provides registering mechanisms 
for concrete implementations of {\tt G4VPreCompound\-Model}, and provides 
concrete intra-nuclear transports with the possibility of delegating 
pre-compound decay to these models. 

{\tt G4VPreCompoundModel} provides a registering mechanism for compound decay 
through the {\tt G4VExcitation\-Handler} interface, and provides concrete 
implementations with the possibility of delegating the decay of a compound 
nucleus.

The concrete scenario of {\tt G4TheoFS\-Generator} using a dual parton model 
and a classical cascade, which in turn uses an exciton pre-compound model that 
delegates to an evaporation phase, would be the following: 
{\tt G4TheoFS\-Generator} receives the conditions of the interaction; a  
primary particle and a nucleus. It asks the dual parton model to perform the 
initial scatterings, and return the final state, along with the by then 
damaged nucleus.  The nucleus records all information on the damage sustained.
{\tt G4TheoFS\-Generator} forwards all information to the classical cascade, 
that propagates the particles in the already damaged nucleus, keeping track of 
interactions, further damage to the nucleus, etc.. Once the cascade assumptions
break down, the cascade will collect the information of the current state of 
the hadronic system, like excitation energy and number of excited particles, 
and interpret it as a pre-compound system.  It delegates the decay of this to 
the exciton model.  The exciton model will take the information provided, and 
calculate
transitions and emissions, until the number of excitons in the system equals the mean number of
excitons expected in equilibrium for the current excitation energy. Then it hands over to the
evaporation phase. The evaporation phase decays the residual nucleus, and the Chain of
Command rolls back to {\tt G4TheoFS\-Generator}, accumulating the information produced in 
the various levels of delegation.
\section{Level 4 Frameworks - String Parton Models and Intra-Nuclear Cascade}

\begin{figure}[htbp] % fig 1
%\includegraphics[scale=0.75]{GuideToExtendFunctionality/HadronicPhysics/Level4_1.ps}
\includegraphics[width=14cm]{GuideToExtendFunctionality/HadronicPhysics/Level4_1.eps}
%% \centerline{\epsfig{file=GuideToExtendFunctionality/HadronicPhysics/Level4_1.ps,scale=0.8,angle=0}}
\caption{Level 4 implementation framework of the hadronic category 
of {\sc Geant4}; parton string aspect.}
\label{Level4_1}
\end{figure}

\begin{figure}[htbp] % fig 1
%\includegraphics[scale=0.75]{GuideToExtendFunctionality/HadronicPhysics/Level4_2.ps}
\includegraphics[width=14cm]{GuideToExtendFunctionality/HadronicPhysics/Level4_2.eps}
%% \centerline{\epsfig{file=GuideToExtendFunctionality/HadronicPhysics/Level4_2.ps,scale=0.8,angle=0}}
\caption{Level 4 implementation framework of the hadronic category 
of {\sc Geant4}; intra-nuclear transport aspect.}
\label{Level4_2}
\end{figure}
The use-cases of this level are related to commonalities and detailed choices 
in string-parton models and cascade models. They are use-cases of an expert
user wishing to alter details of a model, or a theoretical physicist, wishing 
to study details of a particular model.
\paragraph{Requirements}
\begin{enumerate}
\item Allow to select string decay algorithm 
\item Allow to select string excitation.
\item Allow the selection of concrete implementations of three-dimensional 
      models of the nucleus
\item Allow the selection of concrete implementations of final state and 
      cross sections in intra-nuclear scattering.
\end{enumerate}
\paragraph{Design and interfaces}
To fulfil the requirements on string models, two abstract classes are provided,
the {\tt G4VParton\-StringModel} and the {\tt G4VString\-Fragmentation}. 
The base class for parton string models, {\tt G4VParton\-StringModel}, 
declares the {\tt GetStrings()} pure virtual method. 
{\tt G4VString\-Fragmentation}, the pure abstract base class for string 
fragmentation, declares the interface for string fragmentation.

To fulfill the requirements on intra-nuclear transport, two abstract classes 
are provided, {\tt G4V3DNucleus}, and {\tt G4VScatterer}.
At this point in time, the usage of these intra-nuclear transport related classes 
by concrete codes is not enforced by designs, as the details of the
cascade loop are still model dependent, and more experience has to be gathered to achieve
standardisation. It is within the responsibility of the implementers of concrete 
intra-nuclear transport 
codes to use the abstract interfaces as defined in these classes.

The class diagram is shown in figure \ref{Level4_1} for the string parton model aspects, and
in figure \ref{Level4_2} for the intra-nuclear transport. 

\paragraph{Framework functionality}
Again variants of Strategy, Bridge and Chain of Responsibility are used.
{\tt G4VParton\-StringModel} implements the initialisation of a 
three-dimensional model of a nucleus, and the logic of scattering.  It 
delegates secondary production to string fragmentation through a 
{\tt G4VString\-Fragmentation} pointer. It provides a registering service for 
the concrete string fragmentation, and delegates the string excitation to 
derived classes. Selection of string excitation is through selection of 
derived class. Selection of string fragmentation is through registration.

\section{Level 5 Framework - String De-excitation}

\begin{figure}[htbp] % fig 1
%\includegraphics[scale=0.75]{GuideToExtendFunctionality/HadronicPhysics/Level5_1.ps}
\includegraphics[width=14cm]{GuideToExtendFunctionality/HadronicPhysics/Level5_1.eps}
%% \centerline{\epsfig{file=GuideToExtendFunctionality/HadronicPhysics/Level5_1.ps,scale=0.8,angle=0}}
\caption{Level 5 implementation framework of the hadronic category 
of {\sc Geant4}; string fragmentation aspect.}
\label{Level5_1}
\end{figure}
The use-case of this level is that of a user or theoretical physicist wishing 
to understand the systematic effects involved in combining various 
fragmentation functions with individual types of string fragmentation.  Note 
that this framework level is meeting the current state of the art, making 
extensions and changes of interfaces in subsequent releases likely.
\paragraph{Requirements}
\begin{enumerate}
\item Allow the selection of fragmentation function.
\end{enumerate}
\paragraph{Design and interfaces}
A base class for fragmentation functions, {\tt G4VFragmentation\-Function}, is 
provided.  It declares the {\tt GetLightConeZ()} interface.
\paragraph{Framework functionality}
The design is a basic Strategy. The class diagram is shown in 
Fig. \ref{Level5_1}.  At this point in time, the usage of the 
{\tt G4VFragmentation\-Function} is not enforced by design, but made available 
from the {\tt G4VString\-Fragmentation} to an implementer of a concrete string 
decay. {\tt G4VString\-Fragmentation} provides a registering mechanism for the
concrete fragmentation function. It delegates the calculation of $z_f$ of the 
hadron to split of the string to the concrete implementation. Standardisation 
in this area is expected.

\begin{latexonly}
\begin{thebibliography}{999}
\bibitem{Geant4} The GEANT~4 Collaboration, \\
CERN/DRDC/94--29, DRDC/P58 1994.
\bibitem{Patterns} E. Gamm et al., Design Patterns, Addison-Wesley Professional
Computing Series, 1995.
\bibitem{G4Manual} 
{\scriptsize http://cern.ch/wwwasd/geant4/G4UsersDocuments/Overview/html/index.html}
\bibitem{QGSM} Kaidalov A. B., Ter-Martirosyan K. A., Phys. Lett. {\bf B117}
247 (1982); 
\bibitem{ENDFForm} 
Data Formats and Procedures for the Evaluated Nuclear Data File, National 
Nuclear Data Center, Brookhaven National Laboratory, Upton, NY, USA.
\bibitem{QMD} For example: VUU and (R)QMD model of high-energy heavy ion 
collisions.  H. Stocker et al., Nucl. Phys. A538, 53c-64c (1992)
\bibitem{CHIPS} P.V. Degtyarenko, M.V. Kossov, H.P. Wellisch, 
Eur. Phys J. A 8, 217-222 (2000)
\bibitem{VNI} VNI 3.1, Klaus Geiger (Brookhaven), BNL-63762, 
Comput. Phys. Commun. 104, 70-160 (1997)
\bibitem{PYTHIA7} M. Bertini, L. L\"onnblad, T. Sj\"orstrand, Pythia version 
7-0.0 -- a proof-of-concept version, LU-TP 00-23, hep-ph/0006152, May 2000

\end{thebibliography}
\end{latexonly}

\begin{htmlonly}
\section{Bibliography}
\begin{enumerate}

\item The GEANT~4 Collaboration, \\
CERN/DRDC/94--29, DRDC/P58 1994.
\item E. Gamm et al., Design Patterns, Addison-Wesley Professional
Computing Series, 1995.
\item 
{\scriptsize http://cern.ch/wwwasd/geant4/G4UsersDocuments/Overview/html/index.html}
\item Kaidalov A. B., Ter-Martirosyan K. A., Phys. Lett. <b>B117</b> 247 
(1982); 
\item 
Data Formats and Procedures for the Evaluated Nuclear Data File, National 
Nuclear Data Center, Brookhaven National Laboratory, Upton, NY, USA.
\item For example: VUU and (R)QMD model of high-energy heavy ion 
collisions.  H. Stocker et al., Nucl. Phys. A538, 53c-64c (1992)
\item P.V. Degtyarenko, M.V. Kossov, H.P. Wellisch, 
Eur. Phys J. A 8, 217-222 (2000)
\item VNI 3.1, Klaus Geiger (Brookhaven), BNL-63762, 
Comput. Phys. Commun. 104, 70-160 (1997)
\item M. Bertini, L. L\"onnblad, T. Sj\"orstrand, Pythia version 
7-0.0 -- a proof-of-concept version, LU-TP 00-23, hep-ph/0006152, May 2000

\end{enumerate}
\end{htmlonly}