%\documentclass[12pt,a4paper,oneside]{book} %\usepackage[dvips]{graphicx} %\usepackage{html} %%% \usepackage[dvips]{epsfig} %\title{Physics Reference Manual} %\pagestyle{plain} %\begin{document} %{ %\maketitle %\pagestyle {empty} %\setcounter{page}{-10} %\tableofcontents %\setcounter{page}{-0} %\pagestyle {empty} %} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \chapter{Chiral Invariant Phase Space Decay.} % \textheight 8.75in % \textwidth 6.5in % \parskip 1.45ex \newtheorem{theorem}{Theorem} \newtheorem{acknowledgement}[theorem]{Acknowledgement} \newtheorem{algorithm}[theorem]{Algorithm} \newtheorem{axiom}[theorem]{Axiom} \newtheorem{claim}[theorem]{Claim} \newtheorem{conclusion}[theorem]{Conclusion} \newtheorem{condition}[theorem]{Condition} \newtheorem{conjecture}[theorem]{Conjecture} \newtheorem{corollary}[theorem]{Corollary} \newtheorem{criterion}[theorem]{Criterion} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{exercise}[theorem]{Exercise} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{notation}[theorem]{Notation} \newtheorem{problem}[theorem]{Problem} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{remark}[theorem]{Remark} \newtheorem{solution}[theorem]{Solution} \newtheorem{summary}[theorem]{Summary} % \title{Manual for the CHIPS event generator in GEANT4} %\author{M.V.Kossov} %\address{Mikhail.Kossov@itep.ru, Mikhail.Kossov@cern.ch, kossov@jlab.org,\\ %kossov@post.kek.jp} % \date{\today} % \maketitle \section{Introduction} \noindent \qquad The CHIPS computer code is a quark-level event generator for the fragmentation of hadronic systems into hadrons. In contrast to other parton models \cite{Parton_Models} CHIPS is nonperturbative and three-dimensional. It is based on the Chiral Invariant Phase Space (ChIPS) model \cite{CHIPS1,CHIPS2,CHIPS3} which employs a 3D quark-level SU(3) approach. Thus Chiral Invariant Phase Space refers to the phase space of massless partons and hence only light (u, d, s) quarks can be considered. The c, b, and t quarks are not implemented in the model directly, while they can be created in the model as a result of the gluon-gluon or photo-gluon fusion. The main parameter of the CHIPS model is the critical temperature $T_c\approx 200~MeV$. The probability of finding a quark with energy $E$ drops with the energy approximately as $e^{-E/T}$, which is why the heavy flavors of quarks are suppressed in the Chiral Invariant Phase Space. The s quarks, which have masses less then the critical temperature, have an effective suppression factor in the model. The critical temperature $T_c$ defines the number of 3D partons in the hadronic system with total energy $W$. If masses of all partons are zero then the number of partons can be found from the equation $W^2=4T_c^2(n-1)n$. The mean squared total energy can be calculated for any ``parton'' mass (partons are usually massless). The corresponding formula can be found in \cite{hadronMasses}. In this treatment the masses of light hadrons are fitted better than by the chiral bag model of hadrons~\cite{Chiral_Bag} with the same number of parameters. In both models any hadron consists of a few quark-partons, but in the CHIPS model the critical temperature defines the mass of the hadron, consisting of $N$ quark-partons, while in the bag model the hadronic mass is defined by the balance between the quark-parton internal pressure (which according to the uncertainty principle increases when the radius of the ``bag'' decreases) and the external pressure ($B$) of the nonperturbative vacuum, which has negative energy density. In CHIPS the interactions between hadrons are defined by the Isgur quark-exchange diagrams, and the decay of excited hadronic systems in vacuum is treated as the fusion of quark-antiquark or quark-diquark partons. An important feature of the model is the homogeneous distribution of asymptotically free quark-partons over the invariant phase space, as applied to the fragmentation of various types of excited hadronic systems. In this sense the CHIPS model may be considered as a generalization of the well-known hadronic phase space distribution \cite{GENBOD} approach, but it generates not only angular and momentum distributions for a given set of hadrons, but also the multiplicity distributions for different kinds of hadrons, which is defined by the multistep energy dissipation (decay) process. The CHIPS event generator may be applied to nucleon excitations, hadronic systems produced in $e^{+}e^{-}$ and $p\bar p$ annihilation, and high energy nuclear excitations, among others. Despite its quark nature, the nonperturbative CHIPS model can also be used successfully at very low energies. It is valid for photon and hadron projectiles and for hadron and nuclear targets. Exclusive event generation models multiple hadron production, conserving energy, momentum, and other quantum numbers. This generally results in a good description of particle multiplicities, inclusive spectra, and kinematic correlations in multihadron fragmentation processes. Thus, it is possible to use the CHIPS event generator in exclusive modeling of hadron cascades in materials. In the CHIPS model, the result of a hadronic or nuclear interaction is the creation of a quasmon which is essentially an intermediate state of excited hadronic matter. When the interaction occurs in vacuum the quasmon can dissipate energy by radiating particles according to the quark fusion mechanism~\cite{CHIPS1} described in section \ref{annil}. When the interaction occurs in nuclear matter, the energy dissipation of a quasmon can be the result of quark exchange with surrounding nucleons or clusters of nucleons \cite{CHIPS2} (section \ref{picap}), in addition to the vacuum quark fusion mechanism. In this sense the CHIPS model can be a successful competitor of the cascade models, because it does not break the projectile, instead it captures it, creating a quasmon, and then decays the quasmon in nuclear matter. The perturbative mechanisms in deep inelastic scattering are in some sense similar to the cascade calculations, while the parton splitting functions are used instead of interactions. The nonperturbative CHIPS approach is making a ``short cut'' for the perturbative calculations too. Similar to the time-like $s=W^2$ evolution of the number of partons in the nonperturbative chiral phase space (mentioned above) the space-like $Q^2$ evolution of the number of partons is given by $N(Q^2)=n_V+\frac{1}{2\alpha_s(Q^2)}$, where $n_V$ is the number of valence quark-partons. The running $\alpha_s(Q^2)$ value is calculated in CHIPS as $\alpha_s(Q^2)=\frac{4\pi}{\beta_0ln(1+Q^2/T_c^2)}$, where $\beta_0^{n_f=3)=9}$. In other words, the critical temperature $T_c$ plays the role of $\Lambda_QCD$ and still cuts out heavy flavors of quark-partons and high orders of the QCD calculation (NLO, NNLO, N$^3$LO, etc.), substituting for them the effective LO ``short cut''. This simple approximation of $\alpha_s$ fits all the present measurements of this value (Fig.~\ref{alphas}). It is very important that $\alpha_s$ is defined in CHIPS for any $Q^2$, and that the number of partons at $Q^2=0$ converges to the number of valence quarks. \begin{figure} % \centerline{\epsfig{file=hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/mommul.eps, height=3.5in, width=4.5in}} % \resizebox{1.00\textwidth}{!} %{ \includegraphics[angle=0,scale=0.6]{hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/alpha.eps} %\includegraphics[angle=0,scale=0.6]{plots/alpha.eps} %} \caption{The CHIPS fit of the $\alpha_s$ measurements.} \label{alphas} \end{figure} The effective $\alpha_s$ is defined for all $Q^2$, but at $Q^2=0$ it is infinite. In other words at $Q^2=0$ the number of the virtual interacting partons goes to infinity. This means that on the boundary between perturbative and non-perturbative vacuums a virtual ``thermostate'' of gluons with an effective temperature $T_c$ exists. This ``virtual thermostate'' defines the phase space distribution of partons, and the ``thermalization'' can happen very quickly. On the other hand, the CHIPS nonperturbative approach can be used below $Q^2~=~1~GeV^2$. This was done for the neutrino-nuclear interactions (section \ref{numunuc}). \section{Fundamental Concepts} The CHIPS model is an attempt to use a set of simple rules which govern microscopic quark-level behavior to model macroscopic hadronic systems with a large number of degrees of freedom. The invariant phase space distribution as a paradigm of thermalized chaos is applied to quarks, and simple kinematic mechanisms are used to model the hadronization of quarks into hadrons. Along with relativistic kinematics and the conservation of quantum numbers, the following concepts are used: \begin{itemize} \item {\bf Quasmon:} in the CHIPS model, a quasmon is any excited hadronic system; it can be viewed as a continuous spectrum of a generalized hadron. At the constituent level, a quasmon may be thought of as a bubble of quark-parton plasma in which the quarks are massless and the quark-partons in the quasmon are homogeneously distributed over the invariant phase space. It may also be considered as a bubble of the three-dimensional Feynman-Wilson \cite{Feynman-Wilson} parton gas. The traditional hadron is a particle defined by quantum numbers and a fixed mass or a mass with a width. The quark content of the hadron is a secondary concept constrained by the quantum numbers. The quasmon, however, is defined by its quark content and its mass, and the concept of a well defined particle with quantum numbers (a discrete spectrum) is of secondary importance. A given quasmon hadronic state with fixed mass and quark content can be considered as a superposition of traditional hadrons, with the quark content of the superimposed hadrons being the same as the quark content of the quasmon. \item {\bf Quark fusion:} the quark fusion hypothesis determines the rules of final state hadron production, with energy spectra reflecting the momentum distribution of the quarks in the system. Fusion occurs when a quark-parton in a quasmon joins with another quark-parton from the same quasmon and forms a new white hadron, which can be radiated. If a neighboring nucleon (or the nuclear cluster) is present, quark-partons may also be exchanged between the quasmon and the neighboring nucleon (cluster). The kinematic condition applied to these mechanisms is that the resulting hadrons are produced on their mass shells. The model assumes that the u, d and s quarks are effectively massless, which allows the integrals of the hadronization process to be done easily and the modeling decay algorithm to be accelerated. The quark mass is taken into account indirectly in the masses of outgoing hadrons. The type of the outgoing hadron is selected using combinatoric and kinematic factors consistent with conservation laws. In the present version of CHIPS all mesons with three-digit PDG Monte Carlo codes \cite{CH.PDG} up to spin $4$, and all baryons with four-digit PDG codes up to spin $\frac{7}{2}$ are implemented. \item {\bf Critical temperature} the only non-kinematic concept of the model is the hypothesis of the critical temperature of the quasmon. This has a 40-year history, starting with Ref.~\cite{Hagedorn} and is based on the experimental observation of regularities in the inclusive spectra of hadrons produced in different reactions at high energies. Qualitatively, the hypothesis of a critical temperature assumes that the quark-gluon hadronic system (quasmon) cannot be heated above a certain temperature. Adding more energy to the hadronic system increases only the number of constituent quark-partons while the temperature remains constant. The critical temperature is the principal parameter of the model and is used to calculate the number of quark-partons in a quasmon. In an infinite thermalized system, for example, the mean energy of partons is $2T$ per particle, the same as for the dark body radiation. \end{itemize} \section{Code Development} Because the CHIPS event generator was originally developed only for final state hadronic fragmentation, the initial interaction of projectiles with targets requires further development. Hence, the first applications of CHIPS described interactions at rest, for which the interaction cross section is not important \cite{CHIPS1}, \cite{CHIPS2}, and low energy photonuclear reactions \cite{CHIPS3}, for which the interaction cross section can be calculated easily \cite{photNuc}. With modification of the first interaction algorithm the CHIPS event generator can be used for all kinds of hadronic interaction. The Geant4 String Model interface to the CHIPS generator \cite{GEANT4}, \cite{MC2000} also makes it possible to use the CHIPS code for nuclear fragmentation at extremely high energies. In the first published versions of the CHIPS event generator the class {\tt G4Quasmon} was the head of the model and all initial interactions were hidden in its constructor. More complicated applications of the model such as anti-proton nuclear capture at rest and the Geant4 String Model interface to CHIPS led to the multi-quasmon version of the model. This required a change in the structure of the CHIPS event generator classes. In the case of at-rest anti-proton annihilation in a nucleus, for example, the first interaction occurs on the nuclear periphery. After this initial interaction, a fraction (defined by a special parameter of the model) of the secondary mesons independently penetrate the nucleus. Each of these mesons can create a separate quasmon in the interior of the nucleus. In this case the class {\tt G4Quasmon} can no longer be the head of the model. A new head class, {\tt G4QEnvironment}, was developed which can adopt a vector of projectile hadrons ({\tt G4QHadronVector}) and create a vector of quasmons, {\tt G4QuasmonVector}. All newly created quasmons then begin the energy dissipation process in parallel in the same nucleus. The {\tt G4QEnvironment} instance can be used both for vacuum and for nuclear matter. If {\tt G4QEnvironment} is created in vacuum, it is practically identical to the {\tt G4Quasmon} class, because in this case only one instance of {\tt G4Quasmon} is allowed. This leaves the model unchanged for hadronic interactions. The convention adopted for the CHIPS model requires all its class names to use the prefix {\tt G4Q} in order to distinguish them from other Geant4 classes, most of which use the {\tt G4} prefix. The intent is that the {\tt G4Q} prefix will not be used by other Geant4 projects. \section{Nucleon-Antinucleon Annihilation at Rest} \label{annil} In order to generate hadron spectra from the annihilation of a proton with an anti-proton at rest, the number of partons in the system must be found. For a finite system of $N$ partons with a total center-of-mass energy $M$, the invariant phase space integral, $\Phi_N$, is proportional to $M^{2N-4}$. According to the dimensional counting rule, $2N$ comes from $\prod\limits_{i=1}^{N}\frac{d^{3}p_{i}}{E_{i}}$, and $4$ comes from the energy and momentum conservation function, $\delta ^{4}($\b{P}$-\sum $\b{p}$_{i})$. At a temperature $T$ the statistical density of states is proportional to $e^{-\frac{M}{T}}$ so that the probability to find a system of $N$ quark-partons in a state with mass $M$ is $dW \propto M^{2N-4}e^{-\frac{M}{T}}dM$. For this kind of probability distribution the mean value of $M^{2}$ is \begin{equation} =4N(N-1)\cdot T^{2}. \label{temperature} \end{equation} When $N$ goes to infinity one obtains for massless particles the well-known $\equiv \sqrt{}=2NT$ result. After a nucleon absorbs an incident quark-parton, such as a real or virtual photon, for example, the newly formed quasmon has a total of $N$ quark-partons, where $N$ is determined by Eq. \ref{temperature}. Choosing one of these quark-partons with energy $k$ in the center of mass system (CMS) of $N$ partons, the spectrum of the remaining $N-1$ quark-partons is given by \begin{equation} \frac{dW}{kdk} \propto (M_{N-1})^{2N-6}, \end{equation} where $M_{N-1}$ is the effective mass of the $N-1$ quark-partons. This result was obtained by applying the above phase-space relation ($\Phi_N \propto M^{2N-4}$) to the residual $N-1$ quarks. The effective mass is a function of the total mass $M$, \begin{equation} M_{N-1}^{2}=M^{2}-2kM , \label{m_n-1} \end{equation} so that the resulting equation for the quark-parton spectrum is: \begin{equation} \frac{dW}{kdk}\propto (1-\frac{2k}{M})^{N-3}. \label{spectrum_1} \end{equation} \subsection{Meson Production} In this section, only the quark fusion mechanism of hadronization is considered. The quark exchange mechanism can take place only in nuclear matter where a quasmon has neighboring nucleons. In order to decompose a quasmon into an outgoing hadron and a residual quasmon, one needs to calculate the probability of two quark-partons combining to produce the effective mass of the outgoing hadron. This requires that the spectrum of the second quark-parton be calculated. This is done by following the same argument used to determine Eq.~\ref{spectrum_1}. One quark-parton is chosen from the residual $N-1$. It has an energy $q$ in the CMS of the $N-1$ quark-partons. The spectrum is obtained by substituting $N-1$ for $N$ and $M_{N-1}$ for $M$ in Eq.~\ref{spectrum_1} and then using Eq.~\ref{m_n-1} to get \begin{equation} \frac{dW}{q dq }\propto \left( 1-\frac{2q }{M\sqrt{1- \frac{2k}{M}}}\right) ^{N-4}. \label{spectrum_2} \end{equation} Next, one of the residual quark-partons must be selected from this spectrum such that its fusion with the primary quark-parton makes a hadron of mass $\mu$. This selection is performed by the mass shell condition for the outgoing hadron, \begin{equation} \mu^2 = 2 \frac{k}{\sqrt{1-\frac{2k}{M}}} \cdot q \cdot (1-\cos \theta ) . \label{hadron} \end{equation} Here $\theta$ is the angle between the momenta, {\bf k} and {\bf q} of the two quark-partons in the CMS of $N-1$ quarks. Now the kinematic quark fusion probability can be calculated for any primary quark-parton with energy $k$: \begin{eqnarray} P(k,M,\mu )=&&\int \left( 1-\frac{2q }{M\sqrt{1-\frac{2k}{M}}}\right) ^{N-4} \nonumber\\ && \times\ \delta \left( \mu ^{2}-\frac{2kq (1-\cos \theta )}{\sqrt{1- \frac{2k}{M}}}\right) q dq d\cos \theta .\ \ \ \ \end{eqnarray} Using the $\delta$-function\footnote{\protect{ If $g(x_0)$=0, $\int f(x)\delta\left[g(x)\right]dx = \int \frac{f(x)\delta\left[g(x)\right]}{g^\prime(x)} dg(x) = \frac{f(x_0)}{g^\prime(x_0)}$ }} to perform the integration over $q$ one gets: \begin{eqnarray} P(k,M,\mu )=&&\int \left( 1-\frac{\mu ^{2}}{Mk(1-\cos \theta )}\right) ^{N-4} \nonumber\\ && \times\ \left( \frac{\mu ^{2}\sqrt{1-\frac{2k}{M}}}{2k(1-\cos \theta )} \right)^{2}d\left(\frac{1-\cos \theta }{\mu ^{2}}\right) ,\ \ \end{eqnarray} or \begin{eqnarray} P(k,M,\mu )=&&\frac{M-2k}{4k}\int \left(1-\frac{\mu ^{2}}{Mk(1 - \cos\theta)}\right) ^{N-4} \nonumber\\ && \times\ d\left(1-\frac{\mu ^{2}}{Mk(1-\cos \theta )}\right). \end{eqnarray} After the substitution $z=1-\frac{2q }{M_{N-1}}=1-\frac{\mu ^{2}}{Mk(1-\cos \theta )}$, this becomes \begin{equation} P(k,M,\mu ) = \frac{M-2k}{4k} \int z^{N-4} dz , \end{equation} where the limits of integration are $0$ when $\cos\theta = 1 - \frac{\mu ^{2}}{M\cdot k}$, and \begin{equation} z_{\max }=1-\frac{\mu^2}{2Mk}, \label{z_max} \end{equation} when $\cos \theta =-1$. The resulting range of $\theta$\ is therefore $-1<\cos \theta < 1-\frac{\mu ^{2}}{M\cdot k}$. Integrating from $0$ to $z$ yields \begin{equation} \frac{M-2k}{4k\cdot (N-3)}\cdot z^{N-3}, \label{z_probab} \end{equation} and integrating from $0$ to $z_{max}$ yields the total kinematic probability for hadronization of a quark-parton with energy $k$ into a hadron with mass $\mu$: \begin{equation} \frac{M-2k}{4k \cdot (N-3)} \cdot z_{\max}^{N-3} . \label{tot_kin_probab} \end{equation} The ratio of expressions \ref{z_probab} and \ref{tot_kin_probab} can be treated as a random number, $R$, uniformly distributed on the interval [0,1]. Solving for $z$ then gives \begin{equation} z=\sqrt[N-3]{R}\cdot z_{\max }. \label{z_random} \end{equation} In addition to the kinematic selection of the two quark-partons in the fusion process, the quark content of the quasmon and the spin of the candidate final hadron are used to determine the probability that a given type of hadron is produced. Because only the relative hadron formation probabilities are necessary, overall normalization factors can be dropped. Hence the relative probability can be written as \begin{equation} P_h(k,M,\mu )=(2s_h+1)\cdot z_{\max }^{N-3}\cdot C_{Q}^{h} . \label{rel_prob} \end{equation} Here, only the factor $z_{\max }^{N-3}$ is used since the other factors in equation \ref{tot_kin_probab} are constant for all candidates for the outgoing hadron. The factor $2s_h+1$ counts the spin states of a candidate hadron of spin $s_h$, and $C_{Q}^{h}$ is the number of ways the candidate hadron can be formed from combinations of the quarks within the quasmon. In making these combinations, the standard quark wave functions for pions and kaons were used. For $\eta$ and $\eta^{\prime }$ mesons the quark wave functions $\eta=\frac{\bar{u}u+\bar{d}d}{2}-\frac{\bar{s}s}{\sqrt{2}}$ and $\eta^{\prime }=\frac{\bar{u}u+\bar{d}d}{2}+\frac{\bar{s}s}{\sqrt{2}}$ were used. No mixing was assumed for the $\omega $\ and $\phi $\ meson states, hence $\omega =\frac{ \bar{u}u+\bar{d}d}{\sqrt{2}}$ and $\varphi=\bar{s}s$. A final model restriction is applied to the hadronization process: after a hadron is emitted, the quark content of the residual quasmon must have a quark content corresponding to either one or two real hadrons. When the quantum numbers of a quasmon, determined by its quark content, cannot be represented by the quantum numbers of a real hadron, the quasmon is considered to be a virtual hadronic molecule such as $\pi ^{+}\pi ^{+}$ or $K^{+}\pi ^{+}$, in which case it is defined in the CHIPS model to be a Chipolino pseudo-particle. To fuse quark-partons and create the decay of a quasmon into a hadron and residual quasmon, one needs to generate randomly the residual quasmon mass $m$, which in fact is the mass of the residual $N-2$ quarks. Using an equation similar to \ref{m_n-1}) one finds that \begin{equation} m^{2}=z\cdot (M^{2}-2kM). \label{m(z)} \end{equation} Using Eqs. \ref{z_random} and \ref{z_max}, the mass of the residual quasmon can be expressed in terms of the random number $R$: \begin{equation} m^{2}=(M-2k)\cdot (M-\frac{\mu ^{2}}{2k})\cdot \sqrt[N-3]{R} . \label{res_quasmon} \end{equation} At this point, the decay of the original quasmon into a final state hadron and a residual quasmon of mass $m$ has been simulated. The process may now be repeated on the residual quasmon. This iterative hadronization process continues as long as the residual quasmon mass remains greater than $m_{\min }$, whose value depends on the type of quasmon. For hadron-type residual quasmons \begin{equation} m_{\min }=m_{\min }^{QC}+m_{\pi ^{0}}, \label{m_min} \end{equation} where $m_{\min }^{QC}$ is the minimum hadron mass for the residual quark content (QC). For Chipolino-type residual quasmons consisting of hadrons $h_1$ and $h_2$, \begin{equation} m_{\min }=m_{h_1}+m_{h_2}. \label{m_min_chipolino} \end{equation} These conditions insure that the quasmon always has enough energy to decay into at least two final state hadrons, conserving four-momentum and charge. If the remaining CMS energy of the residual quasmon falls below $m_{\min}$, then the hadronization process terminates with a final two-particle decay. If the parent quasmon is a Chipolino consisting of hadrons $h_1$ and $h_2$, then a binary decay of the parent quasmon into $m_{h_1}$ and $m_{h_2}$ takes place. If the parent quasmon is not a Chipolino then a decay into $m_{\min}^{QC}$ and $m_h$ takes place. The decay into $m_{\min}^{QC}$ and $m_\pi^0$ is always possible in this case because of condition \ref{m_min}. If the residual quasmon is not Chipolino-type, and $m>m_{\min}$, the hadronization loop can still be finished by the resonance production mechanism, which is modeled following the concept of parton-hadron duality \cite{Duality}. If the residual quasmon has a mass in the vicinity of a resonance with the same quark content ($\rho$ or $K^{\ast}$ for example), there is a probability for the residual quasmon to convert to this resonance.\footnote{When comparing quark contents, the quark content of the quasmon is reduced by canceling quark-antiquark pairs of the same flavor.} In the present version of the CHIPS event generator the probability of convert to the resonance is given by \begin{equation} P_{\rm{res}}=\frac{m_{\min }^{2}}{m^{2}}. \label{res_probab} \end{equation} Hence the resonance with the mass-squared value $m_{r}^{2}$ closest to $m^{2}$ is selected, and the binary decay of the quasmon into $m_{h}$ and $m_{r}$ takes place. With more detailed experimental data, it will be possible to take into account angular momentum conservation, as well as $C$-, $P$- and $G$-parity conservation. In the present version of the generator, $\eta$ and $\eta ^{\prime }$ are suppressed by a factor of $0.3$. This factor was tuned using data from experiments on antiproton annihilation at rest in liquid hydrogen and can be different for other hadronic reactions. It is possible to vary it when describing other reactions. Another parameter, $s/u$, controls the suppression of heavy quark production \cite{JETSET}. For proton-antiproton annihilation at rest the strange quark-antiquark sea was found to be suppressed by the factor $s/u = 0.1$. In the JETSET \cite{JETSET} event generator, the default value for this parameter is $s/u = 0.3$. The lower value may be due to quarks and anti-quarks of colliding hadrons initially forming a non-strange sea, with the strange sea suppressed by the OZI rule \cite{OZI}. This question is still under discussion \cite{OZI_violation} and demands further experimental measurements. The $s/u$ parameter may differ for other reactions. In particular, for e$^{+}$e$^{-}$ reactions it can be closer to 0.3. Finally, the temperature parameter has been fixed at $T=180$ MeV. In earlier versions of the model it was found that this value successfully reproduced spectra of outgoing hadrons in different types of medium-energy reactions. \begin{figure} % \centerline{\epsfig{file=hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/mommul.eps, height=3.5in, width=4.5in}} % \resizebox{1.00\textwidth}{!} %{ \includegraphics[angle=0,scale=0.6]{hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/mommul.eps} %\includegraphics[angle=0,scale=0.6]{plots/mommul.eps} %} \caption{(a) (left): momentum distribution of charged pions produced in proton-antiproton annihilation at rest. The experimental data are from \protect\cite{pispectrum}, and the histogram was produced by the CHIPS Monte Carlo. The experimental spectrum is normalized to the measured average charged pion multiplicity, 3.0. (b) (right): pion multiplicity distribution. Data points were taken from compilations of experimental data \protect\cite{pap_exdata}, and the histogram was produced by the CHIPS Monte Carlo. The number of events with kaons in the final state is shown in pion multiplicity bin 9, where no real 9-pion events are generated or observed experimentally. In the model, the percentage of annihilation events with kaons is close to the experimental value of 6\% \cite{pap_exdata}. } \label{mommul} \end{figure} \begin{figure} % \centerline{\epsfig{file=hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/channels.eps, height=3.5in, width=4.5in}} % \resizebox{1.00\textwidth}{!} %{ \includegraphics[angle=0,scale=0.6]{hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/channels.eps} %\includegraphics[angle=0,scale=0.6]{plots/channels.eps} %} \caption{Branching probabilities for different channels in proton-antiproton annihilation at rest. The experimental data are from \protect\cite {pap_exdata}, and the histogram was produced by the CHIPS Monte Carlo. } \label{channels} \end{figure} The above parameters were used to fit not only the spectrum of pions Fig.~\ref{mommul},a and the multiplicity distribution for pions Fig.~\ref{mommul},b but also branching ratios of various measured \cite{pispectrum,pap_exdata} exclusive channels as shown in Figs. ~\ref{channels},~\ref{threechan},~\ref{twochan}. In Fig.~\ref{twochan} one can see many decay channels with higher meson resonances. The relative contribution of events with meson resonances produced in the final state is 30 - 40 percent, roughly in agreement with experiment. The agreement between the model and experiment for particular decay modes is within a factor of 2-3 except for the branching ratios to higher resonances. In these cases it is not completely clear how the resonance is defined in a concrete experiment. In particular, for the $a_{2}\omega $ channel the mass sum of final hadrons is 2100 MeV with a full width of about 110 MeV while the total initial energy of the p\={p} annihilation reaction is only 1876.5 MeV. This decay channel can be formally simulated by an event generator using the tail of the Breit-Wigner distribution for the $a_{2}$ resonance, but it is difficult to imagine how the $a_{2}$ resonance can be experimentally identified $2\Gamma $ away from its mean mass value. \subsection{Baryon Production} To model fragmentation into baryons the POPCORN idea \cite{POPCORN} was used, which assumes the existence of diquark-partons. The assumption of massless diquarks is somewhat inconsistent at low energies, as is the assumption of massless s-quarks, but it is simple and it helps to generate baryons in the same way as mesons. Baryons are heavy, and the baryon production in $p\bar p$ annihilation reactions at medium energies is very sensitive to the value of the temperature. If the temperature is low, the baryon yield is small, and the mean multiplicity of pions increases very noticeably with center-of-mass energy as seen in Fig.~\ref{apcmul}. For higher temperature values the baryon yield reduces the pion multiplicity at higher energies. The existing experimental data \cite{Energy_Dep}, shown in Fig.~\ref{apcmul}, can be considered as a kind of ``thermometer'' for the model. This thermometer confirms that the critical temperature is about 200 MeV. \begin{figure} % \centerline{\epsfig{file=hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/threechn.eps, height=4.5in, width=4.5in}} % \resizebox{1.00\textwidth}{!} %{ \includegraphics[angle=0,scale=0.6]{hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/threechn.eps} %\includegraphics[angle=0,scale=0.6]{plots/threechn.eps} %} \caption{Branching probabilities for different channels with three-particle final states in proton-antiproton annihilation at rest. The points are experimental data \protect\cite{pap_exdata} and the histogram is from the CHIPS Monte Carlo. } \label{threechan} \end{figure} \begin{figure} % \centerline{\epsfig{file=hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/twochn.eps, height=4.5in, width=4.5in}} % \resizebox{1.00\textwidth}{!} %{ \includegraphics[angle=0,scale=0.6]{hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/twochn.eps} %\includegraphics[angle=0,scale=0.6]{plots/twochn.eps} %} \caption{Branching probabilities for different channels with two-particle final states in proton-antiproton annihilation at rest. The points are experimental data \protect\cite{pap_exdata} and the histogram is from the CHIPS Monte Carlo. } \label{twochan} \end{figure} \begin{figure} % \centerline{\epsfig{file=hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/apcmul.eps, height=4.5in, width=4.5in}} % \resizebox{1.00\textwidth}{!} %{ \includegraphics[angle=0,scale=0.6]{hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/apcmul.eps} %\includegraphics[angle=0,scale=0.6]{plots/apcmul.eps} %} \caption{Average meson multiplicities in proton-antiproton and in electron-positron annihilation, as a function of the center-of-mass energy of the interacting hadronic system. The points are experimental data \protect\cite {Energy_Dep} and the lines are CHIPS Monte Carlo calculations at several values of the critical temperature parameter $T$. } \label{apcmul} \end{figure} It can be used as a tool for the Monte Carlo simulation of a wide variety of hadronic reactions. The CHIPS event generator can be used not only for ``phase-space background'' calculations in place of the standard GENBOD routine \cite{GENBOD}, but even for taking into account the reflection of resonances in connected final hadron combinations. Thus it can be useful for physics analysis too, even though its main range of application is the simulation of the evolution of hadronic and electromagnetic showers in matter at medium energies. \section[Nuclear Pion Capture Below Delta(3,3)]{Nuclear Pion Capture at Rest and Photonuclear Reactions Below the Delta(3,3) Resonance} \label{picap} When compared with the first ``in vacuum'' version of the model, described in Section \ref{annil}, modeling hadronic fragmentation in nuclear matter is more complicated because of the much greater number of possible secondary fragments. However, the hadronization process itself is simpler in a way. In vacuum, the quark-fusion mechanism requires a quark-parton partner from the external (as in JETSET \cite{JETSET}) or internal (the quasmon itself, Section \ref{annil}) quark-antiquark sea. In nuclear matter, there is a second possibility: quark exchange with a neighboring hadronic system, which could be a nucleon or multinucleon cluster. In nuclear matter the spectra of secondary hadrons and nuclear fragments reflect the quark-parton energy spectrum within a quasmon. In the case of inclusive spectra that are decreasing steeply with energy, and correspondingly steeply decreasing spectra of the quark-partons in a quasmon, only those secondary hadrons which get the maximum energy from the primary quark-parton of energy $k$ contribute to the inclusive spectra. This extreme situation requires the exchanged quark-parton with energy $q$, coming toward the quasmon from the cluster, to move in a direction opposite to that of the primary quark-parton. As a result the hadronization quark exchange process becomes one-dimensional along the direction of $k$. If a neighboring nucleon or nucleon cluster with bound mass $\tilde{\mu}$ absorbs the primary quark-parton and radiates the exchanged quark-parton in the opposite direction, then the energy of the outgoing fragment is $E=\tilde{\mu}+k-q$, and the momentum is $p=k+q$. Both the energy and the momentum of the outgoing nuclear fragment are known, as is the mass $\tilde{\mu}$ of the nuclear fragment in nuclear matter, so the momentum of the primary quark-parton can be reconstructed using the approximate relation \begin{equation} k=\frac{p+E-B\cdot m_{N}}{2} . \label{k} \end{equation} Here $B$ is the baryon number of the outgoing fragment ($\tilde{\mu}\approx B\cdot m_{N}$) and $m_N$ is the nucleon mass. In Ref.~\cite{K_parameter} it was shown that the invariant inclusive spectra of pions, protons, deuterons, and tritons in proton-nucleus reactions at 400~GeV \cite{FNAL} not only have the same exponential slope but almost coincide when they are plotted as a function of $k=\frac{p+E_{\rm{kin}}}{2}$. Using data at 10~GeV \cite{FAS}, it was shown that the parameter $k$, defined by Eq.~\ref{k}, is also appropriate for the description of secondary anti-protons produced in high energy nuclear reactions. This means that the extreme assumption of one-dimensional hadronization is a good approximation. The same approximation is also valid for the quark fusion mechanism. In the one-dimensional case, assuming that $q$ is the momentum of the second quark fusing with the primary quark-parton of energy $k$, the total energy of the outgoing hadron is $E=q+k$ and the momentum is $p=k-q$. In the one-dimensional case the secondary quark-parton must move in the opposite direction with respect to the primary quark-parton, otherwise the mass of the outgoing hadron would be zero. So, for mesons $k=\frac{p+E}{2}$, in accordance with Eq.~\ref{k}. In the case of anti-proton radiation, the baryon number of the quasmon is increased by one, and the primary antiquark-parton will spend its energy to build up the mass of the antiproton by picking up an anti-diquark. Thus, the energy conservation law for antiproton radiation looks like $E+m_{N}=q+k$ and $k=\frac{p+E+m_{N}}{2}$, which is again in accordance with Eq.~\ref{k}. The one-dimensional quark exchange mechanism was proposed in 1984 \cite{K_parameter}. Even in its approximate form it was useful in the analysis of inclusive spectra of hadrons and nuclear fragments in hadron-nuclear reactions at high energies. Later the same approach was used in the analysis of nuclear fragmentation in electro-nuclear reactions \cite{TPC}. Also in 1984 the quark-exchange mechanism developed in the framework of the non-relativistic quark model was found to be important for the explanation of the short distance features of $NN$ interactions \cite{NN QEX}. Later it was successfully applied to $K^{-}p$ interactions \cite{Kp QUEX}. The idea of the quark exchange mechanism between nucleons was useful even for the explanation of the EMC effect \cite{EMC}. For the non-relativistic quark model, the quark exchange technique was developed as an alternative to the Feynman diagram technique at short distances \cite{QUEX}. The CHIPS event generator models quark exchange processes, taking into account kinematic and combinatorial factors for asymptotically free quark-partons. In the naive picture of the quark-exchange mechanism, one quark-parton tunnels from the asymptotically free region of one hadron to the asymptotically free region of another hadron. To conserve color, another quark-parton from the neighboring hadron must replace the first quark-parton in the quasmon. This makes the tunneling mutual, and the resulting process is quark exchange. The experimental data available for multihadron production at high energies show regularities in the secondary particle spectra that can be related to the simple kinematic, combinatorial, and phase space rules of such quark exchange and fusion mechanisms. The CHIPS model combines these mechanisms consistently. \begin{figure}[tbp] % \centerline{\epsfig{file=hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/diagram.eps, height=2.5in, width=2.5in}} %\resizebox{1.00\textwidth}{!} %{ \includegraphics[angle=0,scale=0.6]{hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/diagram.eps} %\includegraphics[angle=0,scale=0.6]{plots/diagram.eps} %} \caption{Diagram of the quark exchange mechanism. } \label{diagram} \end{figure} Fig.~\ref{diagram} shows a quark exchange diagram which helps to keep track of the kinematics of the process. It was shown in Section \ref{annil} that a quasmon, $Q$ is kinematically determined by a few asymptotically free quark-partons homogeneously distributed over the invariant phase space. The quasmon mass $M$ is related to the number of quark-partons $N$ through \begin{equation} =4N(N-1)\cdot T^{2}, \label{temperatureII} \end{equation} where $T$ is the temperature of the system. The spectrum of quark partons can be calculated as \begin{equation} \frac{dW}{k^{\ast }dk^{\ast}}\propto \left(1-\frac{2k^{\ast}}{M} \right)^{N-3}, \label{spectrum_1II} \end{equation} where $k^{\ast}$ is the energy of the primary quark-parton in the center-of-mass system of the quasmon. After the primary quark-parton is randomized and the neighboring cluster, or parent cluster, $PC$, with bound mass $\tilde{\mu}$\ is selected, the quark exchange process begins. To follow the process kinematically one should imagine a colored, compound system consisting of a stationary, bound parent cluster and the primary quark. The primary quark has energy $k$ in the lab system, \begin{equation} k=k^{\ast }\cdot \frac{E_{N}+p_{N}\cdot \cos (\theta _{k})}{M_{N}}, \end{equation} where $M_N$, $E_N$ and $p_N$ are the mass, energy, and momentum of the quasmon in the lab frame. The mass of the compound system, $CF$, is $\mu _{c}=\sqrt{(\tilde{\mu}+k)^{2}}$, where $\tilde{\mu}$ and $k$ are the corresponding four-vectors. This colored compound system decays into a free outgoing nuclear fragment, $F$, with mass $\mu$ and a recoiling quark with energy $q$. $q$ is measured in the CMS of $\tilde{\mu}$, which coincides with the lab frame in the present version of the model because no cluster motion is considered. At this point one should recall that a colored residual quasmon, $CRQ$, with mass $M_{N-1}$ remains after the radiation of $k$. $CRQ$ is finally fused with the recoil quark $q$ to form the residual quasmon $RQ$. The minimum mass of $RQ$ should be greater than $M_{\min}$, which is determined by the minimum mass of a hadron (or Chipolino double-hadron as defined in Section \ref{annil}) with the same quark content. All quark-antiquark pairs with the same flavor should be canceled in the minimum mass calculations. This imposes a restriction, which in the center-of-mass system of $\mu_{c}$, can be written as \begin{equation} 2q\cdot (E-p\cdot \cos \theta_{qCQ})+M_{N-1}^{2}>M_{\min }^{2}, \label{min_mass} \end{equation} where $E$ is the energy and $p$ is the momentum of the colored residual quasmon with mass $M_{N-1}$ in the CMS of $\mu _{c}$. The restriction for $\cos\theta_{qCQ}$ then becomes \begin{equation} \cos \theta _{qCQ}<\frac{2qE-M_{\min }^{2}+M_{N-1}^{2}}{2qp}, \label{cost_restriction} \end{equation} which implies \begin{equation} q>\frac{M_{N-1}^{2}-M_{\min }^{2}}{2\cdot (E+p)}. \label{resid_rest} \end{equation} A second restriction comes from the nuclear Coulomb barrier for charged particles. The Coulomb barrier can be calculated in the simple form: \begin{equation} E_{CB}=\frac{Z_{F}\cdot Z_{R}}{A_{F}^{\frac{1}{3}}+A_{R}^{\frac{1}{3}}}\ (\rm{MeV}), \label{CoulBar} \end{equation} where $Z_F$ and $A_F$ are the charge and atomic weight of the fragment, and $Z_R$ and $A_R$ are the charge and atomic weight of the residual nucleus. The obvious restriction is \begin{equation} q\Delta$. It is similar to the restriction for quasmon fragmentation in vacuum: $k^{\ast}>\frac{\mu^{2}}{2M}$. The second limit is $k=\frac{\mu^{2}}{2\tilde{\mu}}$, when the low limit of randomization becomes equal to zero. If $k<\frac{\mu^{2}}{2\tilde{\mu}}$, then $-1<\cos\theta_{kq}<1$\ and $z_{\rm{low}}=1-\frac{2(k-\Delta)}{\tilde{\mu}}$. If $k>\frac{\mu^{2}}{2\tilde{\mu}}$, then the range of $\cos\theta _{kq}$\ is $-1<\cos\theta_{kq}<\frac{\mu^{2}}{k\tilde{\mu}}-1$\ and $z_{\rm{low}}=0$. This value of $z_{\rm{low}}$\ should be corrected using the Coulomb barrier restriction (\ref{cb_rest}), and the value of $z_{\rm{high}}$ should be corrected using the minimum residual quasmon restriction (\ref{resid_rest}). In the case of a quasmon with momentum much less than $k$ it is possible to impose tighter restrictions than (\ref{resid_rest}) because the direction of motion of the CRQ is opposite to $k$. So $\cos\theta_{qCQ}=-\cos\mathit{\theta}_{\mathit{kq}}$, and from (\ref{q-cos}) one can find that \begin{equation} \cos \theta_{qCQ} =1-\frac{\tilde{\mu}\cdot (k-\Delta -q)}{k\cdot q}. \label{cos_q} \end{equation} So in this case the equation (\ref{resid_rest})\ can be replaced by the more stringent one: \begin{equation} q>\frac{M_{N-1}^{2}-M_{\min }^{2}+2\frac{p\cdot \tilde{\mu}}{k}(k-\Delta )}{2\cdot (E+p+\frac{p\cdot \tilde{\mu}}{k})}. \end{equation} The integrated kinematical quark exchange probability (in the range from $z_{\rm{low}}$ to $z_{\rm{high}}$) is \begin{equation} \frac{\tilde{\mu}}{4k(n-2)}\cdot z^{n-2}, \label{z_probabII} \end{equation} and the total kinematic probability of hadronization of the quark-parton with energy $k$ into a nuclear fragment with mass\ $\mu $ is \begin{equation} \frac{\tilde{\mu}}{4k(n-2)}\cdot \left( z_{\rm{high}}^{n-2}-z_{\rm{low}}^{n-2}\right). \label{tot_kin_probabII} \end{equation} This can be compared with the vacuum probability of the quark fusion mechanism from Section \ref{annil}: \begin{equation} \frac{M-2k}{4k(N-3)}z_{\max }^{N-3}. \end{equation} The similarity is very important, as the absolute probabilities define the competition between vacuum and nuclear channels. Equations (\ref{z_probabII})\ and (\ref{tot_kin_probabII})\ can be used for randomization of $z$: \begin{equation} z=z_{\rm{low}}+\sqrt[n-2]{R}\cdot (z_{\rm{high}}-z_{\rm{low}}), \label{z_randomII} \end{equation} where $R$\ is a random number, uniformly distributed in the interval (0,1). Eq. (\ref{tot_kin_probabII})\ can be used to control the competition between different nuclear fragments and hadrons in the hadronization process, but in contrast to the case of ``in vacuum'' hadronization it is not enough to take into account only the quark combinatorics of the quasmon and the outgoing hadron. In the case of hadronization in nuclear matter, different parent bound clusters should be taken into account as well. For example, tritium can be radiated as a result of quark exchange with a bound tritium cluster or as a result of quark exchange with a bound $^3$He cluster. To calculate the yield of fragments it is necessary to calculate the probability to find a cluster with certain proton and neutron content in a nucleus. One could consider any particular probability as an independent parameter, but in such a case the process of tuning the model would be difficult. We proposed the following scenario of clusterization. A gas of quasi-free nucleons is close to the phase transition to a liquid bound by strong quark exchange forces. Precursors of the liquid phase are nuclear clusters, which may be considered as ``drops'' of the liquid phase within the nucleus. Any cluster can meet another nucleon and absorb it (making it bigger), or it can release one of the nucleons (making it smaller). The first parameter $\varepsilon_{1}$\ is the percentage of quasi-free nucleons not involved in the clusterization process. The rest of the nucleons ($1-\varepsilon_{1}$) clusterize. We assume that since on the periphery of the nucleus the density is lower, one can consider only dibaryon clusters, and neglect triple-baryon clusters. Still we denote the number of nucleons clusterized in dibaryons on the periphery by the parameter $\varepsilon_{2}$. In the dense part of the nucleus, strong quark exchange forces make clusters out of quasi-free nucleons with high probability. To characterize the distribution of clusters the clusterization probability parameter $\omega$ was used. If the number of nucleons involved in clusterization is $a=(1-\varepsilon_{1}-\varepsilon _{2})\cdot A$, then the probability to find a cluster consisting of $\nu$\ nucleons is defined by the distribution \begin{equation} P_{\nu }\propto C_{\nu }^{a}\cdot \omega ^{\nu -1}, \end{equation} where $C_{\nu }^{a}$ is the corresponding binomial coefficient. The coefficient of proportionality can be found from the equation \begin{equation} a=b\cdot \sum\limits_{\nu =1}^{a}\nu \cdot C_{\nu }^{a}\cdot \omega ^{\nu -1}=b\cdot a\cdot (1+\omega )^{a-1}. \end{equation} Thus, the number of clusters consisting of $\nu$\ nucleons is \begin{equation} P_{\nu }=\frac{C_{\nu }^{a}\cdot \omega ^{\nu -1}}{(1+\omega )^{a-1}}. \end{equation} For clusters with an even number of nucleons we used only isotopically symmetric configurations ($\nu=2n$, $n$\ protons and $n$\ neutrons) and for odd clusters ($\nu =2n+1$) we used only two configurations: $n$\ neutrons with $n+1$\ protons and $n+1$\ neutrons with $n$\ protons. This restriction, which we call ``isotopic focusing'', can be considered an empirical rule of the CHIPS model which helps to describe data. It is applied in the case of nuclear clusterization (isotopically symmetric clusters) and in the case of hadronization in nuclear matter. In the hadronization process the quasmon is shifted from the isotopic symmetric state (e.g., by capturing a negative pion) and transfers excess charge to the outgoing nuclear cluster. This tendency is symmetric with respect to the quasmon and the parent cluster. The temperature parameter used to calculate the number of quark-partons in a quasmon (see equation~\ref{temperatureII}) was chosen to be $T=180$ MeV, which is the same as in Section \ref{annil}. CHIPS is mostly a model of fragmentation, conserving energy, momentum, and charge. But to compare it with experimental data one needs to model also the first interaction of the projectile with the nucleus. For proton-antiproton annihilation this was easy, as we assumed that in the interaction at rest, a proton and antiproton always create a quasmon. In the case of pion capture the pion can be captured by different clusters. We assumed that the probability of capture is proportional to the number of nucleons in a cluster. After the capture the quasmon is formed, and the CHIPS generator produces fragments consecutively and recursively, choosing at each step the quark-parton four-momentum $k$, the type of parent and outgoing fragment, and the four-momentum of the exchange quark-parton $q$, to produce a final state hadron and the new quasmon with less energy. In the CHIPS model we consider this process as a chaotic process with large number of degrees of freedom and do not take into account any final state interactions of outgoing hadrons. Nevertheless, when the excitation energy dissipates, and in some step the quasmon mass drops below the mass shell, the quark-parton mechanism of hadronization fails. To model the event exclusively, it becomes necessary to continue fragmentation at the hadron level. Such a fragmentation process is known as nuclear evaporation. It is modeled using the non-relativistic phase space approach. In the non-relativistic case the phase space of nucleons can be integrated as well as in the ultra-relativistic case of quark-partons. The general formula for the non-relativistic phase space can be found starting with the phase space for two particles $\tilde{\Phi}_{2}$. It is proportional to the center-of-mass momentum: \begin{equation} \tilde{\Phi}_2(W_2) \propto \sqrt{W_2}, \label{F2} \end{equation} where $W_2$\ is a total kinetic energy of the two non-relativistic particles. If the phase space integral is known for $n-1$\ hadrons then it is possible to calculate the phase space integral for $n$\ hadrons: \begin{eqnarray} \tilde{\Phi}_{n}(W_n) &=&\int \tilde{\Phi}_{n-1}(W_{n-1}) \cdot \delta (W_{n}-W_{n-1}-E_{\rm{kin}}) \nonumber \\ &&\times \sqrt{E_{\rm{kin}}}dE_{\rm{kin}} dW_{n-1}. \label{Fn} \end{eqnarray} Using (\ref{F2})\ and (\ref{Fn})\ one can find that \begin{equation} \tilde{\Phi}_{n}(W_n)\propto W_{n}^{\frac{3}{2}n-\frac{5}{2}} \end{equation} and the spectrum of hadrons, defined by the phase space of residual $n-1$ nucleons, can be written as \begin{equation} \frac{dN}{\sqrt{E_{\rm{kin}}}dE_{\rm{kin}}} \propto \left(1-\frac{E_{\rm{kin}}}{W_{n}}\right)^{\frac{3}{2}n-4}. \label{evap_spectr} \end{equation} This spectrum can be randomized. The only problem is from which level one should measure the thermal kinetic energy when most nucleons in nuclei are filling nuclear levels with zero temperature. To model the evaporation process we used this unknown level as a parameter $U$\ of the evaporation process. Comparison with experimental data gives $U=1.7$ MeV. Thus, the total kinetic energy of $A$\ nucleons is \begin{equation} W_{A}=U\cdot A+E_{\rm{ex}}, \end{equation} where $E_{\rm{ex}}$ is the excitation energy of the nucleus. To\ be\ radiated,\ \ the nucleon\ \ should\ \ overcome\ \ the threshold \begin{equation} U_{\rm{thresh}}=U+U_{\rm{bind}}+E_{CB}, \end{equation} where $U_{\rm{bind}}$\ is the separation energy of the nucleon, and $E_{CB}$\ is the Coulomb barrier energy which is non-zero only for positive particles and can be calculated using formula (\ref{CoulBar}). From several experimental investigations of nuclear pion capture at rest, four published results have been selected here, which constitute, in our opinion, a representative data set covering a wide range of target nuclei, types of produced hadrons and nuclear fragments, and their energy range. In the first publication \cite{MIPHI}\ the spectra of charged fragments (protons, deuterons, tritons, $^{3}$He, $^{4}$He) in pion capture were measured on 17 nuclei within one experimental setup. To verify the spectra we compared them for a carbon target with detailed measurements of the spectra of charged fragments given in Ref.~\cite{Mechtersheimer}. In addition, we took $^{6}$Li spectra for a carbon target from the same paper. The neutron spectra were added from Ref.~\cite{Cernigoi} and Ref.~\cite{Madey}. We present data and Monte Carlo distributions as the invariant phase space function $f=\frac{d\sigma}{pdE}$\ depending on the variable $k=\frac{p+E_{\rm{kin}}}{2}$\ as defined in equation~(\ref{k}). Spectra on $^{9}$Be, $^{12}$C, $^{28}$Si ($^{27}$Al for secondary neutrons), $^{59}$Co ($^{64}$Cu for secondary neutrons), and $^{181}$Ta\ are shown in Figs.~\ref{be0405}\ through~\ref{ta73108}. The data are well-described, including the total energy spent in the reaction to yield the particular type of fragments. The evaporation process for nucleons is also well-described. It is exponential in $k$, and looks especially impressive for Si/Al and Co/Cu data, where the Coulomb barrier is low, and one can see proton evaporation as a continuation of the evaporation spectra from secondary neutrons. This way the exponential behavior of the evaporation process can be followed over 3 orders of magnitude. Clearly seen is\ the\ transition region at\ \ $k \approx 90$\ MeV\ \ (kinetic energy $15-20$\ MeV)\ \ between the quark-level hadronization process and the hadron-level evaporation process. For light target nuclei the evaporation process becomes much less prominent. The $^{6}$Li spectrum on a carbon target exhibits an interesting regularity when plotted as a function of $k$: it practically coincides with the spectrum of $^{4}$He fragments, and shows exponential behavior in a wide range of $k$, corresponding to a few orders of magnitude in the invariant cross section. To keep the figure readable, the $^{6}$Li spectrum generated by CHIPS was not plotted. It coincides with the $^{4}$He spectrum at $k > 200$\ MeV, and under-estimates lithium emission at lower energies, similarly to the $^{3}$He and tritium data. Between the region where hadron-level processes dominate and the kinematic limit, all hadronic spectrum slopes become similar when plotted as a function of $k$. In addition to this general behavior there is the effect of strong proton-neutron splitting. For protons and neutrons it reaches almost an order of magnitude. To model such splitting in the CHIPS generator, the mechanism of ``isotopic focusing'' was used, which locally transfers the negative charge from the pion to the first radiated nuclear fragment. \begin{table} \caption{Clusterization parameters} \label{tab:1} \begin{tabular}{llllll} \hline\noalign{\smallskip} & $^{9}$Be & $^{12}$C & $^{28}$Si & $^{59}$Co & $^{181}$Ta \\ \noalign{\smallskip}\hline\noalign{\smallskip} $\varepsilon_{1}$ & 0.45 & 0.40 & 0.35 & 0.33 & 0.33 \\ $\varepsilon_{2}$ & 0.15 & 0.15 & 0.05 & 0.03 & 0.02 \\ $\omega $ & 5.00 & 5.00 & 5.00 & 5.00 & 5.00 \\ \noalign{\smallskip}\hline \end{tabular} \end{table} Thus, the model qualitatively describes all typical features of the pion capture process. The question is what can be extracted from the experimental data with this tool. The clusterization parameters are listed in Table~\ref{tab:1}. No formal fitting procedure has been performed. A balanced qualitative agreement with all data was used to tune the parameters. The difference between the $\frac{\varepsilon _{2}}{\varepsilon _{1}}$\ ratio and the parameter $\omega$\ (which is the same for all nuclei) is an indication that there is a phase transition between the gas phase and the liquid phase of the nucleus. The large value of the parameter $\omega$, determining the average size of a nuclear cluster, is critical in describing the model spectra at large $k$, where the fragment spectra approach the kinematic limits. Using the same parameters of clusterization, the $\gamma$\ absorption data \cite{Ryckbosch} on Al and Ca nuclei were compared in Fig.~\ref{gam62}) to the CHIPS results. One can see that the spectra of secondary protons and deuterons are qualitatively described by the CHIPS model. \begin{figure}[tbp] % \centerline{\epsfig{file=hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/be0405k.eps, height=4.5in, width=4.5in}} %\resizebox{1.00\textwidth}{!} %{ \includegraphics[angle=0,scale=0.6]{hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/be0405k.eps} %\includegraphics[angle=0,scale=0.6]{plots/be0405k.eps} %} \caption{\protect{Comparison of the CHIPS model results with experimental data on proton, neutron, and nuclear fragment production in the capture of negative pions on $^9$Be. Proton~\cite{MIPHI} and neutron~\cite{Cernigoi}\ experimental spectra are shown in the upper left panel by open circles and open squares, respectively. The model calculations are shown by the two corresponding solid lines. The same arrangement is used to present $^{3}$He~\cite{MIPHI} and tritium~\cite{MIPHI} spectra in the lower left panel. Deuterium~\cite{MIPHI} and $^{4}$He~\cite{MIPHI} spectra are shown in the right panels of the figure by open squares and lines (CHIPS model). The average kinetic energy carried away by each nuclear fragment is shown in the panels by the two numbers: first is the average calculated using the experimental data shown; second is the model result.}} \label{be0405} \end{figure} \begin{figure}[tbp] % \centerline{\epsfig{file=hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/c0606k.eps, height=4.5in, width=4.5in}} %\resizebox{1.00\textwidth}{!} %{ \includegraphics[angle=0,scale=0.6]{hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/c0606k.eps} %\includegraphics[angle=0,scale=0.6]{plots/c0606k.eps} %} \caption{\protect{Same as in Figure~\ref{be0405}, for pion capture on $^{12}$C. The experimental neutron spectrum is taken from \cite{Madey}. In addition, the detailed data on charged particle production, including the $^{6}$Li spectrum, taken from Ref.~\cite{Mechtersheimer}, are superimposed on the plots as a series of dots.}} \label{c0606} \end{figure} \begin{figure}[tbp] % \centerline{\epsfig{file=hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/si1414k.eps, height=4.5in, width=4.5in}} %\resizebox{1.00\textwidth}{!} %{ \includegraphics[angle=0,scale=0.6]{hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/si1414k.eps} %\includegraphics[angle=0,scale=0.6]{plots/si1414k.eps} %} \caption{\protect{Same as in Figure~\ref{be0405}, for pion capture on $^{28}$Si nucleus. The experimental neutron spectrum is taken from~\cite{Madey}, for the reaction on $^{27}$Al.}} \label{si1414} \end{figure} \begin{figure}[tbp] % \centerline{\epsfig{file=hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/co2732k.eps, height=4.5in, width=4.5in}} %\resizebox{1.00\textwidth}{!} %{ \includegraphics[angle=0,scale=0.6]{hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/co2732k.eps} %\includegraphics[angle=0,scale=0.6]{plots/co2732k.eps} %} \caption{\protect{Same as in Figure~\ref{be0405}, for pion capture on $^{59}$Co. The experimental neutron spectrum is taken from~\cite{Madey}, for the reaction on $^{64}$Cu.}} \label{co2732} \end{figure} \begin{figure}[tbp] % \centerline{\epsfig{file=hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/ta73108k.eps, height=4.5in, width=4.5in}} %\resizebox{1.00\textwidth}{!} %{ \includegraphics[angle=0,scale=0.6]{hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/ta73108k.eps} %\includegraphics[angle=0,scale=0.6]{plots/ta73108k.eps} %} \caption{\protect{Same as in Figure~\ref{be0405}, for pion capture on $^{181}$Ta. The experimental neutron spectrum is taken from~\cite{Madey}.}} \label{ta73108} \end{figure} \begin{figure}[tbp] % \centerline{\epsfig{file=hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/gam62.eps, height=4.5in, width=4.5in}} %\resizebox{0.70\textwidth}{!} %{ \includegraphics[angle=0,scale=0.75]{hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/gam62.eps} %\includegraphics[angle=0,scale=0.75]{plots/gam62.eps} %} \caption{\protect{Comparison of CHIPS model with experimental data~\cite{Ryckbosch} on proton and deuteron production at $90^{\circ}$ in photonuclear reactions on $^{27}$Al and $^{40}$Ca at 59 -- 65 MeV. Open circles and solid squares represent the experimental proton and deuteron spectra, respectively. Solid and dashed lines show the results of the corresponding CHIPS model calculation. Statistical errors in the CHIPS results are not shown and can be judged by the point-to-point variations in the lines. The comparison is absolute, using the values of total photonuclear cross section 3.6 mb for Al and 5.4 mb for Ca, as given in Ref.~\cite{Ahrens}. }} \label{gam62} \end{figure} The CHIPS model covers a wide spectrum of hadronic reactions with a large number of degrees of freedom. In the case of nuclear reactions the CHIPS generator helps to understand phenomena such as the order-of-magnitude splitting of neutron and proton spectra, the high yield of energetic nuclear fragments, and the emission of nucleons which kinematically can be produced only if seven or more nucleons are involved in the reaction. The CHIPS generator allows the extraction of collective parameters of a nucleus such as clusterization. The qualitative conclusion based on the fit to the experimental data is that most of the nucleons are clusterized, at least in heavy nuclei. The nuclear clusters can be considered as drops of a liquid nuclear phase. The quark exchange makes the phase space of quark-partons of each cluster common, stretching the kinematic limits for particle production. The hypothetical quark exchange process is important not only for nuclear clusterization, but also for the nuclear hadronization process. The quark exchange between the excited cluster (quasmon) and a neighboring nuclear cluster, even at low excitation level, operates with quark-partons at energies comparable with the nucleon mass. As a result it easily reaches the kinematic limits of the reaction, revealing the multi-nucleon nature of the process. Up to now the most under-developed part of the model has been the initial interaction between projectile and target. That is why we started with proton-antiproton annihilation and pion capture on nuclei at rest, because the interaction cross section is not involved. The further development of the model will require a better understanding of the mechanism of the first interaction. However, we believe that even the basic model will be useful in the understanding the nature of multi-hadron fragmentation. Because of the model's features, it is a suitable candidate for the hadron production and hadron cascade parts of the newly developed event generation and detector simulation Monte Carlo computer codes. \section[Modeling of real and virtual photon interactions]{Modeling of real and virtual photon interactions with nuclei below pion production threshold} In the example of the photonuclear reaction discussed in the Appendix D, namely the description of $90^{\circ}$ proton and deuteron spectra in $A({\gamma},X)$ reactions at $E_{\gamma} = 59-65$ MeV, the assumption on the initial Quasmon excitation mechanism was the same. The description of the $90^{\circ}$ data was satisfactory, but the generated data showed very little angular dependence, because the velocity of the quasmons produced in the initial state was small, and the fragmentation process was almost isotropic. Experimentally, the angular dependence of secondary protons in photo-nuclear reactions is quite strong even at low energies (see, for example, Ref.~\cite{Ryckebusch}). This is a challenging experimental fact which is difficult to explain in any model. It's enough to say that if the angular dependence of secondary protons in the $\gamma ^{40}$Ca interaction at 60 MeV is analyzed in terms of relativistic boost, then the velocity of the source should reach $0.33 c$; hence the mass of the source should be less than pion mass. The main point of this discussion is to show that the quark-exchange mechanism used in the CHIPS model can not only model the clusterization of nucleons in nuclei and hadronization of intranuclear excitations into nuclear fragments, but it can also model complicated mechanisms of the interaction of photons and hadrons in nuclear matter. In Ref. Appendix D a quark-exchange diagram was defined which helps to keep track of the kinematics of the quark-exchange process (see Fig.~1 in Apendix D). To apply the same diagram to the first interaction of a photon with a nucleus, it is necessary to assume that the quark-exchange process takes place in nuclei continuously, even without any external interaction. Nucleons with high momenta do not leave the nucleus because of the lack of excess energy. The hypothesis of the CHIPS model is that the quark-exchange forces between nucleons \cite{NN QEX}\ continuously create clusters in normal nuclei. Since a low-energy photon (below the pion production threshold) cannot be absorbed by a free nucleon, other absorption mechanisms involving more than one nucleon have to be used. The simplest scenario is photon absorption by a quark-parton in the nucleon. At low energies and in vacuum this does not work because there is no corresponding excited baryonic state. But in nuclear matter it is possible to exchange this quark with a neighboring nucleon or a nuclear cluster. The diagram for the process is shown in Fig.~\ref{diagram1}. In this case the photon is absorbed by a quark-parton from the parent cluster $\rm{PC}_1$, and then the secondary nucleon or cluster $\rm{PC}_2$ absorbs the entire momentum of the quark and photon. The exchange quark-parton $q$ restores the balance of color, producing the final-state hadron F and the residual Quasmon RQ. The process looks like a knockout of a quasi-free nucleon or cluster out of the nucleus. It should be emphasized that in this scenario the CHIPS event generator produces not only ``quasi-free'' nucleons but ``quasi-free'' fragments as well. The yield of these quasi-free nucleons or fragments is concentrated in the forward direction. The second scenario which provides for an angular dependence is the absorption of the photon by a colored fragment ($\rm{CF}_2$ in Fig.~\ref{diagram2}). In this scenario, both the primary quark-parton with momentum $k$ and the photon with momentum $q_{\gamma}$ are absorbed by a parent cluster ($\rm{PC}_2$ in Fig.~\ref{diagram2}), and the recoil quark-parton with momentum $q$ cannot fully compensate the momentum $k+q_{\gamma}$. As a result the radiation of the secondary fragment in the forward direction becomes more probable. In both cases the angular dependence is defined by the first act of hadronization. Further fragmentation of the residual quasmon is almost isotropic. \begin{figure}[tbp] % \centerline{\epsfig{file=hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/diagram1.eps, height=2.5in, width=2.5in}} %\resizebox{0.70\textwidth}{!} %{ \includegraphics[angle=0,scale=0.6]{hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/diagram1.eps} %\includegraphics[angle=0,scale=0.6]{plots/diagram1.eps} %} \caption{\protect{Diagram of photon absorption in the quark exchange mechanism. $\rm{PC}_{1,2}$ stand for parent clusters with bound masses $\tilde{\mu}_{1,2}$, participating in the quark-exchange. $\rm{CF}_{1,2}$ stand for the colored nuclear fragments in the process of quark exchange. F($\mu$) denotes the outgoing hadron with mass $\mu$ in the final state. RQ is the residual Quasmon which carries the rest of the excitation energy and momentum. $M_{\min}$ characterizes its minimum mass defined by its quark content. Dashed lines indicate colored objects. The photon is absorbed by a quark-parton $k$ from the parent cluster $\rm{PC}_1$. }} \label{diagram1} \end{figure} \begin{figure}[tbp] % \centerline{\epsfig{file=hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/diagram2.eps, height=2.5in, width=2.5in}} %\resizebox{0.70\textwidth}{!} %{ \includegraphics[angle=0,scale=0.6]{hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/diagram2.eps} %\includegraphics[angle=0,scale=0.6]{plots/diagram2.eps} %} \caption{\protect{Diagram of photon absorption in the quark-exchange mechanism. The notation is the same as in Fig.~\ref{diagram1}. The photon is absorbed by the colored fragment $\rm{CF}_2$. }} \label{diagram2} \end{figure} It was shown in Section \ref{annil} that the energy spectrum of quark partons in a quasmon can be calculated as \begin{equation} \frac{dW}{k^{\ast }dk^{\ast }}\propto \left(1-\frac{2k^{\ast }}{M} \right)^{N-3}, \label{spectrum_1III} \end{equation} where $k^{\ast }$ is the energy of the primary quark-parton in the center-of-mass system of the quasmon, $M$\ is the mass of the quasmon. The number $N$ of quark-partons in the quasmon can be calculated from the equation \begin{equation} =4\cdot N\cdot (N-1)\cdot T^{2}. \label{temperatureIII} \end{equation} Here $T$ is the temperature of the system. In the first scenario of the $\gamma A$ interaction (Fig.~\ref{diagram1}), because both interacting particles are massless, we assumed that the cross section for the interaction of a photon with a particular quark-parton is proportional to the charge of the quark-parton squared, and inversely proportional to the mass of the photon-parton system $s$, which can be calculated as \begin{equation} s=2\omega k(1-\cos (\theta _{k})). \label{s} \end{equation} Here $\omega $\ is the energy of the photon, and $k$ is the energy of the quark-parton in the laboratory system (LS): \begin{equation} k=k^{\ast }\cdot \frac{E_{N}+p_{N}\cdot \cos (\theta _{k})}{M_{N}}. \end{equation} For a virtual photon, equation~(\ref{s}) can be written as \begin{equation} s=2k(\omega -q_{\gamma}\cdot \cos (\theta _{k})), \end{equation} where $q_{\gamma}$ is the momentum of the virtual photon. In both cases equation~(\ref{spectrum_1III}) transforms into \begin{equation} \frac{dW}{dk^{\ast }}\propto \left(1-\frac{2k^{\ast }}{M} \right)^{N-3}, \end{equation} and the angular distribution in $\cos (\theta _{k})$\ converges to a $\delta $-function. In the case of a real photon $\cos (\theta _{k})=1$, and in the case of a virtual photon $\cos (\theta _{k})=\frac{\omega }{q_{\gamma}}$. In the second scenario for the photon interaction (Fig.~\ref{diagram2}) we assumed that both the photon and the primary quark-parton, randomized according to Eq.~(\ref{spectrum_1III}), enter the parent cluster $\rm{PC}_2$, and after that the normal procedure of quark exchange continues, in which the recoiling quark-parton $q$ returns to the first cluster. An additional parameter in the model is the relative contribution of both mechanisms. As a first approximation we assumed equal probability, but in the future, when more detailed data are obtained, this parameter can be adjusted. \begin{figure}[tbp] % \centerline{\epsfig{file=hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/gam62.eps, height=4.5in, width=4.5in}} %\resizebox{0.80\textwidth}{!} %{ \includegraphics[angle=0,scale=0.75]{hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/gam62.eps} %\includegraphics[angle=0,scale=0.75]{plots/gam62.eps} %} \caption{\protect{Comparison of the CHIPS model results (lines) with the experimental data~\cite{Ryckbosch} on proton spectra at $90^{\circ}$ in the photonuclear reactions on $^{40}$Ca at 59--65 MeV (open circles), and proton spectra at $60^{\circ}$ (triangles) and $150^{\circ}$ (diamonds). Statistical errors in the CHIPS results are not shown but can be judged by the point-to-point variations in the lines. The comparison is absolute, using the value of the total photonuclear cross section of 5.4 mb for Ca, as given in Ref.~\cite{Ahrens}. } } \label{gam62III} \end{figure} \begin{figure}[tbp] % \centerline{\epsfig{file=hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/gamm_c0606_e123.eps, height=4.5in, width=4.5in}} %\resizebox{0.80\textwidth}{!} %{ \includegraphics[angle=0,scale=0.75]{hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/gamm_c0606_e123.eps} %\includegraphics[angle=0,scale=0.75]{plots/gamm_c0606_e123.eps} %} \caption{\protect{Comparison of the CHIPS model results (lines) with the experimental data~\cite{Harty} on proton spectra at $57^{\circ}$, $77^{\circ}$, $97^{\circ}$, $117^{\circ}$, and $127^{\circ}$ in the photonuclear reactions on $^{12}$C at 123 MeV (open circles). The value of the total photonuclear cross section was set to 1.8 mb. } } \label{gam_123} \end{figure} \begin{figure}[tbp] % \centerline{\epsfig{file=hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/gamm_c0606_e151.eps, height=4.5in, width=4.5in}} %\resizebox{0.80\textwidth}{!} %{ \includegraphics[angle=0,scale=0.75]{hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/gamm_c0606_e151.eps} %\includegraphics[angle=0,scale=0.75]{plots/gamm_c0606_e151.eps} %} \caption{\protect{Same as in Fig.~\ref{gam_123}, for the photon energy 151 MeV.} } \label{gam_151} \end{figure} \begin{figure}[tbp] % \centerline{\epsfig{file=hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/vgam_c0606k.eps, height=4.5in, width=4.5in}} %\resizebox{0.80\textwidth}{!} %{ \includegraphics[angle=0,scale=0.75]{hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/vgam_c0606k.eps} %\includegraphics[angle=0,scale=0.75]{plots/vgam_c0606k.eps} %} \caption{\protect{Comparison of the CHIPS model results (line) with the experimental data~\cite{Bates} (open circles) on the proton spectrum measured in parallel kinematics in the $^{12}$C(e,e$^{\prime}$p)\ reaction at an energy transfer equal to 210 MeV and momentum transfer equal to 585 MeV/$c$. Statistical errors in the CHIPS result are not shown but can be judged by the point-to-point variations in the line. The relative normalization is arbitrary. } } \label{vgam} \end{figure} We begin the comparison with the data on proton production in the $^{40}$Ca$(\gamma,X)$\ reaction at $90^{\circ}$\ and 59--65 MeV \cite{Ryckbosch}, and at $60^{\circ}$\ and $150^{\circ}$\ and 60 MeV \cite{Abeele}. We analyzed these data together to compare the angular dependence generated by CHIPS with experimental data. The data are presented as a function of the invariant inclusive cross section $f=\frac{d\sigma }{p_{p}dE_{p}}$\ depending on the variable $k=\frac{T_{p}+p_{p}}{2}$, where $T_{p}$\ and $p_{p}$\ are the kinetic energy and momentum of the secondary proton. As one can see from Fig.~\ref{gam62III}, the angular dependence of the proton yield in photoproduction on $^{40}$Ca at $60$ MeV is reproduced quite well by the CHIPS event generator. The second set of measurements that we use for the benchmark comparison deals with the secondary proton yields in $^{12}$C$(\gamma,X)$ reactions at 123 and 151 MeV \cite{Harty}, which is still below the pion production threshold on a free nucleon. Inclusive spectra of protons have been measured in $\gamma ^{12}$C reactions at $57^{\circ}$, $77^{\circ}$, $97^{\circ}$, $117^{\circ}$, and $127^{\circ}$. Originally, these data were presented as a function of the missing energy. We present the data in Figs.~\ref{gam_123} and \ref{gam_151} together with CHIPS calculations in the form of the invariant inclusive cross section dependent on $k$. All parameters of the model such as temperature $T$ and parameters of clusterization for the particular nucleus were the same as in Appendix D, where pion capture spectra were fitted. The agreement between the experimental data and the CHIPS model results is quite remarkable. Both data and calculations show significant strength in the proton yield cross section up to the kinematic limits of the reaction. The angular distribution in the model is not as prominent as in the experimental data, but agrees well qualitatively. Using the same parameters, we applied the CHIPS event generator to the $^{12}$C(e,e$^{\prime }$p) reaction measured in Ref.\cite{Bates}. The proton spectra were measured in parallel kinematics in the interaction of virtual photons with energy $\omega = 210$ MeV and momentum $q_{\gamma} = 585$ MeV/$c$. To account for the experimental conditions in the CHIPS event generator, we have selected protons generated in the forward direction with respect to the direction of the virtual photon, with the relative angle $\Theta_{qp} < 6^{\circ}$. The CHIPS generated distribution and the experimental data are shown in Fig.~\ref{vgam} in the form of the invariant inclusive cross section as a function of $k$. The CHIPS event generator works only with ground states of nuclei so we did not expect any narrow peaks for $^{1}p_{3/2}$-shell knockout or for other shells. Nevertheless we found that the CHIPS event generator fills in the so-called ``$^{1}s_{1/2}$-shell knockout'' region, which is usually artificially smeared by a Lorentzian~\cite{Lorentzian}. In the regular fragmentation scenario the spectrum of protons below $k = 300$ MeV is normal; it falls down to the kinematic limit. The additional yield at $k > 300$ MeV is a reflection of the specific first act of hadronization with the quark exchange kinematics. The slope increase with momentum is approximated well by the model, but it is obvious that the yield close to the kinematic limit of the $2 \rightarrow 2$ reaction can only be described in detail if the excited states of the residual nucleus are taken into account. The angular dependence of the proton yield in low-energy photo-nuclear reactions is described in the CHIPS model and event generator. The most important assumption in the description is the hypothesis of a direct interaction of the photon with an asymptotically free quark in the nucleus, even at low energies. This means that asymptotic freedom of QCD and dispersion sum rules~\cite{sum_rules} can in some way be generalized for low energies. The knockout of a proton from a nuclear shell or the homogeneous distributions of nuclear evaporation cannot explain significant angular dependences at low energies. The same mechanism appears to be capable of modeling proton yields in such reactions as the $^{16}$C(e,e$^{\prime }$p) reaction measured at MIT Bates \cite{Bates}, where it was shown that the region of missing energy above 50 MeV reflects ``two-or-more-particle knockout'' (or the ``continuum'' in terms of the shell model). The CHIPS model may help to understand and model such phenomena. \section[Chiral invariant phase-space decay]{Chiral invariant phase-space decay in high energy hadron nuclear reactions} \noindent \qquad Chiral invariant phase-space decay can be used to de-excite an excited hadronic system. This possibility can be exploited to replace the intra-nuclear cascading after a high energy primary interaction takes place. The basic assumption in this is that the energy loss of the high energy hadron in nuclear matter is approximately constant per unit path length (about 1 GeV/fm). This energy is extracted from the soft part of the particle spectrum of the primary interaction, and from particles with formation times that place them within the nuclear boundaries. Several approaches of transfering this energy into quasmons were studied, and comparisons with energy spectra of particles emitted in the backward hemisphere were made for a range of materials. Best results were achieved with a model that creates one quasmon per particle absorbed in the nucleus. \section{Neutrino-nuclear interactions} \label{numunuc} The simulation of DIS reactions includes reactions with high $Q^2$. The first approximation of the $Q^2$-dependent photonuclear cross-sections at high $Q^2$ was made in \cite{photNuc}, where the modified photonuclear cross sections of virtual photons \cite{Electronuc} were used. The structure functions of protons and deuterons have been approximated in CHIPS by the sum of non-perturbative multiperipheral and non-perturbative direct interactions of virtual photons with hadronic partons: \begin{figure}[tbp] % \centerline{\epsfig{file=hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/vgam_c0606k.eps, height=4.5in, width=4.5in}} %\resizebox{0.80\textwidth}{!} %{ \includegraphics[angle=0,scale=0.60]{hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/gabsa.eps} %\includegraphics[angle=0,scale=0.60]{plots/gabsa.eps} %} \caption{ Fit of $\gamma A$ cross sections with different $H$ values. Data are from \cite{photNuc}. } \label{gamC} \end{figure} \begin{equation} F_2(x,Q^2)=[A(Q^2)\cdot x^{-\Delta(Q^2)}+B(Q^2)\cdot x]\cdot(1-x)^{N(Q^2)-2}, \label{DIS} \end{equation} where $A(Q^2)=\bar{e^2_S}\cdot D\cdot U$, $B(Q^2)=\bar{e^2_V}\cdot(1-D)\cdot V$, $\bar{e^2}_{V(p)}=\frac{1}{3}$, $\bar{e^2}_{V(d)}=\frac{5}{18}$, $\bar{e^2_S}=\frac{1}{3}-\frac{\frac{1}{3}-\frac{5}{18}}{1+m^2_\phi/Q^2} +\frac{\frac{1}{3}-\frac{5}{18}}{1+m^2_{J/\psi}/Q^2}- \frac{\frac{1}{3}-\frac{19}{63}}{1+m^2_{\Upsilon}/Q^2}$, $N=3+\frac{0.5}{\alpha_s(Q^2)}$, $\alpha_s(Q^2)=\frac{4\pi}{\beta_0 ln(1+\frac{Q^2}{\Lambda^2})}$, $\beta_0^{(n_f=3)}=9$, $\Lambda=200~MeV$, $U=\frac{(3~C(Q^2)+N-3)\cdot\Gamma(N-\Delta)} {N\cdot\Gamma(N-1)\cdot\Gamma(1-\Delta)}$, $V=3(N-1)$, $D(Q^2)=H\cdot S(Q^2)\left(1-\frac{1}{2}S(Q^2)\frac{\bar{e^2_V}}{\bar{e^2_S}} \right)$, $S={\left(1+\frac{m^2_\rho}{Q^2}\right)^{-\alpha_P(Q^2)}}$, $\alpha_P=1+\Delta(Q^2)$, $\Delta=\frac{1+r}{12.5+2r}$, $r=\left(\frac{Q^2}{1.66}\right)^{1/2}$, $C=\frac{1+f}{g\cdot (1+f/.24)}$, $f=\left(\frac{Q^2}{0.08}\right)^2$, $g=1+\frac{Q^2}{21.6}$. The parton distributions are normalized to the unit total momentum fraction. \begin{figure}[tbp] % \centerline{\epsfig{file=hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/vgam_c0606k.eps, height=4.5in, width=4.5in}} %\resizebox{0.80\textwidth}{!} %{ \includegraphics[angle=0,scale=0.60]{hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/f23nud.eps} %\includegraphics[angle=0,scale=0.60]{plots/f23nud.eps} %} \caption{ Fit of $f_{2d}(x,Q^2)$ (filled circles, solid lines) and $f_{3d}(x,Q^2)$ (open circles, dashed lines) structure functions measured by the WA25 experiment \cite{WA25}. } \label{nuD} \end{figure} The photonuclear cross sections are calculated by the eikonal formula: \begin{equation} \sigma_\gamma^{tot}=\left[\frac{4\pi\alpha}{Q^2}F_2\left(\frac{Q^2} {2M\nu},Q^2\right)\right]^{\nu=E}_{Q^2=0}, \label{eikonal} \end{equation} An example of the approximation is shown in Fig.~\ref{gamC}. One can see that the hadronic resonances are ``melted'' in nuclear matter and the multi-peripheral part of the cross section (high energy) is shadowed. The differential cross section of the $(\nu,\mu)$ reaction was approximated as \begin{equation} \frac{yd^2\sigma^{\nu,\bar\nu}}{dydQ^2}=\frac{G^2_F\cdot M^4_W}{4\pi\cdot (Q^2+M^2_W)^2}\left[c_1(y)\cdot f_2(x,Q^2)\pm c_2(y)\cdot xf_3(x,Q^2)\right], \label{difsec} \end{equation} where $c_1(y)=2-2y+\frac{y^2}{1+R}$, $R=\frac{\sigma_L}{\sigma_T}$, $c_2(y)=y(2-y)$. As $\bar{e^2_V}=\bar{e^2_S}=1$ in Eq.\ref{DIS}, hence $f_2(x,Q^2)=\left[D\cdot U\cdot x^{-\Delta}+(1-D)\cdot V\cdot x\right]\cdot(1-x)^{N-2}$, $xf_3(x,Q^2)=\left[ D\cdot U_{f3}\cdot x^{-\Delta} +(1-D)\cdot V\cdot x\right]\cdot(1-x)^{N-2}$, with $D=H\cdot S(Q^2)\cdot\left(1-\frac{1}{2}S(Q^2)\right)$ and $U_{f3}=\frac{3\cdot C(Q^2)\cdot\Gamma(N-\Delta)} {N\cdot\Gamma(N-1)\Gamma(1-\Delta)}$. The approximation is compared with data in Fig.\ref{nuD} for deuterium \cite{WA25} and in Fig.\ref{nuFe} for iron \cite{CDHSW,CCFR}. It must be emphasized that the CHIPS parton distributions are the same as for electromagnetic reactions. \begin{figure}[tbp] % \centerline{\epsfig{file=hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/vgam_c0606k.eps, height=4.5in, width=4.5in}} %\resizebox{0.80\textwidth}{!} %{ \includegraphics[angle=0,scale=0.6]{hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/f23nufe.eps} %\includegraphics[angle=0,scale=0.6]{plots/f23nufe.eps} %} \caption{ Fit of $f_{2Fe}(x,Q^2)$ (filled markers, solid lines) and $f_{3Fe}(x,Q^2)$ (open markers, dashed lines) structure functions measured by the CDHSW \cite{CDHSW} (circles) and CCFR \cite{CCFR} (squares) experiments. } \label{nuFe} \end{figure} For the $(\nu,\mu)$ amplitudes one can not apply the optical theorem, To calculate the total cross sections, it is therefore necessary to integrate the differential cross sections first over $x$ and then over $Q^2$. For the $(\nu,\mu)$ reactions the differential cross section can be integrated with good accuracy even for low energies because it does not have the $\frac{1}{Q^4}$ factor of the boson propagator. The quasi-elastic part of the total cross-section can be calculated for $W 1~GeV^2$. In \cite{Comby} an attempt was made to freeze the DIS parton distributions at $Q^2=1$ and to use them at low $Q^2$. The $W<1.4~GeV$ part of DIS was replaced by the quasi-elastic and one pion production contributions, calculated on the basis of the low energy models. The results of \cite{Comby} are shown by the dotted lines. The nonperturbative CHIPS approximation (solid curves) fits both total and quasi-elastic cross sections even at low energies. \begin{figure}[tbp] % \centerline{\epsfig{file=hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/vgam_c0606k.eps, height=4.5in, width=4.5in}} %\resizebox{0.80\textwidth}{!} %{ \includegraphics[angle=0,scale=0.60]{hadronic/theory_driven/ChiralInvariantPhaseSpace/plots/numu_cs.eps} %\includegraphics[angle=0,scale=0.60]{plots/numu_cs.eps} %} \caption{ Fit of total (a,b) and quasi-elastic (c,d) cross-sections of $(\nu,\mu)$ reactions (Geant4 database). The solid line is the CHIPS approximation (for other lines see text). } \label{totqe} \end{figure} The quasi-elastic $(\nu,\mu)$ cross sections are shown in Fig.\ref{totqe}(c,d). The CHIPS approximation (solid line) is compared with calculations made in \cite{Comby} (the dotted line) and the best fit of the $V-A$ theory was made in \cite{VMA} (the dashed lines). One can see that CHIPS gives reasonable agreement. The $Q^2$ spectra for each energy are known as an intermediate result of the calculation of total or quasi-elastic cross sections. For the quasi-elastic interactions ($Wm_N+m_\pi$ the $Q^2$ value is randomized and therefore the $Q^2$ dependent coefficients (the number of partons in non-perturbative phase space $N$, the Pomeron intercept $\alpha_P$, the fraction of the direct interactions, etc.) can be calculated. Then for fixed energy and $Q^2$ the neutrino interaction with quark-partons (directly or through the Pomeron ladder) can be randomized and the secondary parton distribution can be calculated. In vacuum or in nuclear matter the secondary partons are creating quasmons \cite{CHIPS1,CHIPS2} which decay to secondary hadrons. \section{Conclusion.} \noindent \qquad For users who would like to improve the interaction part of the CHIPS event generator for their own specific reactions, some advice concerning data presentation is useful. It is a good idea to use a normalized invariant function $\rho (k)$% \[ \rho =\frac{2E\cdot d^{3}\sigma }{\sigma _{tot}\cdot d^{3}p}\propto \frac{% d\sigma }{\sigma _{tot}\cdot pdE}, \] where $\sigma _{tot}$\ is the total cross section of the reaction. The simple rule, then, is to divide the distribution over the hadron energy $E$ by the momentum and by the reaction cross section. The argument $k$ can be calculated for any outgoing hadron or fragment as \[ k=\frac{E+p-B\cdot m_{N}}{2}, \] which is the energy of the primary quark-parton. Because the spectrum of the quark-partons is universal for all the secondary hadrons or fragments, the distributions over this parameter have a similar shape for all the secondaries. They should differ only when the kinematic limits are approached or in the evaporation region. This feature is useful for any analysis of experimental data, independent of the CHIPS model. % The released version of the CHIPS event generator is not perfect yet, % so in case of an error it is necessary to distinguish between the error % of the test program ({\bf CHIPStest.cc}) and the error in the body of % the generator. Usually the error printing contains the address of the % routine, but sometimes the name is abbreviated so that instead of % {\bf G4QEnvironment}, {\bf G4Quasmon}, or {\bf G4QNucleus}, one will % find {\bf G4QE}, {\bf G4Q}, or {\bf G4QN}. The errors in % {\bf CHIPStest.cc} can be easily analyzed. Even if sometimes energy or % charge is not conserved, this check can be excluded in order to keep % going. On the other hand, if the error is in the body it is difficult % to fix. The normal procedure is to uncomment the flags of the debugging % prints in the corresponding part of the source code and try to find out % the reason. Anyway inform authors about the error. Do not forget to attach the % {\bf CHIPStest.cc} and the {\bf chipstest.in} files. Some concluding remarks should be made about the parameters of the model. The main parameter, the critical temperature T$_{c}$, should not be varied. A large set of data confirms the value {\bf 180 MeV} while from the mass spectrum of hadrons it can be found more precisely as 182 MeV. The clusterization parameter is {\bf 4.} which is just about 4$\pi /3.$ If the quark exchange starts at the mean distance between baryons in the dense part of the nucleus, then the radius of the clusterization sphere is twice the ''the radius of the space occupied by the baryon''. It gives 8 for the parameter, but the space occupied by the baryon can not be spherical; only cubic subdivision of space is possible so the factor $\pi/6 $ appears. But this is a rough estimate, so {\bf 4} or even {\bf 5} can be tried. The surface parameter $fD$ varies slightly with $A$, growing from 0 to 0.04. For the present CHIPS version the recommended parameters for low energies are: \begin{tabular}{llllllllll} {\bf A} & {\bf T} & {\bf s/u} & {\bf eta} & {\bf noP} & {\bf fN} & {\bf fD} & {\bf Cp} & {\bf rM} & {\bf sA} \\ {\bf Li} & 180. & 0.1 & 0.3 & 223 & .4 & .00 & 4. & 1.0 & 0.4 \\ {\bf Be} & 180. & 0.1 & 0.3 & 223 & .4 & .00 & 4. & 1.0 & 0.4 \\ {\bf C} & 180. & 0.1 & 0.3 & 223 & .4 & .00 & 4. & 1.0 & 0.4 \\ {\bf O} & 180. & 0.1 & 0.3 & 223 & .4 & .02 & 4. & 1.0 & 0.4 \\ {\bf F} & 180. & 0.1 & 0.3 & 223 & .4 & .03 & 4. & 1.0 & 0.4 \\ {\bf Al} & 180. & 0.1 & 0.3 & 223 & .4 & .04 & 4. & 1.0 & 0.4 \\ {\bf Ca} & 180. & 0.1 & 0.3 & 223 & .4 & .04 & 4. & 1.0 & 0.4 \\ {\bf Cu} & 180. & 0.1 & 0.3 & 223 & .4 & .04 & 4. & 1.0 & 0.4 \\ {\bf Ta} & 180. & 0.1 & 0.3 & 223 & .4 & .04 & 4. & 1.0 & 0.4 \\ {\bf U} & 180. & 0.1 & 0.3 & 223 & .4 & .04 & 4. & 1.0 & 0.4 \end{tabular} The vacuum hadronization weight parameter can be bigger for light nuclei and smaller for heavy nuclei, but $1.0$ is a good guess. The s/u parameter is not yet tuned, as it demands strange particle production data. A guess is that if there are as many $u\bar{u}$ and $d\bar{d}$ pairs in the reaction as in the $p\bar{p}$ interaction, the parameter can be 0.1. In other cases it is closer to 0.3 as in other event generators. But it is bestnot to touch any parameters for the first experience with the CHIPS event generator. Only the incident momentum, the PDG code of the projectile, and the CHIPS style PDG code of the target need be changed. \section{Status of this document} 02.12.05 neutrino interactions section and figures added by M.V. Kossov \\ 26.04.03 first four sections re-written by D.H. Wright \\ 01.01.01 created by M.V. Kossov and H.P. Wellisch \\ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%**************************** \begin{latexonly} \begin{thebibliography}{} % \bibitem{STAND_ALONE} \noindent M. V. Kossov, Manual for the CHIPS % event generator,High Energy Accelerator Research Organization (KEK) % Internal 2000-17, February 2001, H/R \bibitem{Parton_Models} B. Andersson, G. Gustafson, G. Ingelman, T. Sj\"{o}strand, Phys. Rep. {\textbf{97}} (1983) 31 \bibitem{CHIPS1} \noindent P. V. Degtyarenko, M. V. Kossov, and H.P. Wellisch, Chiral invariant phase space event generator, I. Nucleon-antinucleon annihilation at rest, Eur. Phys. J. A 8 (2000) 217. \bibitem{CHIPS2} P. V. Degtyarenko, M. V. Kossov, and H. P. Wellisch, Chiral invariant phase space event generator, II.Nuclear pion capture at rest, Eur. Phys. J. A 9 (2000) 411. \bibitem{CHIPS3} P. V. Degtyarenko, M. V. Kossov, and H. P. Wellisch, Chiral invariant phase space event generator, III Photonuclear reactions below $\Delta $(3,3) excitation, Eur. Phys. J. A 9, (2000) 421. \bibitem{hadronMasses} M. V. Kossov, Chiral invariant phase space model, I Masses of hadrons, Eur. Phys. J. A 14 (2002) 265. \bibitem{Chiral_Bag} C.A.Z. Vasconcellos et al., Eur. Phys. J. C {\textbf{4}} (1998) 115; G.A. Miller, A.W. Thomas, S. Theberge, Phys. Lett. B {\textbf{91}} (1980) 192; C.E. de Tar, Phys. Rev. D {\textbf{24}} (1981) 752; M.A.B. B\'{e}g, G.T. Garvey, Comments Nucl. Part. Phys. {\textbf{18}} (1988) 1 \bibitem{GENBOD} F. James, \textit{Monte Carlo Phase Space}, CERN 68-15 (1968) \bibitem{Feynman-Wilson} K.G. Wilson, Proc. Fourteenth Scottish Universities Summer School in Physics (1973), eds R. L. Crawford, R. Jennings (Academic Press, New York, 1974) \bibitem{CH.PDG} Monte Carlo particle numbering scheme, in: Particle Data Group, \textit{Review of Particle Physics}, Eur. Phys. J. C {\textbf{3}} (1998) 180 \bibitem{Hagedorn} R. Hagedorn, Nuovo Cimento Suppl. {\textbf{3}} (1965) 147 \bibitem{photNuc} M. V. Kossov, Approximation of photonuclear interaction cross-sections, Eur. Phys. J. A 14 (2002) 377. \bibitem{GEANT4} S. Giani et al., Geant4: Object Oriented Toolkit for Simulation in HEP, LCB status report CERN/LHCC/98-44, November 1998. \bibitem{MC2000} J. P. Wellisch, On hadronic models in GEANT4, Program and Book of Abstracts.International Conference on Advanced Monte Carlo for Radiation Physics, Particle Transport Simulation and Applications, 23-26 October 2000, IST,Lisbon, Portugal, p. 330. \bibitem{Duality} Yu.L. Dokshitzer, V.S. Fadin and V.A. Khoze, Phys. Lett. {\textbf{115B}} (1982) 242L \bibitem{JETSET} T. Sj\"{o}strand, Comp. Phys. Comm. {\textbf{92}} (1994) 74 \bibitem{OZI} S. Ocubo, Phys. Lett. {\textbf{5}} (1963) 165; G. Zweig, CERN Preprint 8419/TH-412 (1964); I. Iizuka, Progr. Theor. Phys. Suppl. {\textbf{37}} (1966) 21 \bibitem{OZI_violation} V.E. Markushin, M.P. Locher, Eur. Phys. J. A {\textbf{1}} (1998) 91 \bibitem{pispectrum} J. Sedlak and V. Simak, Sov. J. Part. Nucl. {\textbf{19}} (1988) 191 \bibitem{pap_exdata} C. Amsler, Rev.Mod.Phys. {\textbf{70}} (1998) 1293; C. Amsler and F. Myher, Annu. Rev. Nucl. Part. Sci. {\textbf{41}} (1991) 219 \bibitem{POPCORN} B. Andersson, G. Gustafson, T. Sj\"{o}strand, Nucl. Phys. B {\textbf{197}}(1982) 45; B. Andersson, G. Gustafson, T. Sj\"{o}strand, Physica Scripta {\textbf{32}} (1985) 574 \bibitem{Energy_Dep} P. Gregory et al., Nucl. Phys. B {\textbf{102}} (1976) 189 \bibitem{K_parameter} M.V. Kossov and L.M. Voronina, Preprint ITEP 165-84, Moscow (1984) \bibitem{FNAL} V.I.~Efremenko et al., Phys. Rev. C \textbf{22} (1980) 700. \bibitem{FAS} S.V~Boyarinov et al., Phys. At. Nucl. \textbf{56} (1993) 72. \bibitem{TPC} P.V. Degtyarenko et al., Phys. Rev. C {\textbf{50}} (1994) R541 \bibitem{NN QEX} K.~Maltman and N.~Isgur, Phys. Rev. D \textbf{29} (1984) 952. \bibitem{Kp QUEX} K.~Maltman and N.~Isgur, Phys. Rev. D \textbf{34} (1986) 1372. \bibitem{EMC} P.~Hoodbhoy and R.~J.~Jaffe, Phys. Rev. D \textbf{35} (1987) 113. \bibitem{QUEX} N.~Isgur, Nucl. Phys. \textbf{A497} (1989) 91. %%%%%%%%%%%%%%% \bibitem{massSpectr} M. V. Kossov, CHIPS: masses of hadrons. (be published). \bibitem{eqPhotons} L. D. Landau, E. M. Lifshitz, ``Course of Theoretical Physics'' v.4, part 1, ``Relativistic Quantum Theory'', Pergamon Press, paragraph 96, The method of equivalent photons. \bibitem{Shadowing} J. Eickmeyer et al. Phys. Rev. Letters {\bf 36 }(1976) 289-291. \bibitem{Guilo} D'Agostini, Hard Scattering Process in High Energy Gamma-Induced Reactions, DESY 94-169, September 1994. \bibitem{Electronuc} F. W. Brasse et al. Nuclear Physics {\bf B39 }(1972) 421-431. \bibitem{WA25} D. Allasia {\textit {et~al}}, Z. Phys C {\textbf{28}}, 321 (1985) \bibitem{CDHSW} P. Berg {\textit {et~al}}, Z. Phys C {\textbf{49}}, 187 (1991) \bibitem{CCFR} E. Oltman {\textit {et~al}}, Z. Phys C {\textbf{53}}, 51 (1992) \bibitem{GRV} M. Gl\"uck {\textit {et~al}}, Z. Phys. C {\textbf{48}}, 471 (1990) \bibitem{KMRS} J. Kviecinski {\textit {et~al}}, Phys. Rev. D {\textbf{42}}, 3645 (1990) \bibitem{Comby} P. Lipari {\textit {et~al}}, Phys. Rev. Let. {\textbf{74}}, 4384 (1995) \bibitem{VMA} S.V. Belikov {\textit {et~al}}, Z. Phys. A {\textbf{320}}, 625 (1985) \bibitem{PenCB} A. Lepretre et al. Nuclear Physics {\bf A390 }(1982) 221-239. \bibitem{DINREG} P.V. Degtyarenko and M.V. Kossov, Preprint ITEP 11-92, Moscow (1992) \bibitem{ARGUS} P.V. Degtyarenko et al., Z. Phys. A - Atomic Nuclei, {\textbf{335}} (1990) 231 \bibitem{GDINR} P.V. Degtyarenko, \textit{Applications of the photonuclear fragmentation model to radiation protection problems}, in: Proceedings of Second Specialist's Meeting on Shielding Aspects of Accelerators, Targets and Irradiation Facilities (SATIF-2), CERN, Geneva, Switzerland, 12-13 October 1995, published by Nuclear Energy Agency, Organization for Economic Co-operation and Development, pages 67 - 91 (1996) \bibitem{sum_rules} C. Bernard, A. Duncan, J. LoSecco, and S. Weinberg, Phys. Rev. D \textbf{12} (1975) 792; E. Poggio, H. Quinn, and S. Weinberg, Phys. Rev. D \textbf{13} (1976) 1958 \bibitem{MIPHI} A.~I.~Amelin et al., ``Energy spectra of charged particles in the reaction of $\pi^-$ absorption at rest by $^{6,7}$Li, $^{9}$Be, $% ^{10,11}$B, $^{12}$C, $^{28}$Si, $^{40}$Ca, $^{59}$Co, $^{93}$Nb, $% ^{114,117,120,124}$Sn, $^{169}$Tm, $^{181}$Ta and $^{209}$Bi nuclei'', Moscow Physics and Engineering Institute Preprint No. 034-90, Moscow, 1990. \bibitem{Mechtersheimer} G.~Mechtersheimer et al., Nucl. Phys. \textbf{A324} (1979) 379. \bibitem{Cernigoi} C.~Cernigoi et al., Nucl. Phys. \textbf{A456} (1986) 599. \bibitem{Madey} R.~Madey et al., Phys. Rev. C \textbf{25} (1982) 3050. \bibitem{Ryckbosch} D.~Ryckbosch et al., Phys. Rev. C \textbf{42} (1990) 444. \bibitem{Ahrens} J.~Ahrens et al., Nucl. Phys. \textbf{A446} (1985) 229c. \bibitem{Ryckebusch} Jan~Ryckebusch et al., Phys. Rev. C \textbf{49} (1994) 2704. \bibitem{Abeele} C.~Van~den~Abeele; private communication cited in the reference: Jan~Ryckebusch et al., Phys. Rev. C \textbf{49} (1994) 2704. \bibitem{Harty} P.D.~Harty et al. (unpublished); private communication cited in the reference: Jan~Ryckebusch et al., Phys. Rev. C \textbf{49} (1994) 2704. \bibitem{Bates} L.B.~Weinstein et al., Phys. Rev. Lett. \textbf{64} (1990) 1646. \bibitem{Lorentzian} J.P.~Jeukenne and C.~Mahaux, Nucl. Phys. A \textbf{394} (1983) 445. \end{thebibliography} \end{latexonly} \begin{htmlonly} \section{Bibliography} \begin{enumerate} % \bibitem{STAND_ALONE} \noindent M. V. Kossov, Manual for the CHIPS % event generator,High Energy Accelerator Research Organization (KEK) % Internal 2000-17, February 2001, H/R \item B. Andersson, G. Gustafson, G. Ingelman, T. Sj\"{o}strand, Phys. Rep. {\textbf{97}} (1983) 31 \item \noindent P. V. Degtyarenko, M. V. Kossov, and H.P. Wellisch, Chiral invariant phase space event generator, I. Nucleon-antinucleon annihilation at rest, Eur. Phys. J. A {\bf 8}, 217-222 (2000). \item P. V. Degtyarenko, M. V. Kossov, and H. P. Wellisch, Chiral invariant phase space event generator, II.Nuclear pion capture at rest, Eur. Phys. J. A 9, (2001). \item P. V. Degtyarenko, M. V. Kossov, and H. P. Wellisch, Chiral invariant phase space event generator, III Photonuclear reactions below $\Delta $(3,3) excitation, Eur. Phys. J. A 9, (2001). \item C.A.Z. Vasconcellos et al., Eur. Phys. J. C {\textbf{4}} (1998) 115; G.A. Miller, A.W. Thomas, S. Theberge, Phys. Lett. B {\textbf{91}} (1980) 192; C.E. de Tar, Phys. Rev. D {\textbf{24}} (1981) 752; M.A.B. B\'{e}g, G.T. Garvey, Comments Nucl. Part. Phys. {\textbf{18}} (1988) 1 \item F. James, \textit{Monte Carlo Phase Space}, CERN 68-15 (1968) \item K.G. Wilson, Proc. Fourteenth Scottish Universities Summer School in Physics (1973), eds R. L. Crawford, R. Jennings (Academic Press, New York, 1974) \item Monte Carlo particle numbering scheme, in: Particle Data Group, \textit{Review of Particle Physics}, Eur. Phys. J. C {\textbf{3}} (1998) 180 \item R. Hagedorn, Nuovo Cimento Suppl. {\textbf{3}} (1965) 147 \item S. Giani et al., Geant4: Object Oriented Toolkit for Simulation in HEP, LCB status report CERN/LHCC/98-44, November 1998. \item J. P. Wellisch, On hadronic models in GEANT4, Program and Book of Abstracts.International Conference on Advanced Monte Carlo for Radiation Physics, Particle Transport Simulation and Applications, 23-26 October 2000, IST,Lisbon, Portugal, p. 330. \item Yu.L. Dokshitzer, V.S. Fadin and V.A. Khoze, Phys. Lett. {\textbf{115B}} (1982) 242L \item T. Sj\"{o}strand, Comp. Phys. Comm. {\textbf{92}} (1994) 74 \item S. Ocubo, Phys. Lett. {\textbf{5}} (1963) 165; G. Zweig, CERN Preprint 8419/TH-412 (1964); I. Iizuka, Progr. Theor. Phys. Suppl. {\textbf{37}} (1966) 21 \item V.E. Markushin, M.P. Locher, Eur. Phys. J. A {\textbf{1}} (1998) 91 \item J. Sedlak and V. Simak, Sov. J. Part. Nucl. {\textbf{19}} (1988) 191 \item C. Amsler, Rev.Mod.Phys. {\textbf{70}} (1998) 1293; C. Amsler and F. Myher, Annu. Rev. Nucl. Part. Sci. {\textbf{41}} (1991) 219 \item B. Andersson, G. Gustafson, T. Sj\"{o}strand, Nucl. Phys. B {\textbf{197}}(1982) 45; B. Andersson, G. Gustafson, T. Sj\"{o}strand, Physica Scripta {\textbf{32}} (1985) 574 \item P. Gregory et al., Nucl. Phys. B {\textbf{102}} (1976) 189 \item M.V. Kossov and L.M. Voronina, Preprint ITEP 165-84, Moscow (1984) \item V.I.~Efremenko et al., Phys. Rev. C \textbf{22} (1980) 700. \item S.V~Boyarinov et al., Phys. At. Nucl. \textbf{56} (1993) 72. \item P.V. Degtyarenko et al., Phys. Rev. C {\textbf{50}} (1994) R541 \item K.~Maltman and N.~Isgur, Phys. Rev. D \textbf{29} (1984) 952. \item K.~Maltman and N.~Isgur, Phys. Rev. D \textbf{34} (1986) 1372. \item P.~Hoodbhoy and R.~J.~Jaffe, Phys. Rev. D \textbf{35} (1987) 113. \item N.~Isgur, Nucl. Phys. \textbf{A497} (1989) 91. %%%%%%%%%%%%%%% \item M. V. Kossov, CHIPS: masses of hadrons. (be published). \item L. D. Landau, E. M. Lifshitz, ``Course of Theoretical Physics'' v.4, part 1, ``Relativistic Quantum Theory'', Pergamon Press, paragraph 96, The method of equivalent photons. \item J. Eickmeyer et al. Phys. Rev. Letters {\bf 36 }(1976) 289-291. \item D'Agostini, Hard Scattering Process in High Energy Gamma-Induced Reactions, DESY 94-169, September 1994. \item F. W. Brasse et al. Nuclear Physics {\bf B39 }(1972) 421-431. \item A. Lepretre et al. Nuclear Physics {\bf A390 }(1982) 221-239. \item P.V. Degtyarenko and M.V. Kossov, Preprint ITEP 11-92, Moscow (1992) \item P.V. Degtyarenko et al., Z. Phys. A - Atomic Nuclei, {\textbf{335}} (1990) 231 \item P.V. Degtyarenko, \textit{Applications of the photonuclear fragmentation model to radiation protection problems}, in: Proceedings of Second Specialist's Meeting on Shielding Aspects of Accelerators, Targets and Irradiation Facilities (SATIF-2), CERN, Geneva, Switzerland, 12-13 October 1995, published by Nuclear Energy Agency, Organization for Economic Co-operation and Development, pages 67 - 91 (1996) \item C. Bernard, A. Duncan, J. LoSecco, and S. Weinberg, Phys. Rev. D \textbf{12} (1975) 792; E. Poggio, H. Quinn, and S. Weinberg, Phys. Rev. D \textbf{13} (1976) 1958 \item A.~I.~Amelin et al., ``Energy spectra of charged particles in the reaction of $\pi^-$ absorption at rest by $^{6,7}$Li, $^{9}$Be, $% ^{10,11}$B, $^{12}$C, $^{28}$Si, $^{40}$Ca, $^{59}$Co, $^{93}$Nb, $% ^{114,117,120,124}$Sn, $^{169}$Tm, $^{181}$Ta and $^{209}$Bi nuclei'', Moscow Physics and Engineering Institute Preprint No. 034-90, Moscow, 1990. \item G.~Mechtersheimer et al., Nucl. Phys. \textbf{A324} (1979) 379. \item C.~Cernigoi et al., Nucl. Phys. \textbf{A456} (1986) 599. \item R.~Madey et al., Phys. Rev. C \textbf{25} (1982) 3050. \item D.~Ryckbosch et al., Phys. Rev. C \textbf{42} (1990) 444. \item J.~Ahrens et al., Nucl. Phys. \textbf{A446} (1985) 229c. \item Jan~Ryckebusch et al., Phys. Rev. C \textbf{49} (1994) 2704. \item C.~Van~den~Abeele; private communication cited in the reference: Jan~Ryckebusch et al., Phys. Rev. C \textbf{49} (1994) 2704. \item P.D.~Harty et al. (unpublished); private communication cited in the reference: Jan~Ryckebusch et al., Phys. Rev. C \textbf{49} (1994) 2704. \item L.B.~Weinstein et al., Phys. Rev. Lett. \textbf{64} (1990) 1646. \item J.P.~Jeukenne and C.~Mahaux, Nucl. Phys. A \textbf{394} (1983) 445. \end{enumerate} \end{htmlonly} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %\end{document}