1 | \section{Introduction} |
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2 | |
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3 | Additional electromagnetic physics processes for photons, electrons, hadrons |
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4 | and ions have been implemented in Geant4 in order to extend the validity |
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5 | range of particle interactions to lower energies than those available in the |
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6 | standard Geant4 electromagnetic processes~\cite{ov-leg4,ov-had,ov-ion}. |
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7 | Because atomic shell structure is more important in most cases at low energies |
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8 | than it is at higher energies, the low energy processes make direct use of |
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9 | shell cross section data. The standard processes, which are optimized for |
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10 | high energy physics applications, rely on parameterizations of these data. |
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11 | |
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12 | The low energy processes include the photo-electric effect, Compton scattering, |
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13 | Rayleigh scattering, gamma conversion, bremsstrahlung and ionization. |
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14 | Fluorescence of excited atoms is also considered. |
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15 | |
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16 | Some features common to all low energy processes currently implemented in |
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17 | Geant4 are summarized in this section. Subsequent sections provide more |
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18 | detailed information for each process. |
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19 | |
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20 | \subsection{Physics} |
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21 | |
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22 | The low energy processes of Geant4 represent electromagnetic interactions |
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23 | at lower energies than those covered by the equivalent Geant4 standard |
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24 | electromagnetic processes. |
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25 | |
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26 | The current implementation of low energy processes is valid for energies |
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27 | down to 250 eV (and can be used up to approximately 100 GeV), unless |
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28 | differently specified. It covers elements with atomic number between 1 and |
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29 | 99. |
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30 | |
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31 | All processes involve two distinct phases: |
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32 | \begin{itemize} |
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33 | \item the calculation and use of total cross sections, and |
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34 | \item the generation of the final state. |
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35 | \end{itemize} |
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36 | Both phases are based on the theoretical models and on |
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37 | exploitation of evaluated data. |
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38 | |
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39 | \subsection{Data Sources} |
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40 | |
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41 | The data used for the determination of cross-sections and |
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42 | for sampling of the final state are extracted |
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43 | from a set of publicly distributed evaluated data |
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44 | libraries: |
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45 | \begin{itemize} |
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46 | \item |
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47 | EPDL97 (Evaluated Photons Data Library)~\cite{ov-EPDL97}; |
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48 | \item |
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49 | EEDL (Evaluated Electrons Data Library)~\cite{ov-EEDL}; |
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50 | \item |
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51 | EADL (Evaluated Atomic Data Library)~\cite{ov-EADL}; |
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52 | \item |
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53 | stopping power data~\cite{ov-Ziegler771,ov-Ziegler774,ov-Ziegler85,ov-ICRU49}; |
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54 | \item |
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55 | binding energy values based on data of Scofield~\cite{ov-bindingEnergies}. |
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56 | \end{itemize} |
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57 | |
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58 | Evaluated data sets are produced through the process of critical comparison, |
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59 | selection, renormalization and averaging of the available experimental data, |
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60 | normally complemented by model calculations. |
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61 | %Evaluated Libraries are computer files of evaluated data which, appropriately |
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62 | %processed, form the input data to computations for a wide variety of nuclear |
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63 | %science and technology applications. Each of these evaluated libraries |
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64 | %may consist of individual evaluated data sets for several hundred isotopes |
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65 | %or elements (commonly referred to as 'materials')~\cite{ov-NEA}. |
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66 | These libraries provide the following data relevant for the simulation of |
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67 | Geant4 low energy processes: |
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68 | |
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69 | \begin{itemize} |
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70 | |
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71 | \item |
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72 | total cross-sections for photoelectric effect, Compton scattering, |
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73 | Rayleigh scattering, pair production and bremsstrahlung, |
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74 | \item |
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75 | subshell integrated cross sections for photo-electric effect and ionization, |
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76 | \item |
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77 | energy spectra of the secondaries for electron processes, |
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78 | \item |
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79 | scattering functions for the Compton effect, |
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80 | \item |
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81 | form factors for Rayleigh scattering, |
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82 | \item |
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83 | binding energies for electrons for all subshells, |
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84 | \item |
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85 | transition probabilities between subshells for fluorescence and the Auger |
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86 | effect, and |
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87 | \item |
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88 | stopping power tables. |
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89 | \end{itemize} |
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90 | |
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91 | The energy range covered by the data libraries extends from 100 GeV |
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92 | down to 1 eV for Rayleigh and Compton effects, down to the lowest binding |
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93 | energy for each element for photo-electric effect and ionization, and |
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94 | down to 10 eV for bremsstrahlung. |
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95 | |
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96 | %\subsubsection{Data validity and accuracy} |
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97 | %For a rough estimate of the accuracy of EPDL97 data libraries in different |
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98 | %energy regimes, see \cite{ov-data-est}. |
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99 | %The data are only applicable to cold, neutral, |
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100 | %ground-state and isolated atoms, |
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101 | %i.e. solid-state effects, plasmas, |
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102 | %external electric or magnetic fields are not taken into |
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103 | %account although they could have significant |
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104 | %effects on the cross-sections near photoeffect |
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105 | %thresholds of inner-shell electrons, |
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106 | %and completely alter the cross-sections near the |
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107 | %thresholds of outer-shells~\cite{ov-EPDL97}. |
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108 | |
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109 | %The precision of the binding energies is estimated |
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110 | %to be better than 1\%~\cite{ov-EPDL97} |
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111 | %which is small compared to the differences expected due |
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112 | %to elements combining into radicals or |
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113 | %compounds. |
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114 | %For example, the K shell binding energy of |
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115 | %H is 13.6 eV, and that of H2 is 16.4 eV, |
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116 | %about 21\% higher. This will effect accuracy |
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117 | %over narrow energy ranges near photoionisation |
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118 | %edges. |
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119 | |
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120 | %Precision estimates on the data can be |
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121 | %found in~\cite{ov-EPDL97},~\cite{ov-EEDL} and~\cite{ov-EADL}. |
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122 | |
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123 | \subsection{Distribution of the Data Sets} |
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124 | |
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125 | The author of EPDL97~\cite{ov-EPDL97}, who is also responsible for the |
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126 | EEDL~\cite{ov-EEDL} and EADL~\cite{ov-EADL} data libraries, Dr. Red Cullen, |
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127 | has kindly permitted the libraries and their related documentation to be |
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128 | distributed with the Geant4 toolkit. The data are reformatted for Geant4 |
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129 | input. They can be downloaded from the source code section of the Geant4 |
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130 | page: http://cern.ch/geant4/geant4.html. |
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131 | |
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132 | The EADL, EEDL and EPDL97 data-sets are also available from several |
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133 | public distribution centres in a format different |
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134 | from the one used by Geant4~\cite{ov-NEA}. |
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135 | |
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136 | Stopping power data are taken from |
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137 | publications~\cite{ov-Ziegler771,ov-Ziegler774,ov-Ziegler85,ov-ICRU49}. |
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138 | |
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139 | \subsection{Calculation of Total Cross Sections}\label{subsubsigmatot} |
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140 | |
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141 | The energy dependence of the total cross section is derived for each |
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142 | process from the evaluated data libraries. Since the libraries provide |
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143 | cross sections for a set of discrete incident energies, the total cross |
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144 | section at a given energy, $E$, is obtained by interpolation according to |
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145 | the formula~\cite{ov-stepanek}: |
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146 | \begin{equation} |
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147 | \label{eqloglog} |
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148 | \log(\sigma(E)) = {log(\sigma_1)log(E_2/E) + log(\sigma_2)log(E/E_1) |
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149 | \over log(E_2/E_1)} |
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150 | \end{equation} |
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151 | where $E_1$ and $E_2$ are respectively the closest lower and higher energy |
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152 | for which data ($\sigma_1$ and $\sigma_2$) are available. |
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153 | |
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154 | For each process a production threshold energy is defined; by default it |
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155 | is set to the low end of the energy validity range of the process (250~eV |
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156 | in the current implementation), but a higher or lower value can be set by |
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157 | the user. |
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158 | |
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159 | For a particle of energy $E$, the mean free path for interacting via a |
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160 | given process is calculated as: |
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161 | \begin{equation} |
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162 | \lambda = {1\over{\Sigma_i\\ \sigma_{i}(E)\cdot n_i}} |
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163 | \end{equation} |
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164 | where $\sigma_{i}(E)$ is the microscopic |
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165 | integrated cross-section of the process considered at energy $E$, and $n_i$ |
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166 | is the atomic density of the $i-th$ element contributing to the material |
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167 | composition. The sum runs over all the elements of which the material is |
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168 | composed. The cross sections are determined as described in this section. |
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169 | An exception to this method is the implementation of the chemical effect on |
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170 | hadron/ion stopping powers for a set of materials. |
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171 | |
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172 | |
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173 | \subsection{Sampling of Relevant Physics Quantities} |
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174 | |
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175 | The final state products of the processes are generated by sampling |
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176 | relevant physical quantities, such as energies and angular distributions |
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177 | of secondaries, from distributions derived from theoretical models and |
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178 | evaluated data. The energy dependence of the parameters which characterize |
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179 | the distributions is taken into account either by direct interpolation of |
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180 | the data available in the libraries, or by interpolation of values obtained |
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181 | from fits to the data. |
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182 | |
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183 | When generating the final state, an atom of the material in which the |
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184 | interaction occurs is randomly selected and atomic de-excitation is |
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185 | simulated. |
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186 | |
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187 | Secondaries which would be produced with energies below their user defined |
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188 | production threshold are not created and their energy is deposited locally. |
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189 | |
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190 | |
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191 | \subsection{Status of the document} |
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192 | |
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193 | \noindent |
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194 | 30.09.1999 created by Alessandra Forti\\ |
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195 | 07.02.2000 modified by V\'eronique Lef\'ebure\\ |
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196 | 08.03.2000 reviewed by Petteri Nieminen and Maria Grazia Pia\\ |
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197 | 04.12.2001 reviewed by Vladimir Ivanchenko\\ |
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198 | 26.01.2003 minor re-write by D.H. Wright . |
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199 | |
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200 | |
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201 | \begin{latexonly} |
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202 | |
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203 | \begin{thebibliography}{99} |
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204 | \bibitem{ov-leg4} |
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205 | ``Geant4 Low Energy Electromagnetic Models for Electrons and Photons", |
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206 | J.Apostolakis et al., CERN-OPEN-99-034(1999), INFN/AE-99/18(1999) |
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207 | \bibitem{ov-had} |
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208 | V.N.~Ivanchenko et al., GEANT4 Simulation of |
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209 | Energy Losses of Slow Hadrons, CERN-99-121, INFN/AE-99/20, (September 1999). |
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210 | \bibitem{ov-ion} |
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211 | S.~Giani et al., GEANT4 Simulation of |
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212 | Energy Losses of Ions, CERN-99-300, INFN/AE-99/21, (November 1999). |
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213 | \bibitem{ov-EPDL97} |
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214 | %http://reddog1.llnl.gov/homepage.red/photon.htm |
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215 | ``EPDL97: the Evaluated Photon Data Library, '97 version", |
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216 | D.Cullen, J.H.Hubbell, L.Kissel, |
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217 | UCRL--50400, Vol.6, Rev.5 |
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218 | \bibitem{ov-EEDL} |
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219 | %http://reddog1.llnl.gov/homepage.red/Electron.htm |
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220 | ``Tables and Graphs of Electron-Interaction Cross-Sections from 10~eV to 100~GeV Derived from |
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221 | the LLNL Evaluated Electron Data Library (EEDL), Z=1-100" |
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222 | S.T.Perkins, D.E.Cullen, S.M.Seltzer, |
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223 | UCRL-50400 Vol.31 |
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224 | \bibitem{ov-EADL} |
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225 | %http://reddog1.llnl.gov/homepage.red/ATOMIC.htm |
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226 | ``Tables and Graphs of Atomic Subshell and Relaxation Data Derived from |
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227 | the LLNL Evaluated Atomic Data Library (EADL), Z=1-100" |
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228 | S.T.Perkins, D.E.Cullen, M.H.Chen, J.H.Hubbell, J.Rathkopf, J.Scofield, |
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229 | UCRL-50400 Vol.30 |
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230 | \bibitem{ov-Ziegler771} |
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231 | H.H.~Andersen and J.F.~Ziegler, |
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232 | The Stopping |
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233 | and Ranges of Ions in Matter. Vol.3, Pergamon Press, 1977. |
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234 | \bibitem{ov-Ziegler774} |
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235 | J.F.~Ziegler, The Stopping |
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236 | and Ranges of Ions in Matter. Vol.4, Pergamon Press, 1977. |
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237 | \bibitem{ov-Ziegler85} |
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238 | J.F.~Ziegler, J.P.~Biersack, |
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239 | U.~Littmark, The Stopping |
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240 | and Ranges of Ions in Solids. Vol.1, Pergamon Press, 1985. |
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241 | \bibitem{ov-ICRU49} |
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242 | ICRU (A.~Allisy et al), |
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243 | Stopping Powers and Ranges for Protons and Alpha |
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244 | Particles, |
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245 | ICRU Report 49, 1993. |
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246 | \bibitem{ov-bindingEnergies} |
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247 | J.H. Scofield, ``Radiative Transitions", in ``Atomic Inner-Shell Processes", |
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248 | B.Crasemann ed. (Academic Press, New York, 1975),pp.265-292. |
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249 | %\bibitem{ov-data-est} |
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250 | % http://reddog1.llnl.gov/homepage.red/DOCUMENT/EPDL97/epdl97.htm |
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251 | \bibitem{ov-NEA} |
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252 | http://www.nea.fr/html/dbdata/nds\_evaluated.htm |
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253 | \bibitem{ov-stepanek} |
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254 | ``New Photon, Positron and Electron Interaction Data |
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255 | for Geant in Energy Range |
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256 | from 1 eV to 10 TeV", |
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257 | J. Stepanek, Draft to be submitted for publication |
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258 | |
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259 | \end{thebibliography} |
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260 | |
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261 | \end{latexonly} |
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262 | |
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263 | \begin{htmlonly} |
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264 | |
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265 | \subsection{Bibliography} |
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266 | |
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267 | \begin{enumerate} |
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268 | \item |
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269 | ``Geant4 Low Energy Electromagnetic Models for Electrons and Photons", |
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270 | J.Apostolakis et al., CERN-OPEN-99-034(1999), INFN/AE-99/18(1999) |
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271 | \item |
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272 | V.N.~Ivanchenko et al., GEANT4 Simulation of |
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273 | Energy Losses of Slow Hadrons, CERN-99-121, INFN/AE-99/20, (September 1999). |
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274 | \item |
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275 | S.~Giani et al., GEANT4 Simulation of |
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276 | Energy Losses of Ions, CERN-99-300, INFN/AE-99/21, (November 1999). |
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277 | \item |
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278 | %http://reddog1.llnl.gov/homepage.red/photon.htm |
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279 | ``EPDL97: the Evaluated Photon Data Library, '97 version", |
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280 | D.Cullen, J.H.Hubbell, L.Kissel, |
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281 | UCRL--50400, Vol.6, Rev.5 |
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282 | \item |
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283 | %http://reddog1.llnl.gov/homepage.red/Electron.htm |
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284 | ``Tables and Graphs of Electron-Interaction Cross-Sections from 10~eV to 100~GeV Derived from |
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285 | the LLNL Evaluated Electron Data Library (EEDL), Z=1-100" |
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286 | S.T.Perkins, D.E.Cullen, S.M.Seltzer, |
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287 | UCRL-50400 Vol.31 |
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288 | \item |
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289 | %http://reddog1.llnl.gov/homepage.red/ATOMIC.htm |
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290 | ``Tables and Graphs of Atomic Subshell and Relaxation Data Derived from |
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291 | the LLNL Evaluated Atomic Data Library (EADL), Z=1-100" |
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292 | S.T.Perkins, D.E.Cullen, M.H.Chen, J.H.Hubbell, J.Rathkopf, J.Scofield, |
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293 | UCRL-50400 Vol.30 |
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294 | \item |
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295 | H.H.~Andersen and J.F.~Ziegler, |
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296 | The Stopping |
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297 | and Ranges of Ions in Matter. Vol.3, Pergamon Press, 1977. |
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298 | \item |
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299 | J.F.~Ziegler, The Stopping |
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300 | and Ranges of Ions in Matter. Vol.4, Pergamon Press, 1977. |
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301 | \item |
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302 | J.F.~Ziegler, J.P.~Biersack, |
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303 | U.~Littmark, The Stopping |
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304 | and Ranges of Ions in Solids. Vol.1, Pergamon Press, 1985. |
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305 | \item |
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306 | ICRU (A.~Allisy et al), |
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307 | Stopping Powers and Ranges for Protons and Alpha |
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308 | Particles, |
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309 | ICRU Report 49, 1993. |
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310 | \item |
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311 | J.H. Scofield, ``Radiative Transitions", in ``Atomic Inner-Shell Processes", |
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312 | B.Crasemann ed. (Academic Press, New York, 1975),pp.265-292. |
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313 | %\bibitem{ov-data-est} |
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314 | % http://reddog1.llnl.gov/homepage.red/DOCUMENT/EPDL97/epdl97.htm |
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315 | \item |
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316 | http://www.nea.fr/html/dbdata/nds\_evaluated.htm |
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317 | \item |
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318 | ``New Photon, Positron and Electron Interaction Data |
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319 | for Geant in Energy Range |
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320 | from 1 eV to 10 TeV", |
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321 | J. Stepanek, Draft to be submitted for publication |
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322 | \end{enumerate} |
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323 | |
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324 | \end{htmlonly} |
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325 | |
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