[1208] | 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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