1 | \section{Ionisation} |
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2 | \label{secioni} |
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3 | |
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4 | The total cross section at a given incident kinetic energy T is calculated by |
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5 | summing the partial cross sections at such energy for all the subshells of an |
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6 | element. The partial subshell cross sections at incident energy T are obtained |
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7 | from an interpolation of the evaluated cross section data in the EEDL library, |
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8 | according to the formula \ref{eqloglog}. |
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9 | |
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10 | The subshell from which the electron is emitted is randomly selected according |
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11 | to the cross sections of the subshells, determined at the energy T by |
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12 | interpolating the evaluated cross section data from the EEDL data library. |
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13 | |
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14 | The probability of emission of an electron ($\delta$ ray) with kinetic energy |
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15 | $t$ from a subshell of binding energy $B_i$ as the result of the interaction of |
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16 | an incoming electron of kinetic energy $T$ is described by: |
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17 | \begin{equation} |
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18 | \label{eqionihigh} |
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19 | Prob(T, t, B_i) = {\sum^7}_{j=2}{a_j(T)\over(t+b_i)^j} |
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20 | \end{equation} |
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21 | for $t < t_0$ and |
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22 | \begin{equation} |
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23 | \label{eqionilow} |
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24 | Prob(T, t, B_i) = {c(T)\over t^2} |
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25 | \end{equation} |
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26 | for $t > t_0$, where $t_0$ is a parameter. |
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27 | Both formulas result from empirical fits to the EEDL data and |
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28 | are normalized to 1. |
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29 | The $a$, $b$ and $c$ coefficients are |
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30 | determined by fitting the data; their energy dependence is evaluated from a |
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31 | semilogarithmic interpolation of the fitted data. |
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32 | |
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33 | The sampling of the final state proceeds |
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34 | through two steps: first the range of the energy ($t < t_0$ or $t > t_0$) is |
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35 | determined by a random number extraction, taking into account the relative area |
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36 | determined by the two functions \ref{eqionihigh} and \ref{eqionilow}, then the |
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37 | energy of the $\delta$ ray is generated according to the corresponding |
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38 | probability distribution. |
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39 | |
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40 | The angle of emission of the scattered electron and of the $\delta$ ray |
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41 | is determined by energy-momentum conservation. |
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42 | |
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43 | The interaction leaves the atom in an excited state, with excitation energy |
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44 | equal to the binding energy of the subshell from which the electron has been |
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45 | emitted. The deexcitation of the atom proceeds via the emission of fluorescence |
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46 | photons, as described in section \ref{secphoto}. |
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47 | |
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48 | \section{Status of the document} |
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49 | 30.9.99 created by Alessandra Forti |
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50 | |
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51 | |
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