1 | \section{Atomic relaxation}\label{relax} |
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2 | |
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3 | The atomic relaxation can be triggered |
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4 | by other electromagnetic interactions such as the photoelectric effect or |
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5 | ionisation, which leave the atom in an excited state. |
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6 | |
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7 | The Livermore Evaluation Atomic Data Library EADL~\cite{EADL} |
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8 | contains data to describe the relaxation of atoms back to neutrality after they |
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9 | are ionised. |
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10 | %, regardless of what physical process ionised the atom, e.g., |
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11 | %photoelectric effect, electron ionisation, internal conversion, |
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12 | %etc~\cite{reda}~\cite{step2}. |
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13 | |
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14 | It is assumed that the binding energy of all subshells are the same for neutral |
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15 | ground state atoms as for ionised atoms~\cite{EADL}. |
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16 | |
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17 | The data in EADL includes the radiative and non-radiative transition |
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18 | probabilities for each sub-shell of each element, for Z=1 to 100. The atom has |
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19 | been ionised by a process that has caused an electron to be ejected |
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20 | from an atom, leaving a vacancy or ``hole" in a given subshell. The EADL data |
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21 | are then used to calculate the complete radiative and non-radiative |
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22 | spectrum of X-rays and electrons emitted as the atom |
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23 | relaxes back to neutrality. |
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24 | |
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25 | %In a radiative transition, a vacancy in one subshell is filled by |
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26 | %an electron from an outer subshell with the release of fluorescence, i.e. X-ray |
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27 | %emission. |
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28 | |
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29 | %In a non-radiative transition, the initial vacancy is filled by an electron from |
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30 | %an outer subshell, and the available energy is given to the removal of |
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31 | %an electron from the same subshell or one further out. |
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32 | %This process results in two electron vacancies. |
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33 | Non-radiative de-excitation can occur via the |
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34 | Auger effect (the initial and secondary vacancies are in different shells) or |
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35 | Coster-Kronig effect (transitions within the same shell). |
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36 | |
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37 | |
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38 | \subsection{Fluorescence}\label{fluo} |
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39 | |
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40 | The simulation procedure for the fluorescence process is the following: |
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41 | \begin{enumerate} |
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42 | \item If the vacancy subshell is not included in the data, |
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43 | a photon is emitted in a random direction in 4$\pi$ |
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44 | with an energy equal to the corresponding binding |
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45 | energy, and the procedure is terminated. |
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46 | \item If the vacancy subshell is included in the data, |
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47 | an outer subshell is randomly selected taking into account the relative |
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48 | transition probabilities for all possible outer subshells. |
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49 | \item In the case where the energy corresponding to the selected transition |
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50 | is larger than a user defined cut value (equal |
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51 | to zero by default), a photon particle is created and |
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52 | emitted in a random direction in 4$\pi$, |
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53 | with an energy equal to the transition energy. |
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54 | \item the procedure is repeated from step 1, for the new vacancy subshell. |
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55 | \end{enumerate} |
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56 | |
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57 | The final local energy deposit is the difference between the |
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58 | binding energy of the initial vacancy subshell and the sum of |
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59 | all transition energies which were taken by fluorescence photons. |
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60 | The atom is assumed to be initially ionised with an electric charge of $+1e$. |
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61 | |
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62 | Sub-shell data are provided in the EADL data bank~\cite{EADL} |
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63 | for Z=1 through 100. |
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64 | However, transition probabilities are only explicitly |
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65 | included for Z=6 through 100, from the subshells of the K, L, M, N shells and |
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66 | some O subshells. |
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67 | For subshells O,P,Q: transition probabilities are negligible |
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68 | (of the order of 0.1\%) and |
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69 | smaller than the precision with which they are known. |
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70 | Therefore, for the time being, for Z=1 through 5, |
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71 | only a local energy deposit corresponding to the binding energy B |
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72 | of an electron in the ionised subshell is simulated. |
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73 | For subshells of the O, P, and Q shells, a photon is emitted with that energy B. |
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74 | |
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75 | |
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76 | |
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77 | \subsection{Auger process}\label{auger} |
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78 | |
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79 | The Auger effect is complimentary to fluorescence, hence the simulation |
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80 | process is the same as for the fluorescence, with the exception |
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81 | that two random shells are selected, one for the transition electron that fills the original |
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82 | vacancy, and the other for selecting the shell generating the Auger electron. |
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83 | |
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84 | Subshell data are provided in the EADL data bank~\cite{EADL} |
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85 | for $Z=6$ through 100. Since in EADL no data for elements with $Z < 5$ are |
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86 | provided, Auger effects are only considered for $5 < Z < 100$ and always due |
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87 | to the EADL data tables, only for those transitions |
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88 | which have a probabiliy to occur $> 0.1\%$ of the total non-radiative transition probability. |
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89 | EADL probability data used are, however, normalized to one for Fluorescence + Auger. |
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90 | |
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91 | \subsection{Status of the document} |
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92 | |
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93 | \noindent |
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94 | 08.02.2000 created by V\'eronique Lef\'ebure\\ |
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95 | 08.03.2000 reviewed by Petteri Nieminen and Maria Grazia Pia\\ |
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96 | 05.06.2002 added Auger Effect description by Alfonso Mantero\\ |
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97 | |
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98 | \begin{latexonly} |
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99 | |
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100 | \begin{thebibliography}{99} |
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101 | \bibitem{EADL} |
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102 | %http://reddog1.llnl.gov/homepage.red/ATOMIC.htm |
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103 | "Tables and Graphs of Atomic Subshell and Relaxation Data Derived from |
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104 | the LLNL Evaluated Atomic Data Library (EADL), Z=1-100" |
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105 | S.T.Perkins, D.E.Cullen, M.H.Chen, J.H.Hubbell, J.Rathkopf, J.Scofield, |
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106 | UCRL-50400 Vol.30 |
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107 | \bibitem{reda} |
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108 | "A simple model of photon transport", |
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109 | D.E. Cullen, Nucl. Instr. Meth. in Phys. Res. B 101(1995)499-510 |
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110 | \bibitem{step2} |
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111 | "A program to determine the radiation spectra due to a single atomic-subshell |
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112 | ionisation by a particle or due to deexcitation or decay of radionuclides", |
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113 | J. Stepanek, Comp. Phys. Comm. 106(1997)237-257 |
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114 | %\bibitem{redb} |
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115 | % "PROGRAM RELAX, A Code Designed to Calculate Atomic Relaxation Spectra of |
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116 | % X-rays and Electrons", |
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117 | % D.E.Cullen, UCRL-ID-110438, March 1992 |
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118 | \end{thebibliography} |
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119 | |
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120 | \end{latexonly} |
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121 | |
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122 | \begin{htmlonly} |
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123 | |
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124 | \subsection{Bibliography} |
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125 | |
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126 | \begin{enumerate} |
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127 | \item |
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128 | %http://reddog1.llnl.gov/homepage.red/ATOMIC.htm |
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129 | "Tables and Graphs of Atomic Subshell and Relaxation Data Derived from |
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130 | the LLNL Evaluated Atomic Data Library (EADL), Z=1-100" |
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131 | S.T.Perkins, D.E.Cullen, M.H.Chen, J.H.Hubbell, J.Rathkopf, J.Scofield, |
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132 | UCRL-50400 Vol.30 |
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133 | \item |
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134 | "A simple model of photon transport", |
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135 | D.E. Cullen, Nucl. Instr. Meth. in Phys. Res. B 101(1995)499-510 |
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136 | \item |
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137 | "A program to determine the radiation spectra due to a single atomic-subshell |
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138 | ionisation by a particle or due to deexcitation or decay of radionuclides", |
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139 | J. Stepanek, Comp. Phys. Comm. 106(1997)237-257 |
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140 | %\bibitem{redb} |
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141 | % "PROGRAM RELAX, A Code Designed to Calculate Atomic Relaxation Spectra of |
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142 | % X-rays and Electrons", |
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143 | % D.E.Cullen, UCRL-ID-110438, March 1992 |
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144 | \end{enumerate} |
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145 | |
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146 | \end{htmlonly} |
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147 | |
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