[1208] | 1 | \section{Atomic relaxation}\label{relax} |
---|
| 2 | |
---|
| 3 | The atomic relaxation can be triggered |
---|
| 4 | by other electromagnetic interactions such as the photoelectric effect or |
---|
| 5 | ionisation, which leave the atom in an excited state. |
---|
| 6 | |
---|
| 7 | The Livermore Evaluation Atomic Data Library EADL~\cite{EADL} |
---|
| 8 | contains data to describe the relaxation of atoms back to neutrality after they |
---|
| 9 | are ionised. |
---|
| 10 | %, regardless of what physical process ionised the atom, e.g., |
---|
| 11 | %photoelectric effect, electron ionisation, internal conversion, |
---|
| 12 | %etc~\cite{reda}~\cite{step2}. |
---|
| 13 | |
---|
| 14 | It is assumed that the binding energy of all subshells are the same for neutral |
---|
| 15 | ground state atoms as for ionised atoms~\cite{EADL}. |
---|
| 16 | |
---|
| 17 | The data in EADL includes the radiative and non-radiative transition |
---|
| 18 | probabilities for each sub-shell of each element, for Z=1 to 100. The atom has |
---|
| 19 | been ionised by a process that has caused an electron to be ejected |
---|
| 20 | from an atom, leaving a vacancy or ``hole" in a given subshell. The EADL data |
---|
| 21 | are then used to calculate the complete radiative and non-radiative |
---|
| 22 | spectrum of X-rays and electrons emitted as the atom |
---|
| 23 | relaxes back to neutrality. |
---|
| 24 | |
---|
| 25 | %In a radiative transition, a vacancy in one subshell is filled by |
---|
| 26 | %an electron from an outer subshell with the release of fluorescence, i.e. X-ray |
---|
| 27 | %emission. |
---|
| 28 | |
---|
| 29 | %In a non-radiative transition, the initial vacancy is filled by an electron from |
---|
| 30 | %an outer subshell, and the available energy is given to the removal of |
---|
| 31 | %an electron from the same subshell or one further out. |
---|
| 32 | %This process results in two electron vacancies. |
---|
| 33 | Non-radiative de-excitation can occur via the |
---|
| 34 | Auger effect (the initial and secondary vacancies are in different shells) or |
---|
| 35 | Coster-Kronig effect (transitions within the same shell). |
---|
| 36 | |
---|
| 37 | |
---|
| 38 | \subsection{Fluorescence}\label{fluo} |
---|
| 39 | |
---|
| 40 | The simulation procedure for the fluorescence process is the following: |
---|
| 41 | \begin{enumerate} |
---|
| 42 | \item If the vacancy subshell is not included in the data, |
---|
| 43 | a photon is emitted in a random direction in 4$\pi$ |
---|
| 44 | with an energy equal to the corresponding binding |
---|
| 45 | energy, and the procedure is terminated. |
---|
| 46 | \item If the vacancy subshell is included in the data, |
---|
| 47 | an outer subshell is randomly selected taking into account the relative |
---|
| 48 | transition probabilities for all possible outer subshells. |
---|
| 49 | \item In the case where the energy corresponding to the selected transition |
---|
| 50 | is larger than a user defined cut value (equal |
---|
| 51 | to zero by default), a photon particle is created and |
---|
| 52 | emitted in a random direction in 4$\pi$, |
---|
| 53 | with an energy equal to the transition energy. |
---|
| 54 | \item the procedure is repeated from step 1, for the new vacancy subshell. |
---|
| 55 | \end{enumerate} |
---|
| 56 | |
---|
| 57 | The final local energy deposit is the difference between the |
---|
| 58 | binding energy of the initial vacancy subshell and the sum of |
---|
| 59 | all transition energies which were taken by fluorescence photons. |
---|
| 60 | The atom is assumed to be initially ionised with an electric charge of $+1e$. |
---|
| 61 | |
---|
| 62 | Sub-shell data are provided in the EADL data bank~\cite{EADL} |
---|
| 63 | for Z=1 through 100. |
---|
| 64 | However, transition probabilities are only explicitly |
---|
| 65 | included for Z=6 through 100, from the subshells of the K, L, M, N shells and |
---|
| 66 | some O subshells. |
---|
| 67 | For subshells O,P,Q: transition probabilities are negligible |
---|
| 68 | (of the order of 0.1\%) and |
---|
| 69 | smaller than the precision with which they are known. |
---|
| 70 | Therefore, for the time being, for Z=1 through 5, |
---|
| 71 | only a local energy deposit corresponding to the binding energy B |
---|
| 72 | of an electron in the ionised subshell is simulated. |
---|
| 73 | For subshells of the O, P, and Q shells, a photon is emitted with that energy B. |
---|
| 74 | |
---|
| 75 | |
---|
| 76 | |
---|
| 77 | \subsection{Auger process}\label{auger} |
---|
| 78 | |
---|
| 79 | The Auger effect is complimentary to fluorescence, hence the simulation |
---|
| 80 | process is the same as for the fluorescence, with the exception |
---|
| 81 | that two random shells are selected, one for the transition electron that fills the original |
---|
| 82 | vacancy, and the other for selecting the shell generating the Auger electron. |
---|
| 83 | |
---|
| 84 | Subshell data are provided in the EADL data bank~\cite{EADL} |
---|
| 85 | for $Z=6$ through 100. Since in EADL no data for elements with $Z < 5$ are |
---|
| 86 | provided, Auger effects are only considered for $5 < Z < 100$ and always due |
---|
| 87 | to the EADL data tables, only for those transitions |
---|
| 88 | which have a probabiliy to occur $> 0.1\%$ of the total non-radiative transition probability. |
---|
| 89 | EADL probability data used are, however, normalized to one for Fluorescence + Auger. |
---|
| 90 | |
---|
| 91 | \subsection{Status of the document} |
---|
| 92 | |
---|
| 93 | \noindent |
---|
| 94 | 08.02.2000 created by V\'eronique Lef\'ebure\\ |
---|
| 95 | 08.03.2000 reviewed by Petteri Nieminen and Maria Grazia Pia\\ |
---|
| 96 | 05.06.2002 added Auger Effect description by Alfonso Mantero\\ |
---|
| 97 | |
---|
| 98 | \begin{latexonly} |
---|
| 99 | |
---|
| 100 | \begin{thebibliography}{99} |
---|
| 101 | \bibitem{EADL} |
---|
| 102 | %http://reddog1.llnl.gov/homepage.red/ATOMIC.htm |
---|
| 103 | "Tables and Graphs of Atomic Subshell and Relaxation Data Derived from |
---|
| 104 | the LLNL Evaluated Atomic Data Library (EADL), Z=1-100" |
---|
| 105 | S.T.Perkins, D.E.Cullen, M.H.Chen, J.H.Hubbell, J.Rathkopf, J.Scofield, |
---|
| 106 | UCRL-50400 Vol.30 |
---|
| 107 | \bibitem{reda} |
---|
| 108 | "A simple model of photon transport", |
---|
| 109 | D.E. Cullen, Nucl. Instr. Meth. in Phys. Res. B 101(1995)499-510 |
---|
| 110 | \bibitem{step2} |
---|
| 111 | "A program to determine the radiation spectra due to a single atomic-subshell |
---|
| 112 | ionisation by a particle or due to deexcitation or decay of radionuclides", |
---|
| 113 | J. Stepanek, Comp. Phys. Comm. 106(1997)237-257 |
---|
| 114 | %\bibitem{redb} |
---|
| 115 | % "PROGRAM RELAX, A Code Designed to Calculate Atomic Relaxation Spectra of |
---|
| 116 | % X-rays and Electrons", |
---|
| 117 | % D.E.Cullen, UCRL-ID-110438, March 1992 |
---|
| 118 | \end{thebibliography} |
---|
| 119 | |
---|
| 120 | \end{latexonly} |
---|
| 121 | |
---|
| 122 | \begin{htmlonly} |
---|
| 123 | |
---|
| 124 | \subsection{Bibliography} |
---|
| 125 | |
---|
| 126 | \begin{enumerate} |
---|
| 127 | \item |
---|
| 128 | %http://reddog1.llnl.gov/homepage.red/ATOMIC.htm |
---|
| 129 | "Tables and Graphs of Atomic Subshell and Relaxation Data Derived from |
---|
| 130 | the LLNL Evaluated Atomic Data Library (EADL), Z=1-100" |
---|
| 131 | S.T.Perkins, D.E.Cullen, M.H.Chen, J.H.Hubbell, J.Rathkopf, J.Scofield, |
---|
| 132 | UCRL-50400 Vol.30 |
---|
| 133 | \item |
---|
| 134 | "A simple model of photon transport", |
---|
| 135 | D.E. Cullen, Nucl. Instr. Meth. in Phys. Res. B 101(1995)499-510 |
---|
| 136 | \item |
---|
| 137 | "A program to determine the radiation spectra due to a single atomic-subshell |
---|
| 138 | ionisation by a particle or due to deexcitation or decay of radionuclides", |
---|
| 139 | J. Stepanek, Comp. Phys. Comm. 106(1997)237-257 |
---|
| 140 | %\bibitem{redb} |
---|
| 141 | % "PROGRAM RELAX, A Code Designed to Calculate Atomic Relaxation Spectra of |
---|
| 142 | % X-rays and Electrons", |
---|
| 143 | % D.E.Cullen, UCRL-ID-110438, March 1992 |
---|
| 144 | \end{enumerate} |
---|
| 145 | |
---|
| 146 | \end{htmlonly} |
---|
| 147 | |
---|