\section{Atomic relaxation}\label{relax}

The atomic relaxation can be triggered
by other electromagnetic interactions such as the photoelectric effect or
ionisation, which leave the atom in an excited state.

The Livermore Evaluation Atomic Data Library EADL~\cite{EADL}
contains data to describe the relaxation of atoms back to neutrality after they
are ionised.
%, regardless of what physical process ionised the atom, e.g.,
%photoelectric effect, electron ionisation, internal conversion,
%etc~\cite{reda}~\cite{step2}.

It is assumed that the binding energy of all subshells are the same for neutral
ground state atoms as for ionised atoms~\cite{EADL}.

The data in EADL includes the radiative and non-radiative transition
probabilities for each sub-shell of each element, for Z=1 to 100. The atom has
been ionised by a process that has caused an electron to be ejected
from an atom, leaving a vacancy or ``hole" in a given subshell.  The EADL data 
are then used to calculate the complete radiative and non-radiative
spectrum of X-rays and electrons emitted as the atom
relaxes back to neutrality. 

%In a radiative transition, a vacancy in one subshell is filled by
%an electron from an outer subshell with the release of fluorescence, i.e. X-ray
%emission.

%In a non-radiative transition, the initial vacancy is filled by an electron from
%an outer subshell, and the available energy is given to the removal of 
%an electron from the same subshell or one further out.
%This process results in two electron vacancies. 
Non-radiative de-excitation can occur via the 
Auger effect (the initial and secondary vacancies are in different shells) or
Coster-Kronig effect (transitions within the same shell).


\subsection{Fluorescence}\label{fluo}

The simulation procedure for the fluorescence process is the following:
\begin{enumerate}
\item If the vacancy subshell is not included in the data, 
      a photon is emitted in a random direction in 4$\pi$
      with an energy equal to the corresponding binding
      energy, and the procedure is terminated.
\item If the vacancy subshell is included in the data, 
      an outer subshell is randomly selected taking into account the relative
      transition probabilities for all possible outer subshells. 
\item In the case where the energy corresponding to the selected transition
      is larger than a user defined cut value (equal
      to zero by default), a photon particle is created and 
      emitted in a random direction in 4$\pi$,
      with an energy equal to the transition energy.
\item the procedure is repeated from step 1, for the new vacancy subshell.
\end{enumerate}
                   
The final local energy deposit is the difference between the
binding energy of the initial vacancy subshell and the sum of 
all transition energies which were taken by fluorescence photons. 
The atom is assumed to be initially ionised with an electric charge of $+1e$.

Sub-shell data are provided in the EADL data bank~\cite{EADL} 
for Z=1 through 100.
However, transition probabilities are only explicitly
included for Z=6 through 100, from the subshells of the K, L, M, N shells and
some O subshells.
For subshells O,P,Q: transition probabilities are negligible 
(of the order of 0.1\%) and
smaller than the precision with which they are known.
Therefore, for the time being, for Z=1 through 5, 
only a local energy deposit corresponding to the binding energy B
of an electron in the ionised subshell is simulated. 
For subshells of the O, P, and Q shells, a photon is emitted with that energy B.



\subsection{Auger process}\label{auger}

The Auger effect is complimentary to fluorescence, hence the simulation 
process is the same as for the fluorescence, with the exception 
that two random shells are selected, one for the transition electron that fills the original
vacancy, and the other for selecting the shell generating the Auger electron.

Subshell data are provided in the EADL data bank~\cite{EADL} 
for $Z=6$ through 100. Since in EADL no data for elements with $Z < 5$ are
provided, Auger effects are only considered for $5 < Z < 100$ and always due 
to the EADL data tables, only for those transitions
which have a probabiliy to occur $> 0.1\%$ of the total non-radiative transition probability. 
EADL probability data used are, however, normalized to one for Fluorescence + Auger.  

\subsection{Status of the document}

\noindent
08.02.2000 created by V\'eronique Lef\'ebure\\
08.03.2000 reviewed by Petteri Nieminen and Maria Grazia Pia\\
05.06.2002 added Auger Effect description by Alfonso Mantero\\ 

\begin{latexonly}

\begin{thebibliography}{99}
\bibitem{EADL} 
  %http://reddog1.llnl.gov/homepage.red/ATOMIC.htm
  "Tables and Graphs of Atomic Subshell and Relaxation Data Derived from
  the LLNL Evaluated Atomic Data Library (EADL), Z=1-100"
  S.T.Perkins, D.E.Cullen, M.H.Chen, J.H.Hubbell, J.Rathkopf, J.Scofield,
  UCRL-50400 Vol.30
\bibitem{reda}
  "A simple model of photon transport", 
  D.E. Cullen, Nucl. Instr. Meth. in Phys. Res. B 101(1995)499-510 
\bibitem{step2} 
  "A program to determine the radiation spectra due to a single atomic-subshell
  ionisation by a particle or due to deexcitation or decay of radionuclides",
  J. Stepanek, Comp. Phys. Comm. 106(1997)237-257 
%\bibitem{redb}
%  "PROGRAM RELAX, A Code Designed to Calculate Atomic Relaxation Spectra of
%  X-rays and Electrons",
%  D.E.Cullen, UCRL-ID-110438, March 1992  
\end{thebibliography}

\end{latexonly}

\begin{htmlonly}

\subsection{Bibliography}

\begin{enumerate}
\item
  %http://reddog1.llnl.gov/homepage.red/ATOMIC.htm
  "Tables and Graphs of Atomic Subshell and Relaxation Data Derived from
  the LLNL Evaluated Atomic Data Library (EADL), Z=1-100"
  S.T.Perkins, D.E.Cullen, M.H.Chen, J.H.Hubbell, J.Rathkopf, J.Scofield,
  UCRL-50400 Vol.30
\item
  "A simple model of photon transport", 
  D.E. Cullen, Nucl. Instr. Meth. in Phys. Res. B 101(1995)499-510 
\item 
  "A program to determine the radiation spectra due to a single atomic-subshell
  ionisation by a particle or due to deexcitation or decay of radionuclides",
  J. Stepanek, Comp. Phys. Comm. 106(1997)237-257 
%\bibitem{redb}
%  "PROGRAM RELAX, A Code Designed to Calculate Atomic Relaxation Spectra of
%  X-rays and Electrons",
%  D.E.Cullen, UCRL-ID-110438, March 1992  
\end{enumerate}

\end{htmlonly}