2.3 Atomic Relaxations Excited ions, produced by the interaction of photons and charged particles when they travel through matter, relax to their ground state by migration of the initial vacancy to outer shells

2: Radiation transport in EGSnrc


via the emission of characteristic X-rays and/or Auger or Coster-Kronig electrons (see e.g.
Ref. [39]).


In the current standard version of EGS4, only K-shell relaxations following photo-electric absorption via the emission of K?and K?fluorescence are treated and are intrinsically associated with the PHOTO routine. An extension to include L-shell fluorescence was developed by the KEK group [7] and is available for use with the EGS4 system.


In EGSnrc we have extended the treatment of atomic relaxations to include higher shells
as well as the production of Auger and Coster-Kronig electrons. With these extensions,the treatment within the PHOTO routine has become unpractical. In addition, the relaxation cascade is a separate process, it can be initiated after any photon or electron interaction that has produced an inner shell vacancy. The most general approach for treating excited atoms or ions would have been to define a separate particle type, an excited atom or ion,and to put such particles on the stack whenever they are produced. Such an approach would have been too a large departure from the EGS4 logic and potentially render many user codes unusable. We have therefore abandoned this idea and decided to treat relaxations in a separate routine (relax), which is called whenever an inner shell vacancy is created. In this release of EGSnrc, such vacancies can be created in photo-absorption events (see section2.2.3) and in Compton scattering events (see section 2.2.2). It is anticipated that the next release of the system will include the explicit modelling of inner shell ionizations by electron or positron impact.


The de-excitation cascade is a complex process, there are hundreds of possible transitions for high-Z elements. A complete treatment goes beyond the scope of a general purpose code for the simulation of electron and photon transport such as EGSnrc. In addition, we consider 1 keV to be the lowest limit for the applicability of the code. We have therefore imposed a lower limit of 1 keV on the relaxation process, i.e. only vacancies in shells with binding energies above 1 keV are treated.5 If we then take into account that only elements with Z ?52 have M-shells with binding energies above the limit of 1 keV and that M-shells have binding energies less than 10 keV for all elements (the MI binding energy for lead is 3.8 keV and 7.2 keV for Einsteinium [39]), it is a reasonable approach to model transitions from and transitions to M-shells in an 揳verage?way. There is of course no unique procedure to set the binding energies of the 揳verage?M-shells for the elements, UhMi(Z), to be used in the de-excitation cascade. Assuming that for most applications K to M transitions are more important than L to M or M to a lower shell, we have defined UhMi(Z) to be the weighted average of the binding energies UMj (Z) of the element Z with weights given by the K to Mj transition probabilities 篕Mj ,


UhMi(Z) ?
P
P篕MjUMj
篕Mj
(3.0.6)


For instance, UhMi determined by this procedure using transition probabilities from the Evaluated Atom Data Library (EADL) [39] for lead is 3.1 keV, the MI binding energy is 3.8 keV and the MV binding energy 2.5 keV. A simple averaging with the occupation numbers would result in an average M-shell binding energy of 2.9 keV. If distinguishing between any of the above numbers is important for your application, EGSnrc is most likely not the most


5Another motivation for imposing this limit is the fact that uncertainties on transition probabilities
rapidly increase with decreasing binding energies, they are perhaps 10 or 20% even for L-shells


Last edited 2007/02/08 21:00:46 2.3 Atomic Relaxations
48 NRCC Report PIRS-701


appropriate simulation package for your purposes.


Having said all this, it is apparent that N shells are also treated in an average way. The only elements with 揳verage?N-shell binding energies above 1 keV are those with Z > 95.


In an implementation consistent with the overall logic of the EGS system, the relaxation algorithm should put all particles produced in the course of the de-excitation cascade on the particle stack, they would then be discarded in the PHOTON or ELECTR routines if their energies were below the specified transport threshold energies. It is easy to see that such an approach may become extremely wasteful if the transport threshold energies are large compared to the lower limit of 1 keV for the de-excitation cascade. We have therefore decided to stop the relaxation process for vacancies with binding energies less then Emin,


Emin = Max{1 keV, Min{PCUT, ECUT - m}} (3.0.7)


and to score their energy locally. In addition, the energy of photons or electrons that are below the thresholds are also deposited locally, even if they were produced in transitions from vacancies with binding energies above Emin. The total sub-threshold energy is collected in the variable EDEP, which is in the COMON/EPCONT/, and made known to the user via an
IARG=4 call to the scoring routine.


To facilitate the handling of the relaxation cascade, we define a shell number n for each
of the shells treated. K-shells have n = 1, LI through LIII have n = 2 to 4, hMi corresponds
to n = 5, hNi to n = 6, all other shells have n = 7. A list of possible transitions, Ln, is
associated with each shell,


Ln = {(?, s1), (?, s2), ???, (簁n, skn)} (3.0.8)


where kn is the number of possible transitions for the shell of type n and 篿 the transition
probabilities for a transition into final state si. The final states si are defined as follows:


si =
8<
:
ni , for fluorescent transitions
10 + ni , for Coster-Kronig transitions
100ni,1 + ni,2 , for Auger transitions
(3.0.9)


where ni or ni,1 and ni,2 are the shell numbers of the new vacancies created in fluorescent
and Coster-Kronig or Auger transitions. Table 1 summarizes all transitions handled in the
current version of the relaxation routine.


In addition, we define a 搗acancy stack?which holds all vacancies at a given stage of the
relaxation cascade.


With these definitions in place, the simulation of the relaxations cascade becomes fairly
simple:


1. Put the initial vacancy in the "vacancy stack",set the "vacancy stack"counter m to 1

2. If m = 0, return control to the calling routine

3. Take the top vacancy, to be denoted by ni in the following, from the 搗acancy stack?
reduce m by 1


2: Radiation transport in EGSnrc


Table 1: Relaxation transitions handled by EGSnrc.
initial vacancy ; shell code ; transition ; final state code


4. If Uni < Emin, then EDEP = EDEP + Uni , go to step 2

5. Pick a random number r, set j = 1

6. If r · ºj , go to step 8

7. r = (1 − r)/(1 − ºj), j = j + 1, go to step 6

8. j is the number of the selected transition,


8.1 if sj < 10, then the new vacancy is in shell nj = sj , put it on the “vacancy stac□□e m by one, produce a fluorescent photon with energy E = Uni − Unj . If
E < PCUT, then EDEP = EDEP+E, else, select the photon direction uniformly and
put it on the EGSnrc particle stack


8.2 else if sj < 100, then the new vacancy is in shell nj = sj−10, put it on the “vacancy stack”, increase m by one, produce a Coster-Kronig electron with kinetic energy
E = Uni −Unj . If E < ECUT−m, then EDEP = EDEP + E, else, select the electron
direction uniformly and put it on the EGSnrc particle stack


8.3 else, the two new vacancies are nj,1 = (sj mod 100) and nj,2 = sj − 100 nj,1, put
them on the “vacancy stack”, increase m by two, produce an Auger electron with
a kinetic energy E = Uni −Unj,1 −Unj,2 . If E < ECUT−m, then EDEP = EDEP+E,
else, select the electron direction uniformly and put it on the EGSnrc particle
stack


9. Go to step 2

Finally, we have defined for each of the steps 8.1 to 8.3 new calls to the routine AUSGAB with arguments IARG = 25 to 27. This gives the possibility for the user to take some actions with the relaxation particles, e.g., set their LATCH variable to an appropriate value, or play Russian Roulette with them.