CERN Program Library Long Writeup W5013 - CERNLIB ...

2 Method
If the energy of the radiation incident on an atom is E γ , then the quanta can be absorbed if E γ >E shell .
The photoelectron is emitted with total energy:
E photoelectron = E γ − E shell + m e . (1)
In the above equation it is assumed that the atom has infinite mass. One should note that there exists a
correction term (see [20] and references therein) which becomes more and more important with increasing
E γ [21] [22] [23].
2.1 Probability of Interaction with an Atom
Probability of the interaction with an atom is calculated taking into account partial cross-sections of atoms
of a mixture or a compound.
2.2 Probability of Interaction with a Shell
To calculate the probability of the interaction with a particular shell we use the jump ratios defined as:
J shell = σ(E shell + δE)
σ(E shell − δE)
(2)
where δE → 0. In addition we assume that the jump ratio is also valid away from the edges.
From (2) it follows that the probability p shell to interact with a shell is:
p shell =1− 1
J shell
(3)
We use the following parametrisation of the jump ratios for K and L I shells [24]:
J K = 125 +3.5
Z
(4)
J LI =1.2 (5)
For the L II and L III shells we adopt approximation of the formulae calculated by Gavrila [25]:
σ LII = γβ m {
}
e
γ 3 − 5γ 2 +24γ − 16 − (γ 2 log(γ(1 + β))
+3γ − 8)
E γ γβ
(6)
and
where
σ LIII = γβ m {
}
e
4γ 3 − 6γ 2 +5γ +3− (γ 2 log(γ(1 + β))
− 3γ +4)
E γ γβ
(7)
γ,β are the emitted photoelectron Lorentz gamma and beta factors;
E γ is the incident radiation energy;
m e is the electron mass.
Below an example of the shell interaction probability calculations for E γ >E K is given.
If
Σ II,III = σ LII + σ LIII
r LII =
σ LII
Σ II,III
r LIII = σ L III
Σ II,III
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