PENELOPE 2003 - OECD Nuclear Energy Agency

2.6. Atomic relaxation 67
two vacancies, in the S1 and S2 shells).
Non-radiative transitions of the type LI-LJ-Xq, which involve an electron transition
between two L-subshells and the ejection of an electron from an outer shell Xq are
known as L-shell Coster-Kronig transitions.
The information furnished to penelope for each element consists of a table of possible
transitions, transition probabilities and energies of the emitted x-rays or electrons
for ionized atoms with a single vacancy in the K-shell or in an L-subshell. These data
are entered through the material definition file. The transition probabilities are extracted
from the LLNL Evaluated Atomic Data Library (Perkins et al., 1991). Fig.
2.11 displays transition probabilities for the transitions that fill a vacancy in the K shell
as functions of the atomic number Z; the curve labelled “Auger” corresponds to the
totality of non-radiative transitions. We see that for low-Z elements, the relaxation
proceeds mostly through non-radiative transitions. It is worth noting that the ratio of
probabilities of the radiative transitions K-S2 and K-S3 (where S stands for L, M or N)
is approximately 1/2, as obtained from the dipole approximation (see e.g. Bransden and
Joachain, 1983); radiative transitions K-S1 are strictly forbidden (to first order) within
the dipole approximation.
The energies of x-rays emitted in radiative transitions are taken from Bearden’s
(1967) review and reevaluation of experimental x-ray wavelengths. The energy of the
electron emitted in the non-radiative transition S0-S1-S2 is set equal to
E e = U S0 − U S1 − U S2 , (2.109)
where U Si is the binding energy of an electron in the shell Si of the neutral atom, which
is taken from the penelope database. These emission energies correspond to assuming
that the presence of the vacancy (or vacancies) does not alter the ionization energies
of the active electron shells, which is an approximation. It should be noted that these
prescriptions are also used to determine the energies of the emitted radiation at any
stage of the de-excitation cascade, which means that we neglect the possible relaxation
of the ion (see e.g. Sevier, 1972). Therefore, our approach will not produce L α and L β
x-ray satellite lines; these arise from the filling of a vacancy in a doubly-ionized L-shell
(generated e.g. by a Coster-Kronig transition), which releases an energy that is slightly
different from the energy liberated when the shell contains only a single vacancy. It is
also worth recalling that the adopted transition probabilities are approximate. For K
shells they are expected to be accurate to within one per cent or so, but for other shells
they are subject to much larger uncertainties. Even the L-shell fluorescence yield (the
sum of radiative transition probabilities for an L-shell vacancy) is uncertain by about
20% (see e.g. Hubbell, 1989; Perkins et al., 1991).
The simulation of the relaxation cascade is performed by subroutine RELAX. The
transition that fills the initial vacancy is randomly selected according to the adopted
transition probabilities, by using Walker’s aliasing method (section 1.2.3). This transition
leaves the ion with one or two vacancies. If the energy of the emitted characteristic
x ray or Auger electron is larger than the corresponding absorption energy, the state
variables of the particle are stored in the secondary stack (which contains the initial