Geant4 Simulations for the Radon Electric Dipole Moment Search at

lower its total energy. Internal conversion occurs when the excited nucleus interacts
with an electron in one of the lower atomic orbitals (K, L, etc), causing the electron
to be ejected from the atom. This process becomes dominate for higher Z nuclei and
is more probable for transitions of lower energy. The γ decay and internal conversion
processes are competitive. For any excited state the probabilities for either process
are given by
P γ = 1
1+α , P IC = α
1+α , (3.1)
where α is the total internal conversion coefficient.
Internal conversion coefficients used in the RnEDM simulations were calculated
with the BrIcc v2.2b program [44]. The BrIcc program calculates theoretical internal
conversion coefficients based on a relativistic self-consistent Dirac-Fock model [44].
Given the proton number and energy of the transition, the program outputs the total
and individual shell conversion coefficients for multipolarities up to L = 5. For mixed
transitions involving multipolarities L1 and L2, such as an M1+E2 transition, the
conversion coefficient can be calculated by [44]
α = δ2 α L2 +α L1
(1+δ 2 )
(3.2)
where δ, the mixing ratio, is defined as
δ = 〈J f||L 2 ||J i 〉
〈J f ||L 1 ||J i 〉 . (3.3)
The total internal conversion coefficient is defined as a sum of all the individual shell
internal conversion coefficients, such that α Tot = α K + α L + α M + ···. Thus, the
probabilities for an electron to be emitted from a particular shell is easily calculated
from the BrIcc output. For example, the probability for an electron to be emitted
from the K shell is simply α K /α Tot . Simulating the atomic shell structure enabled
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