Geant4 Simulations for the Radon Electric Dipole Moment Search at

an accurate description of the electron energy and resulting X-ray energy. X rays are
produced when electrons transition from higher orbitals to the lower vacant orbitals.
The simulation of the X-rays are described in detail in Section 3.3.2.
3.3.1 Timing
The time of each individual β-decay event from the ensemble of 223 Rn nuclei was
generated using Monte Carlo from the input half-life and number of nuclei remaining.
The time differences between successive events in a radioactive decay can be
simulated using a well known Monte Carlo method for sampling from an exponential
distribution [45]. The time intervals are given by
∆t = −1 ln(1−χ) , (3.4)
N ′ λ
where λ is the decay constant (λ = ln(2)
t 1/2
), N ′ is the remaining number of nuclei
and χ is a random number generated from a uniform distribution between [0.0, 1.0).
Keeping track of these small time differences generated the absolute time of each
decay event in the simulation. Figure 3.2 illustrates the decay of one hundred million
223 Rn nuclei detected by a ring of GRIFFIN detectors and confirms the validity of
the Monte Carlo by fitting the decay with a maximum likelihood function resulting
in excellent agreement of the input 24.3 minute half-life.
3.3.2 Particle Emission
Particle emission was handled by the Geant4 Particle Gun. The Particle Gun
was passed the type of particle to be emitted (photon, electron or positron), its energy,
initial position and momentum direction. The emission direction generally had
two main user options which were selected in the GUGI program before running the
42