Geant4 Simulations for the Radon Electric Dipole Moment Search at

was to use an average X-ray energy per vacancy. These tables for all elements were
coded directly into the Geant4 simulation. The other more accurate option was to
provide an input file of the X-ray energies and intensities per shell vacancy. This
method was important to accurately simulate Fr K shell vacancies as the energy
of the X rays approach 100 keV, which are easily measured and resolved within
the GRIFFIN γ-ray detectors. The input data for Fr K shell vacancies is given in
Table 3.2. Careful inspection of these data reveals the intensities total to greater than
100% (per 100 K-shell vacancies). For every K vacancy one or more X-rays may be
emitted. For example, an electron from the L shell can drop down and occupy the
K shell vacancy, while leaving a new vacancy in the L shell. Another electron will
cascade down from the M shell to fill the L shell vacancy and so on. This process
was incorporated into the Geant4 simulations to provide an accurate simulation of
the entire X-ray cascade following internal conversion.
3.4 Simulating Angular Distributions
3.4.1 Beta Particle Anisotropies
The directional distribution of β particles from aligned nuclei has the form [50]
W(θ) = 1+A β P cos(θ), (3.8)
where A β is thebeta-asymmetry correlationcoefficient, P isthedegree ofpolarization
and θ is the angle of emission relative to the polarization axis. The beta-asymmetry
correlation coefficient depends on the initial and final spins and parities of the nuclear
levels, as well as the relative contributions of Fermi and Gamow-Teller β decay for
mixed transitions. These input data are not known for many of the β decay branches
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