Geant4 Simulations for the Radon Electric Dipole Moment Search at

The second optionfor particle emission was anangle dependent distribution based
on the orientation of the nucleus. The orientation of the nuclei in the RnEDM experiment
refers to the polarization along a time-dependent axis of quantization rotating
with the polarized ensemble of Rn nuclei, such that the population of the m = J
sublevel is significantly higher than that of the other 2J sublevels. The 223 Rn nuclear
spins are initially aligned along the magnetic field axis. Following the application
of an RF pulse, these spins precess in the plane of the detectors as described in
Section 2.3.3.
The angle of emission, θ, with respect to the axis of quantization can be generally
expressed in powers of cos(θ) [46],
W(θ) = ∑
A k cos k (θ) , (3.5)
k=0,1,2,...
where A k are the angular-distribution coefficients and k is even for γ radiation and
odd for β radiation. The exact form of W(θ) for β and γ radiation is described in
detail in Section 3.4.
β Particle Emission
In the process of β decay, the emitted β particle has a range of kinetic energies
between zero and the Q-value of the β decay. This energy spectrum results from the
existence of the neutrino or anti-neutrino in the decay processes shown below:
β − decay:
A
Z X N → A
Z+1 Y N−1 +e − + ¯ν e
β + decay:
A
Z X N → A
Z−1 Y N+1 +e + +ν e
Through the conservation of energy, the electron (or positron) and anti-neutrino (or
neutrino)sharethekineticenergyofthedecay, whichgeneratesanenergydistribution
for bothparticles. The spectral intensity for theelectron (or positron) may bewritten
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