Geant4 simulations of the absorption of photons in CsI and NaI produced by electrons with energies up to 4 MeV and their application to precision measurements of the β -energy spectrum with a calorimetric technique

The yield of photons produced by electrons slowing down in CsI and NaI was studied with four electromagnetic physics constructors included in the Geant4 toolkit. The subsequent absorption of photons in detector geometries used for measurements of the $\beta$ spectrum shape was also studied with a focus on the determination of the absorption fraction. For electrons with energies in the range 0.5–4 MeV, the relative photon yields determined with the four Geant4 constructors differ at the level of $10^{-2}$ in amplitude and the relative absorption fractions differ at the level of $10^{-4}$ in amplitude. The differences among constructors enabled the estimation of the sensitivity to Geant4 simulations for the measurement of the $\beta$ energy spectrum shape in ${}^6$He decay using a calorimetric technique with ions implanted in the active volume of detectors. The size of the effect associated with photons escaping the detectors was quantified in terms of a slope which, on average, is respectively $-5.4$ %/MeV and $-4.8$ %/MeV for the CsI and NaI geometries. The corresponding relative uncertainties as determined from the spread of results obtained with the four Geant4 constructors are 0.0067 and 0.0058.