Optical studies of scintillation detectors for precision beta-energy measurements

TL;DR

The paper tackles the challenge of nonlinear detector responses in scintillation-based beta-energy measurements and their impact on extracting the Fierz interference term $b$. It develops analytical (Birks, Cherenkov) and numerical (Geant4 optical tracking) tools to quantify how light production, Cherenkov emission, and SiPM readout nonlinearities bias energy reconstruction, applying them to the InESS@WISArD and bSTILED setups. By linking energy resolution to light-detection efficiency and by mapping light collection across detector volumes, the authors quantify systematic shifts in $b$ and propose corrective strategies, including explicit Cherenkov and SiPM-nonlinearity corrections and robust LCE benchmarking. The work demonstrates that permille-level precision demands careful control of $k_B$ for quenching, accurate PDE-based modeling of Cherenkov light, and reliable treatment of SiPM saturation and cross-talk, all anchored by validated optical simulations.

Abstract

This work presents optical calculations and simulations for scintillation detectors used in precision measurements of beta-particle energy spectra. Particular attention is given to Cherenkov photons and the impact of the light detection efficiency in the detector ensemble. We present an approach to estimate this light detection efficiency from the measured energy resolution of a detector. This is essential for the inclusion of scintillation photons in optical tracking Monte-Carlo simulations. A method to account for possible saturation and cross-talk of silicon photo-multipliers is also discussed. The impact of these effects is quantified in terms of systematic shifts in the extraction of the Fierz interference term from measurements of beta-energy spectra using scintillator detectors.

Figures (15)

• Figure 1: Nonlinearity due to light quenching as described by Eq. \ref{['eq:Birks']} using the literature values for a PVT scintillator of the type NE-102.
• Figure 2: The scintillation emission spectrum for PVT EJ200 (red) and YAP:Ce (black) compared with the Cherenkov spectrum (blue) and the PDE of a SiPM-Hamamatsu S13360-6050CS (solid green) and a PMT Hamamatsu R7723 (dash-dotted green). The blue dash-dotted line is the product of the Cherenkov spectrum and the SiPM PDE. Note the second axis for the PDE.
• Figure 3: Nonlinearities deduced from Eq. \ref{['eq:Cherenkov_nonlinearity']}, induced by Cherenkov photons in the $278.8-970$ nm range. Top: for a PVT EJ200 scintillator, with $n=1.58$, $\rho = 1.023~g/cm^3$, and threshold energy $E_{\rm th} = 149.0$ keV. Bottom: for a YAP:Ce scintillator with $n=1.95$, $\rho = 5.37~g/cm^3$, and $E_{\rm th} =84.2$ keV. Note the different y-scale for both materials. See text for details.
• Figure 4: Difference (top) and ratio (bottom) between the average number of pixels triggered, $N_{\rm pix}$, calculated using Eq. \ref{['eq:NmbPixelsSiPM']} or Eq. \ref{['eq:SiPM_nonlinearity_distribution']}, and the number of photons expected to be detected in absence of saturation and cross-talk, $N_{\rm det}$. The gray bands illustrate a variation by $\pm 1\%$ of the cross-talk probability from its nominal value of 3%.
• Figure 5: Scheme of the detection setup for the InESS@WISArD proof-of-principle experiment, with a zoom around the $^{114m}$In radioactive source. The set-up consists of two plastic scintillators (grey) in a symmetrical configuration, located at $11.5$ mm from the source in the center. The $6\times6$ mm$^2$ SiPM are shown in black.