Scintillation Quenching Factors (QFs)

• Scintillation Quenching Factors (QFs) are dimensionless ratios comparing the light yield from various ionizing particles to that from electrons or gammas, thereby quantifying quenching effects.
• They are measured using methods such as monoenergetic neutron scattering and alpha-source calibration, with models like Birks’ law capturing energy-dependent nonlinearity.
• Accurate QF determination is critical for calibrating rare-event detectors in dark matter searches and neutrino physics, as it directly impacts energy threshold setting and background discrimination.

Scintillation quenching factors (QFs) quantify the relative light yield reduction in scintillators when different ionizing particles deposit energy, compared to a reference (typically $\gamma$ or $\beta$) particle. QFs are foundational for interpreting experimental observables in rare-event searches, dark matter direct detection, neutrino physics, and radiation dosimetry. They encapsulate how densely ionizing projectiles—such as $\alpha$ particles, nuclear recoils, or heavy ions—produce less scintillation light per unit energy than sparsely ionizing electrons or gammas, due to complex energy partition and non-radiative loss processes in the scintillator medium.

1. Fundamental Definitions and Theoretical Framework

A scintillation quenching factor, $QF_i$, for ionizing species $i$, is conventionally defined as the normalized ratio of light yields:

$QF_i(E) = \frac{LY_i(E)}{LY_e(E)}$

where $LY_i(E)$ is the light yield from species $i$ depositing energy $E$ in the scintillator, and $LY_e(E)$ is the corresponding yield from electron or $\gamma$ recoils of the same energy. This dimensionless metric directly quantifies the degree of scintillation suppression ("quenching") for nuclear recoils or heavy ions relative to electromagnetic events.

The physical origin of quenching is rooted in the density of energy deposition (stopping power, $dE/dx$). Highly ionizing particles create dense excitation tracks, promoting non-radiative recombination and bi-excitonic annihilation, which channel deposited energy into heat or phonons rather than scintillation photons. Birks' semi-empirical model captures this nonlinearity:

$$\frac{dL}{dx} = \frac{S \; dE/dx}{1 + kB \;(dE/dx)}$$

where $S$ is a normalization factor and $kB$ is the Birks factor (units: g/(MeV cm$^2$)). $dL/dx$ describes the incremental scintillation produced as a function of localized energy loss. Integrating this expression over the particle's track and normalizing by the electron case yields the QF as a function of energy.

The semi-empirical approach can be generalized:

$$QF_i(E) = \frac{\int_0^E \frac{dE}{1 + kB (dE/dr)_i}}{\int_0^E \frac{dE}{1 + kB (dE/dr)_e}}$$

where $(dE/dr)_i$ and $(dE/dr)_e$ are the stopping powers for ion $i$ and electron, respectively. This exact integral is typically solved using $dE/dr$ data from SRIM (for ions) and ESTAR (for electrons) (Tretyak, 2013).

2. Experimental Methodologies in Measuring QFs

A range of sophisticated experimental designs exist for QF determination, distinguished by target material, type of ionizing particle, and energy regime of interest.

• Monoenergetic Neutron Scattering: Nuclear recoils are precisely induced via elastic neutron scattering at controlled angles. The scattered neutron is tagged in coincidence or by time-of-flight (TOF), enabling unambiguous reconstruction of the nuclear recoil energy. This approach is key in crystals (e.g., NaI(Tl), CsI(Tl), CaWO$_4$, BGO) (Joo et al., 2018, Ommura et al., 2023, Strauss et al., 2014, Lee et al., 23 Feb 2024).
• $\alpha$-Source Peaks and Decay Chains: For $\alpha$-particle QFs, intrinsic or surface contamination (e.g., $^{210}$Po, $^{222}$Rn chains) provides energy-calibrated peaks in the energy spectrum (Collaboration et al., 12 Jun 2024). Analysis of the peak-to-peak ratios, often within a single detector, allows for relative measurements with effective cancellation of systematic effects associated with non-linear response and saturation.
• Compton Scattering/Electron Recoils: For organic/liquid scintillators, the light yield from Compton electrons (using tagged $\gamma$ sources and fixed scattering geometries) establishes the electron-equivalent calibration baseline, vital for precise QF extraction for nuclear recoils (Luo et al., 2018).
• Multichannel and Systematics-Controlled Approaches: Recent studies deploy multiple detector modules fabricated under identical conditions and measured in the same beamline setup to directly assess intercrystal variation and universal systematics (Cintas et al., 19 Feb 2024).

Precision is typically limited by systematics originating from electron-equivalent energy calibration, non-proportional response at low energies, detector geometry, and background discrimination (e.g., PMT noise, pile-up, or neutron multiple scattering).

3. Energy Dependence and Modeling of QFs

QFs are generally energy-dependent, particularly in the few-keV to MeV regime critical for rare-event experiments:

• Energy Dependence: Lighter nuclei (e.g., O, Na) in wide-bandgap crystals show an QF that increases as the nuclear recoil energy decreases, sometimes by up to ~30% over a tens-of-keV range (Strauss et al., 2014). For heavier nuclei or $\alpha$-particles, this dependence is less pronounced but can still be significant.
• Deviation from Simple Birks Model: Below specific thresholds (e.g., 300 keV for proton recoils in plastic scintillators), QFs can fall more rapidly than predicted by a pure Birks formalism, indicating the onset of additional quenching mechanisms or the influence of defect states and exciton-exciton annihilation (Reichhart et al., 2011, Westerdale et al., 2017).
• Quadratic and Advanced Models: In some organic scintillators, modified Birks models with quadratic denominator terms ($1 + kB\;dE/dx + C\;(dE/dx)^2$) significantly improve fits to measured QFs, especially in the high ionization-density (low-energy) regime (Westerdale et al., 2017).

Universal Birks factors $kB$ have been found to provide predictive power for QFs of different ion species within the same scintillator under identical conditions, supporting the use of a single parameter to describe quenching phenomenology across different detector calibrants (Tretyak, 2013).

4. Applications and Impact on Rare Event Detectors

Reliable knowledge of QFs is critical in setting energy thresholds, background modeling, and event classification in several classes of rare-event search experiments:

• Dark Matter Direct Detection: WIMP-induced nuclear recoils are typically of low energy and must be distinguished from electron recoils resulting from $\gamma$/backgrounds. Underestimated QFs can lead to incorrect conversion of detector observables (keVee) into true recoil energy (keVnr), shifting or diluting exclusion regions in WIMP parameter space, as seen in comparisons between DAMA/LIBRA and COSINE-100 (Ko et al., 2019, Cintas et al., 19 Feb 2024).
• Coherent Elastic Neutrino–Nucleus Scattering (CE$\nu$NS): The conversion from recoil energy to detected scintillation is QF-dependent. Improved, energy-dependent QF measurements with reduced uncertainty (e.g., 3.6% versus prior 25%) yield tighter constraints on weak mixing angle, neutron radius, and non-standard neutrino interactions in experiments such as COHERENT (Papoulias, 2019).
• Bolometric Cryogenic Detectors and Pulse Decorrelation: In combined light-heat detectors, such as CdWO$_4$ bolometers, anticorrelation between heat and light channels (arising from energy conservation partitioning) is exploited to minimize stochastic fluctuation and optimize energy resolution via linear coordinate transformation/rotation. Accurate knowledge of QF and its impact on channel calibration ensures that event classification (e.g., $\alpha$ versus $\beta/\gamma$ discrimination) is robust (Arnaboldi et al., 2010).

5. Material, Structural, and Environmental Dependencies

QF behavior is sensitively dependent on material properties, defect structures, and environmental factors:

• Crystal Quality and Optical Defects: In CaWO$_4$, variations in absolute QF of up to 11% have been observed across different detector modules, correlated with differences in optical quality and defect density (Strauss et al., 2014). Scaling factors can be introduced to calibrate each module independently.
• Dielectric and Molecular Effects: In liquid scintillators, quenching is directly tied to dielectric constant and molecular polarization. Polar groups (e.g., hydroxyls in TeBD) and high $\epsilon$ suppress recombination and Förster transfer rates, significantly quenching the scintillation yield relative to conventional solvents (e.g., LAB) (Wang et al., 27 Aug 2025).
• Temperature and Doping: In Ce-doped silicate crystals, thermal quenching is governed by Arrhenius-type nonradiative processes—thermal ionization and nonradiative crossover from excited to ground states. The activation energy for quenching and the quenching temperature $T_{50\%}$ are reduced with increasing Ce concentration, with practical implications for detector operation in high-temperature environments (Horiai et al., 2021, Yoshino et al., 2021).

6. Modeling and Extrapolation for Low-Energy Regimes

Given the paucity of direct low-energy QF measurements (especially for high-mass or heavy species), extrapolation from higher-energy anchor points using physics-informed models is necessary:

• Combined Electronic and Nuclear Quenching: In liquid argon, for $\alpha$-induced backgrounds, the total QF is factorized into nuclear (Lindhard-type) and electronic (Birks-type) contributions. Fitting model parameters to observed $\alpha$ peaks from radon chain decays yields an uncertainty-bounded extrapolation from MeV to keV regimes crucial for background modeling in dark matter searches (Collaboration et al., 12 Jun 2024).
• Validation and Uncertainty Quantification: Systematic uncertainties in the modeling—arising from nuclear stopping cross-sections, calibration stability, or energy-dependent light yield nonproportionality—are propagated either through Monte Carlo or analytical error propagation, with direct impact on background rejection strategies and signal sensitivity.

7. Summary Table: Representative Quenching Factors

Material/Experiment	Particle	Energy Range (keV or MeV)	QF (%)	Notable Features / Parameters
CdWO$_4$ bolometer (Arnaboldi et al., 2010)	$\alpha$	~5 MeV	16–20	LY$\sim$constant for $\gamma/\beta$, QF$_\alpha<1$, neutron QF$\sim$0.14
CaWO$_4$ (CRESST) (Strauss et al., 2014)	O/Ca/W	10–40 keV	O: $\sim$11, Ca: $\sim$6, W: $\sim$1.7	Strong energy dependence for O, intercrystal variation
NaI(Tl) (Joo et al., 2018, Lee et al., 23 Feb 2024)	Na/I	4–150 keV	Na: 11–23, I: 4–6	High light yield with new encapsulation, energy-dependent nonproportionality
CsI(Tl) (Lee et al., 2015)	Cs/I	20–100 keV	$\sim$8–12	Channeling increases QF, but $<$1% occurrence
Plastic scintillator (Reichhart et al., 2011)	H/C nuclei	125–850 keV	$\sim$10 and falls rapidly below 300 keV	Birks $kB=0.014\pm0.002$, below 300 keV steeper fall-off
LAr (DEAP-3600) (Collaboration et al., 12 Jun 2024)	$\alpha$	5–8 MeV (anchor)	model-extrapolation	Measured relative in situ, extrapolated using nuclear and electronic quenching models

This tabulation illustrates typical QFs for major scintillator materials and highlights the necessity of precise contextual, energy-dependent, and material-specific characterization for accurate detector calibration and modeling.

• (Arnaboldi et al., 2010) CdWO$_4$ scintillating bolometer for Double Beta Decay: Light and Heat anticorrelation, light yield and quenching factors
• (Reichhart et al., 2011) Quenching Factor for Low Energy Nuclear Recoils in a Plastic Scintillator
• (Tretyak, 2013) Semi-empirical calculation of quenching factors for scintillators: new results
• (Strauss et al., 2014) Energy-Dependent Light Quenching in CaWO$_4$ Crystals at mK Temperatures
• (Lee et al., 2015) Measurement of the quenching and channeling effects in a CsI crystal used for a WIMP search
• (Westerdale et al., 2017) Quenching Measurements and Modeling of a Boron-Loaded Organic Liquid Scintillator
• (Joo et al., 2018) Quenching factor measurement for NaI(Tl) scintillation crystal
• (Ko et al., 2019) Comparison between DAMA/LIBRA and COSINE-100 in the light of Quenching Factors
• (Papoulias, 2019) COHERENT constraints after the COHERENT-2020 quenching factor measurement
• (Cintas et al., 19 Feb 2024) A measurement of the sodium and iodine scintillation quenching factors across multiple NaI(Tl) detectors to identify systematics
• (Lee et al., 23 Feb 2024) Measurements of low-energy nuclear recoil quenching factors for Na and I recoils in the NaI(Tl) scintillator
• (Collaboration et al., 12 Jun 2024) Relative Measurement and Extrapolation of the Scintillation Quenching Factor of $\alpha$-Particles in Liquid Argon using DEAP-3600 Data
• (Wang et al., 27 Aug 2025) Molecular structure, electric property, and scintillation and quenching of liquid scintillators