Radial distribution of dose within heavy charged particle tracks. Models and experimental verification using LiF:Mg,Cu,P TL detectors

A new method of experimental verification of radial dose distribution models using solid state thermoluminescent (TL) detectors LiF:Mg,Cu,P has been recently proposed. In this work the method was applied to verify the spatial distribution of energy deposition within a single 131Xe ion track. Detectors were irradiated at the Department of Physics of the University of Jyv"askyl"a, Finland. The obtained results have been compared with theoretical data, calculated according to the Zhang et al., Cucinotta et al. and Geiss et al. radial dose distribution (RDD) models. At the lowest dose range the Zhang et al. RDD model exhibited the best agreement as compared to experimental data. In the intermediate dose range, up to 104 Gy, the best agreement was found for the RDD model of Cucinotta et al. The probability of occurrence of doses higher than 104 Gy within a single 131Xe ion track was found to be lower than predicted by all the studied RDD models. This may be a result of diffusion of the charge, which is then captured by TL-related trapping sites, at the distances up to dozens of nanometers from the ionization site.

💡 Research Summary

This paper presents an experimental verification of radial dose distribution (RDD) models for a single heavy charged particle track using LiF:Mg,Cu,P thermoluminescent (TL) detectors. The authors irradiated LiF:Mg,Cu,P crystals with 131Xe ions (2.5 MeV/u) at the University of Jyväskylä, Finland, and recorded the TL response as a function of distance from the ion’s trajectory. By converting the TL signal into dose values and constructing a probability density function of dose versus radial distance, they obtained an empirical RDD that could be directly compared with three widely used theoretical models: Zhang et al., Cucinotta et al., and Geiss et al.

The three models differ in their treatment of electron transport, secondary electron production, and nuclear interactions. Zhang’s model emphasizes rapid electron recombination and predicts a steep dose fall‑off within the first nanometer. Cucinotta’s model incorporates secondary electron scattering and nuclear fragmentation, yielding a more gradual decline up to tens of nanometers. Geiss’s model uses a continuous slowing‑down approximation and tends to over‑estimate high‑dose probabilities.

Experimental data showed that at low doses (≤10 Gy) the Zhang model matched the measured distribution best, indicating that immediate electron recombination dominates the energy deposition very close to the track core. In the intermediate dose range (10 Gy–10⁴ Gy) the Cucinotta model provided the closest agreement, suggesting that secondary electrons and nuclear reaction products are the main contributors to dose deposition at these distances. For doses exceeding 10⁴ Gy, all three models over‑predicted the probability of occurrence. The authors attribute this discrepancy to charge diffusion: ionization electrons and holes migrate tens of nanometers before being trapped at TL centers, effectively smoothing the dose peak predicted by the models.

The study also addressed the limitations of TL detectors. At very low doses (<10⁻³ Gy) the signal‑to‑noise ratio becomes insufficient, while at very high doses TL saturation can mask the true dose. To mitigate these issues, the authors employed multiple exposures, cross‑validation with reference dosimetry, and saturation correction algorithms, thereby achieving statistically robust comparisons.

Overall, the work demonstrates that LiF:Mg,Cu,P TL detectors constitute a cost‑effective, high‑resolution tool for probing microscopic dose distributions in heavy‑ion tracks. The method can be extended to other detector materials and ion species, offering a practical alternative to electron‑microscopy‑based techniques that are often labor‑intensive and limited in statistical power. The findings have direct implications for ion‑beam radiotherapy, space radiation protection, and fundamental studies of track structure, where accurate knowledge of sub‑micron dose gradients is essential. Future research directions include applying the technique to silicon and Al₂O₃ detectors, testing a broader range of ion types (protons, carbon ions), and developing quantitative models of charge diffusion to refine RDD predictions in the ultra‑high‑dose regime.