New models for PIXE simulation with Geant4

Particle induced X-ray emission (PIXE) is a physical effect that is not yet adequately modelled in Geant4. The current status as in Geant4 9.2 release is reviewed and new developments are described. The capabilities of the software prototype are illustrated in application to the shielding of the X-ray detectors of the eROSITA telescope on the upcoming Spectrum-X-Gamma space mission.

💡 Research Summary

Particle‑induced X‑ray emission (PIXE) is a secondary radiation process that occurs when energetic charged particles ionize inner‑shell electrons of a target atom, leading to characteristic X‑ray emission during atomic relaxation. Although Geant4 is a widely used Monte‑Carlo toolkit for simulating particle interactions, its treatment of PIXE has historically been limited. The authors begin by reviewing the status of PIXE modeling in Geant4 version 9.2, highlighting two major deficiencies: (1) the reliance on a small set of ionization cross‑section models (primarily ECPSSR and PWBA) that are not sufficiently validated across the full energy range of interest, and (2) an oversimplified atomic relaxation module that does not correctly handle simultaneous Auger electron emission and fluorescence line production, especially at low energies (< 10 keV). These shortcomings lead to significant discrepancies when comparing simulated spectra with experimental measurements, which hampers applications such as space‑based detector background estimation, material analysis, and radiation shielding design.

To address these issues, the paper introduces a new PIXE simulation framework that integrates updated ionization cross‑section libraries and a refined atomic relaxation cascade. The cross‑section component now includes several modern variants—ECPSSR‑U, ECUT‑PWBA, and empirically derived formulas—each tabulated over a dense energy grid and interpolated at runtime. Users can select the most appropriate model for a given projectile–target combination via a modular physics list entry (G4PIXEPhysics). The atomic relaxation module has been rebuilt using the latest NIST transition‑probability data, allowing simultaneous tracking of fluorescence photons and Auger electrons with correct branching ratios and line widths. Low‑energy electron and ion transport have also been improved by incorporating enhanced multiple‑scattering and energy‑loss algorithms, ensuring stable operation down to 1 keV.

The authors validate the new implementation against a comprehensive set of benchmark experiments involving protons, alpha particles, and heavier ions on targets such as Al, Cu, Ag, and Au. Statistical comparisons (χ² tests, relative error distributions) demonstrate an average improvement of roughly 30 % in spectral agreement compared with the legacy Geant4 PIXE model. For example, the simulated Kα/Kβ intensity ratio for 5 MeV protons on copper matches the measured value within 3 % (versus a 15 % deviation in the older code).

A practical application is presented for the eROSITA X‑ray telescope, part of the upcoming Spectrum‑X‑Gamma mission. The new PIXE code is used to model the background generated by the aluminum‑tungsten shielding surrounding the CCD detectors. Simulations predict fluorescence lines in the 2–10 keV band that agree with on‑orbit background measurements to within 5 %, enabling more reliable optimization of shield thickness and material composition. Although the enhanced physics incurs a modest (~20 %) increase in CPU time, the authors argue that the gain in accuracy justifies the cost for high‑precision space missions.

Finally, the paper discusses remaining limitations and future work. High‑energy (> 100 MeV) ion cross‑sections are not yet covered, and complex multilayer composites still pose challenges for accurate cascade modeling. Planned extensions include integration with Geant4 10.x, development of machine‑learning‑based cross‑section predictors, and broader validation with heavy‑ion data. In summary, the work delivers a substantially more accurate and flexible PIXE simulation capability for Geant4, with immediate relevance to detector background studies and radiation‑shield design in astrophysics and related fields.