Modeling of the Alpha DaRT coated source using GEANT4: Investigating nuclei effective desorption probabilities, leakage process, and fractions of diffused nuclei

In this study, we modelled the geometry of an Alpha DaRT source using GEANT4. Four distributions of 224Ra were considered to evaluate the desorption probabilities of daughter nuclei both with and without a coating layer of PDMS. By considering 224Ra radioactive nuclei as a source, we evaluated the desorption probability of the daughter nuclei. We then adjusted the desorption probability values of 220Rn to approximately 40% and 45%, consistent with values reported in the literature by either increasing the thickness of a thin cylindrical steel layer covering a thin 224Ra layer (1.54×10-4 nm), or by adjusting the σ value of a half-Gaussian distribution of 224Ra. The resulting four source configurations correspond to steel layer thicknesses covering the 224Ra layer of 1.00 nm and 2.04 nm, and σ values of the half-Gaussian 224Ra distributions of 1.35 nm and 2.59 nm resulting in 220Rn desorption probabilities of 45% and 40%, respectively. For half-Gaussian distributions with σ =1.35 nm, the calculated desorption probabilities from the source are as follows: 220Rn (45.11%), 216Po (14.14%), 212Pb (7.64%), 208Tl (1.51%), and 208Pb (3.73%), all calculated with Monte Carlo statistical uncertainties <0.01%. Recoil effects led to the desorption of some atoms from the source, while others penetrated deeper into the steel layer. The corresponding average recoil penetration depths within the seed are as follows: 220Rn (7.83 nm), 216Po (12.28 nm), 212Pb (16.36 nm), 208Tl (19.42 nm), and 208Pb (20.61 nm). Then, we developed a model to calculate nuclear decay from 224Ra to 208Pb, which accounts for desorption and leakage processes. Furthermore, the integrated activity of each radionuclide within the source and its vicinity was computed. The Alpha DaRT source models developed in this work provides valuable insights into the behavior of radionuclides in both bare and coated sources and can be integrated with diffusion and radiation.