A Semi-Analytical Model for Calculating the X-Ray Energy Spectrum of Thin Tritium-Containing Sample in BIXS Analysis

There are two methods for implementing the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula>-decay induced X-ray spectroscopy (BIXS) analysis for tritium contents and depth profile in materials. One is the analytical BIXS method, which can provide tritium content information quickly, but cannot accurately consider the multiple scattering of electrons and geometric complexity. The other is the BIXS method based on Monte Carlo (MC) simulations, where the X-ray energy spectra generated at different depths need to be first obtained through the MC simulations, but the MC simulations are very time-consuming. In this article, a semi-analytical model is proposed to greatly reduce the calculation time of the MC-based BIXS method and simultaneously retain the calculation accuracy. In this model, the energy and angle distributions of electrons inside the tritium-containing sample at different depths are calculated by MC simulations and then combined with the differential cross sections and shape functions of bremsstrahlung radiation to calculate the corresponding external bremsstrahlung (EB) energy spectrum. The total semi-analytical X-ray energy spectra are compared with those obtained by MC simulations and found that they are in excellent agreement in both amplitude and shape, within 1% difference, and the calculation time is greatly reduced compared with the MC simulations. Furthermore, the semi-analytical BIXS method proposed in this article is applied to the previous experimental data and observed that the tritium content and depth profile obtained using the semi-analytical BIXS method are consistent with the results obtained by MC-based BIXS analysis, within 0.82% difference.