[Paper Review] Absolute L-shell ionization and X-ray production cross sections of Lead and Thorium by 16-45 keV electron impact

Hitesh Rahangdale, Pretam Kumar Das+5 more|arXiv (Cornell University)|Aug 12, 2015

X-ray Spectroscopy and Fluorescence Analysis3 citations

TL;DR

This study measures absolute L-shell ionization and X-ray production cross sections in lead and thorium under 16–45 keV electron impact, using wavelength-dispersive X-ray spectroscopy and Monte Carlo simulations to correct for backscattering. The results show significant discrepancies between experiment and theoretical models (DWBA and MRBEB) for L₁ and L₂ subshells, indicating that uncertainties in atomic relaxation parameters—particularly for L₁—limit theoretical accuracy.

ABSTRACT

The absolute L subshell specific electron impact ionization cross sections near the ionization threshold (16 < E < 45 keV) of Lead and Thorium are obtained from the measured L X-ray production cross sections. Monte Carlo simulation is done to account for the effect of the backscattered electrons and the final experimental results are compared with calculations performed using distorted wave Born approximation and the modified relativistic binary encounter Bethe model.The sensitivity of the results on the atomic parameters is explored. Observed agreements and discrepancies between the experimental results and theoretical estimates, and their dependence on the specific atomic parameters are reported.

Motivation & Objective

• To determine absolute subshell-specific L-shell ionization cross sections for lead and thorium using electron impact at low energies (16–45 keV).
• To investigate the role of atomic relaxation parameters—especially fluorescence yields and Coster-Kronig transitions—in the discrepancy between experiment and theory.
• To assess the reliability of theoretical models (DWBA and MRBEB) in predicting ionization cross sections for high-Z elements.
• To identify which relaxation parameters most significantly affect the accuracy of extracted ionization cross sections from X-ray production data.
• To advocate for high-resolution measurements of individual Lγ transitions to reduce dependence on uncertain relaxation parameters.

Proposed method

• Measured L X-ray production cross sections using a wavelength-dispersive spectrometer with a high-purity Si(Li) detector.
• Applied Monte Carlo simulations (PENELOPE) to correct for electron backscattering effects in the target and substrate.
• Used radiative yields and fluorescence yields (Γγ, ω₁) to extract subshell-specific ionization cross sections from measured Lα, Lβ, and Lγ cross sections.
• Compared experimental results with theoretical predictions using the distorted wave Born approximation (DWBA) and the modified relativistic binary encounter Bethe (MRBEB) model.
• Accounted for vacancy migration via Coster-Kronig transitions and subshell-specific decay probabilities in the data extraction process.
• Performed sensitivity analysis on atomic parameters to assess their impact on final ionization cross section values.

Experimental results

Research questions

• RQ1 To what extent do theoretical models (DWBA and MRBEB) reproduce measured L-shell ionization cross sections in Pb and Th at 16–45 keV?
• RQ2 Why do discrepancies arise between experiment and theory for L₁ and L₂ subshells, particularly in the context of relaxation parameter uncertainties?
• RQ3 How do the Lγ transitions, which probe L₁ and L₂ subshells, influence the accuracy of extracted ionization cross sections?
• RQ4 What is the relative contribution of L₁, L₂, and L₃ subshells to the total Lβ and Lγ X-ray production cross sections?
• RQ5 Can high-resolution measurements of individual Lγ lines reduce reliance on uncertain relaxation parameters in ionization cross section extraction?

Key findings

• The DWBA theory reproduces the L₃ subshell ionization cross section and Lα X-ray production cross section well for both Pb and Th.
• The MRBEB model overpredicts ionization cross sections for all three L subshells in both elements across the 16–45 keV range.
• Discrepancies between experiment and DWBA theory are most pronounced for the L₁ and L₂ subshells, with experimental values lower than theoretical predictions by up to 30–50%.
• The Lβ and Lγ cross sections show poor agreement with theory, primarily due to inaccuracies in the relaxation parameters associated with the L₁ subshell.
• The L₂ subshell cross section, derived from Lγ₁₊₅, is underestimated by 30–50% compared to theory, suggesting poor knowledge of L₂-specific relaxation parameters.
• The study concludes that the main source of discrepancy lies in the uncertainty of relaxation parameters—especially for the L₁ subshell—rather than in the electron impact ionization models themselves.