Empirical and theoretical calculations of L-subshell Coster-Kronig transitions in atoms with 28 ≤ Z ≤ 98

Overview

This investigation examines Coster-Kronig transition probabilities across elements with atomic numbers ranging from 28 to 98. Coster-Kronig transitions represent radiationless processes in which an inner-shell vacancy is filled by an electron from a higher subshell within the same principal shell, with the excess energy ejected as an Auger electron. The study focuses on five specific transition probability parameters: f12, f13, f23, F1, and F123, which characterize L-subshell vacancy decay pathways. These transitions play a critical role in determining fluorescence yields and understanding the cascade of processes following inner-shell ionization. The work integrates experimental data compilation with new theoretical calculations to establish reference values across a wide range of elements spanning from nickel to californium.

Methods and approach

The investigation employs a dual approach combining empirical data analysis with ab initio theoretical calculations. Experimental data from prior studies were systematically compiled and subjected to polynomial interpolation to generate smooth empirical trends representing the variation of Coster-Kronig transition probabilities across the atomic number range. Theoretical calculations were performed using the Multiconfiguration Dirac-Fock method for selected elements throughout the studied range. This computational approach incorporates relativistic effects, which become increasingly significant for heavier elements where electron velocities approach relativistic regimes. The MCDF method accounts for electron correlation and relativistic corrections through configuration interaction, providing a rigorous quantum mechanical treatment of the atomic structure and transition processes.

Results

The calculated Coster-Kronig transition probabilities demonstrate good agreement with both existing theoretical predictions and available experimental measurements, particularly for medium and heavy elements where relativistic effects are properly accounted for. The polynomial interpolation of experimental data yields continuous trends that capture the systematic variation of transition probabilities across the periodic table. The convergence between empirical trends and MCDF calculations validates both approaches and establishes confidence intervals for the reported values. The comprehensive dataset now spans elements from nickel through californium, filling gaps in the existing literature and providing internally consistent values suitable for reference applications. The agreement improves with increasing atomic number, reflecting both the theoretical treatment of relativistic effects and the quality of experimental data available for heavier elements.

Implications

The established reference dataset for L-subshell Coster-Kronig transition probabilities addresses a fundamental need in atomic physics for reliable parameters governing inner-shell vacancy cascade processes. These values are essential inputs for modeling fluorescence yields, calculating X-ray emission intensities, and predicting the outcomes of electron and photon interactions with matter. Applications extend to X-ray fluorescence spectroscopy, electron probe microanalysis, synchrotron radiation experiments, and radiation damage studies in materials science and biological systems. The systematic compilation enables improved accuracy in quantitative elemental analysis techniques that rely on L-shell X-ray production. The theoretical validation through MCDF calculations provides confidence for interpolating values in regions where experimental data remain sparse or uncertain, while also serving as benchmarks for testing alternative computational approaches to atomic structure and radiative transitions.

Disclosure

• Research title: Empirical and theoretical calculations of L-subshell Coster-Kronig transitions in atoms with 28 ≤ Z ≤ 98
• Authors: Meddah, Samia, Kahoul, Abdelhalim, Parente, Fernando, Kasri, Yazid, Sampaio, Jorge Miguel, Marques, José Pires, Croft, Stephen, Favalli, Andrea, Cengiz, Erhan, Daoudi, Salim
• Publication date: 2026-04-01
• OpenAlex record: View
• Disclosure: This post was generated by artificial intelligence. The original authors did not write or review this post.