Generalised oscillator strength for core-shell electron excitation by fast electrons based on Dirac solutions

Inelastic excitation as exploited in Electron Energy Loss Spectroscopy (EELS) contains a rich source of information that is revealed in the scattering process. To accurately quantify core-loss EELS, it is common practice to fit the observed spectrum with scattering cross-sections calculated using experimental parameters and a Generalized Oscillator Strength (GOS) database [1].

The GOS is computed using Fermi’s Golden Rule and orbitals of bound and excited states. Previously, the GOS was based on Hartree-Fock solutions [2], but more recently Density Functional Theory (DFT) has been used [3]. In this work, we have chosen to use the Dirac equation to incorporate relativistic effects and have performed calculations using Flexible Atomic Code (FAC) [4]. This repository contains a tabulated GOS database based on Dirac solutions for computing double differential cross-sections under experimental conditions.

We hope the Dirac-based GOS database can benefit the EELS community for both academic use and industry integration.

Database Details:

- Covers all elements (Z: 1-108) and all edges

- Large energy range: 0.01 - 4000 eV

- Large momentum range: 0.05 -50 Å-1

- Fine log sampling: 128 points for energy and 256 points for momentum

- Data format: GOSH [3]

Calculation Details:

- Single atoms only; solid-state effects are not considered

- Unoccupied states before continuum states of ionization are not considered; no fine structure

- Plane Wave Born Approximation

- Frozen Core Approximation is employed; electrostatic potential remains unchanged for orthogonal states when - core-shell electron is excited

- Self-consistent Dirac–Fock–Slater iteration is used for Dirac calculations; Local Density Approximation is assumed for electron exchange interactions; continuum states are normalized against asymptotic form at large distances

- Both large and small component contributions of Dirac solutions are included in GOS

- Final state contributions are included until the contribution of the previous three states falls below 0.1%. A convergence log is provided for reference.

[1] Verbeeck, J., and S. Van Aert. Ultramicroscopy 101.2-4 (2004): 207-224.

[2] Leapman, R. D., P. Rez, and D. F. Mayers. The Journal of Chemical Physics 72.2 (1980): 1232-1243.

[3] Segger, L, Guzzinati, G, & Kohl, H. Zenodo (2023). doi:10.5281/zenodo.7645765

[4] Gu, M. F. Canadian Journal of Physics 86(5) (2008): 675-689.