Abstract text (incl. figure legends and references)

The extraction of quantitative compositional data from anelectron energy loss spectrum relies on the theoretical modeling and simulation of the core-loss (ionisation) edges. This allows to fit a simulated spectrum to theexperimental one, using the concentrations of each element as a free parameter. Cross sections can be obtained from the "generalised oscillator strengths" (GOS) which in turn depend on the wave functions of the target atoms which cannot be analytically described except in the hydrogen atom [1]. While the hydrogenic model is adequate to describe the K edges which is useful for some light elements, many elements require more complex computations in order to be quantified. While these calculations can be quite fast on a modern computer, tabulating the results is the most efficient approach for a wide deployment. Progress in methods for quantitative EELS has beenlimited by the existing GOS tables, which have been computed 40 years ago [2] and are not freely available.

To remedy this, we have computed a high-resolution GOS dataset covering all known EELS edges, which is now freely available [3]. We calculated the atomic wave functions self-consistently within the local density approximation, using the exchange correlation potential after Perdew [4]. For this a modified version of a program by Hamann is used [5]. Using this atomic potential, the wave function of the ejected free electron is calculated. To normalize the free wave functions they are matched to spherical Bessel and Neumann functions at large distances from the core. The remaining integral constitutes a spherical Bessel transform. Using the convolution theorem this integral is solved with a fast Fourier transformation. More details can be found in [6].

We assess the quality of the resulting data by comparing it to existing sets [2]. The agreement is good, but the new data offers better sampling, covers a larger number of edges (many minor ones), and is available over a wider range of energy and momentum. The comparison between the simulated edges, including ones simulated based on the hydrogenic model, offers good agreement across the board.

Finally, we have devised a HDF5-based file format for the distribution of GOS data which can be used in the future to ensure that new GOS data is immediately compatible with existing software.

The data, the code, and format specifications are freely available [3]. The new data can be used in CEOS Panta Rhei and in hyperspy.

[1] R. Egerton, (2011) Electron Energy-Loss Spectroscopy in the Electron Microscope, Springer

[2] R. D. Leapman, P. Rez and F. Mayers, J. Chem. Phys 72 (1980), p. 1232

[3] L. Segger, G. Guzzinati and H. Kohl, DOI: 10.5281/zenodo.6599071

[4] J. P. Perdew and A. Zunger, Phys. Rev. B 23 (1981), p. 5048

[5] D. R. Hamann, Phys. Rev. B 40 (1989), p. 2980

[6] L. Segger and H. Kohl, EMC 2020 Proceedings, 181

Fig.1. Comparison between generalised oscillator strengthsfor the Ti L3 edge. Our new data is compared to an existing reference [2], across energy and momentum (top row) and for specific energies (bottom row). The datasets show good agreement, but the new data has a finer sampling and covers a wider parameter space.

Fig. 2. Simulated edges for the different GOS datasets, and the hydrogenic approximation. The two tabulated datasets are in good agreement, while the hydrogenic data diverges significantly already for the L edges, and is not computed for higher edges.