Open Access

Markus Dutschke

• The Lock-Crisp-West (LCW) theorem relates spectroscopic data in momentum space with the corresponding quantities in the repetitive crystal momentum space. The back-folding operation translates a measured distribution into the corresponding (periodic) distributions in the crystal. This is important in Angular Correlation of electron-positron Annihilation Radiation (ACAR) spectroscopy resolving one (1D-ACAR) or two (2D-ACAR) momentum components and in Compton scattering experiments. Besides its intuitive appearance, it turns out, that numerical implementations of the LCW theorem introduce artifacts. These can lead to misinterpretation of the back-folded data. In this work we systematically analyze existing two-dimensional back-folding techniques and develop a new optimized back-folding strategy. This is applicable to 2D-ACAR spectra to extract Fermi surface features from a smaller momentum range (implying a lower number of experimental counts) than previous back-folding implementations.The Lock-Crisp-West (LCW) theorem relates spectroscopic data in momentum space with the corresponding quantities in the repetitive crystal momentum space. The back-folding operation translates a measured distribution into the corresponding (periodic) distributions in the crystal. This is important in Angular Correlation of electron-positron Annihilation Radiation (ACAR) spectroscopy resolving one (1D-ACAR) or two (2D-ACAR) momentum components and in Compton scattering experiments. Besides its intuitive appearance, it turns out, that numerical implementations of the LCW theorem introduce artifacts. These can lead to misinterpretation of the back-folded data. In this work we systematically analyze existing two-dimensional back-folding techniques and develop a new optimized back-folding strategy. This is applicable to 2D-ACAR spectra to extract Fermi surface features from a smaller momentum range (implying a lower number of experimental counts) than previous back-folding implementations. By this, we developed further an alternative to the commonly used tomographic methods, which perform the back-folding operation in three dimensions. While tomographic methods rely on data from several measured directions, our direct approach allows an analysis of the back-folded spectra from just one measured direction. We validate our results on 2D-ACAR data obtained from all-electron Full-Potential Linearized Augmented Plane Wave (FP-LAPW) calculations and experiments.…