A pure state decomposition approach of the mixed dynamic form factor for mapping atomic orbitals

TL;DR

This paper introduces a matrix diagonalization approach to simplify the calculation of the mixed dynamic form factor (MDFF) in electron scattering, enabling clearer visualization of atomic orbitals in crystals.

Contribution

It presents a novel pure state decomposition method for the MDFF, facilitating reduced computational complexity and improved physical insight in electron scattering analysis.

Findings

Matrix diagonalization reduces MDFF calculation complexity.

New basis clarifies the physics of inelastic electron scattering.

Predictions enable direct imaging of atomic orbitals.

Abstract

We demonstrate how the mixed dynamic form factor (MDFF) can be interpreted as a quadratic form. This makes it possible to use matrix diagonalization methods to reduce the number of terms that need to be taken into account when calculating the inelastic scattering of electrons in a crystal. It also leads in a natural way to a new basis that helps elucidate the underlying physics. The new method is applied to several cases to show its versatility. In particular, predictions are made for directly imaging atomic orbitals in crystals.