van Veenendaal, Michel | Engineering Papers

DOE OSTI2024

Dichroic $K_β$ x-ray emission as a probe of orbital moments

Strong dichroism of the outgoing x rays is demonstrated in $K_β$ x-ray emission. Here, it is shown that while the integrated intensities are zero, the first moments of the dichroic spectra can be directly related to the orbital moments. The first moment is caused by the Coulomb interaction between the 3p core hole and the 3d valence electrons. Contributions from other interactions are negligibly small or zero. Calculations for a divalent cobalt ion in the presence of a Jahn-Teller distortion show strong dependencies of the dichroic $K_β$ emission on the angular momentum and the quadrupolar moment.

van Veenendaal, Michel↗

DOE OSTI2023

The spatial wavefunction of half-integer spins

Within a nonrelativistic framework, spin is generally included as an intrinsic angular momentum. It is proposed here that consistent results can be obtained with a spatial wavefunction of an oriented complex exponential ${e}^{\mp {\boldsymbol{i}}\hat{{\bf{a}}}\varphi }$, where the bivector ${\boldsymbol{i}}\hat{{\bf{a}}}$ is written in terms of the pseudoscalar i = e x e y e z and the axis of rotation given by the unit vector $\hat{{\bf{a}}}$, which is generally an (effective) magnetic field direction (this can also be written as ${e}^{\mp i{\boldsymbol{\sigma }}\cdot \hat{{\bf{a}}}\varphi }$ in terms of the Pauli vector σ). The wavefunction is a multivector and not a complex scalar. The signs in the exponential correspond to the two directions of rotation around the axis. The transformation properties of these wavefunctions are given by the Pauli spinors. Finally, spin can be viewed as a zero-point rotation arising from the noncommutativity of the momentum and the vector potential.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗