# Electric quadrupole moment and the tensor magnetic polarizability of twisted electrons and a potential for their measurements

## TL;DR

This paper derives the relativistic Hamiltonian for twisted electrons, revealing they have a measurable electric quadrupole moment and tensor magnetic polarizability, with proposed methods for experimental detection and potential applications.

## Contribution

The paper introduces the first theoretical prediction that twisted electrons possess a measurable electric quadrupole moment and tensor magnetic polarizability, including methods for their experimental measurement.

## Key findings

- Twisted electrons have a significant electric quadrupole moment.
- Tensor magnetic polarizability of twisted electrons can be measured in storage rings.
- Proposed methods include freezing orbital angular momentum and resonance techniques.

## Abstract

For a twisted (vortex) Dirac particle in nonuniform electric and magnetic fields, the relativistic Foldy-Wouthuysen Hamiltonian is derived including high order terms describing new effects. The result obtained shows for the first time that a twisted spin-1/2 particle possesses a tensor magnetic polarizability and a measurable (spectroscopic) electric quadrupole moment. We have calculated the former parameter and have evaluated the latter one for a twisted electron. The tensor magnetic polarizability of the twisted electron can be measured in a magnetic storage ring because a beam with an initial orbital tensor polarization acquires a horizontal orbital vector polarization. The electric quadrupole moment is rather large and strongly influences the dynamics of the intrinsic orbital angular momentum. Three different methods of its measurements, freezing the intrinsic orbital angular momentum and two resonance methods, are proposed. The existence of the quadrupole moment of twisted electrons can lead to practical applications.