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 (OAM). 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.
Highlights
While a twisted electron is a single pointlike particle described by the standard Dirac equation, its wave function has a nontrivial spatial structure
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
We demonstrate for the first time that a twisted spin1/2 particle can possess a large measurable electric quadrupole moment (EQM) and a tensor magnetic polarizability (TMP)
Summary
Its appearance results in a small correction to the spin precession frequency. The sign of this correction is defined by the sign of Lz. The EQM of the twisted electron can be measured by the magnetic-resonance method In this case, a constant electric field is not needed. We expect that the existence of the EQM of twisted electrons can find practical applications because the EQM interaction with nonuniform electric fields in matter depends on the intrinsic-OAM direction. Electron vortex beams in a magnetic field: A new twist on Landau levels and Aharonov-Bohm states, Phys. Bandyopadhyay, Electron vortex beams in a magnetic field and spin filter, Phys. B. Gotte, Nonuniform currents and spins of relativistic electron vortices in a magnetic field, Phys. J. Silenko, Potential for the measurement of the tensor electric and magnetic polarizabilities of the deuteron in storage-ring experiments with polarized beams, J. We consider the initial orbital tensor polarization which differs in sign and value from the above-mentioned polarization
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