Revisiting the Problem of Positronium Moving Across a Magnetic Field

TL;DR

This paper analyzes how positronium behaves when moving across a magnetic field, revealing complex energy spectra and potential implications for pulsar radio emission suppression.

Contribution

It provides an analytical determination of the positronium energy spectrum in a magnetic field considering pseudomomentum, a novel approach for this problem.

Findings

Energy spectrum determined analytically for various magnetic fields and pseudomomenta.

Identification of the outer potential well where the ground state resides.

Comparison of ground state energy with Bethe-Salpeter equation results.

Abstract

Positronium spectrum and lifetimes are known with high precision. The situation is different for positronium moving across a magnetic field. The total momentum does not commute with the Hamiltonian and is replaced by the conserved pseudomomentum. The internal dynamics is not separated from the motion of the system as a whole. The Coulomb potential well is distorted and a wide outer potential well is created. We analytically determine the energy spectrum for a broad range of magnetic field and pseudomomentum values. The ground state energy is compared with the result obtained by solving the Bethe-Salpeter equation. The gauge independence of the pseudomomentum expectation value is established. On the pseudomomentum-magnetic field plane we locate the region in which the ground state resides in the outer well. The results may play a role in the suppression of pulsars' radio emission (polar cap problem).