Revisiting the problem of positronium moving across a magnetic field

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).