Long-lived states of positronium in crossed electric and magnetic fields

Abstract

The problem of a two-body Coulomb system in crossed electric and magnetic fields has a long history. Unlike the field-free case, the center of mass motion cannot be separated from the internal motion. When center of mass effects are treated correctly, the crossed fields problem and the problemof transverse motion in a pure magnetic field can be treated in a unified manner. For a neutral system, the total pseudomomentum b K 1⁄4 b P ðe=2ÞB r is a conserved quantity and one can carry out a pseudoseparation of the Hamiltonian. The effective potential for the internal motion depends on j, the eigenvalue of the pseudomomentum.When j exceeds a critical value, a local minimum and maximum form on the potential surface, giving rise to a second potential well. This outer well (OW), which is separated from the Coulomb well (CW) by a barrier, can support bound states. The OW states are characterized by a large interparticle separation. With increasing j, the CW becomes narrower and the CW states are pushed into the continuum; in contrast, the OW moves further from the origin and widens, supporting more and more bound states. We have carried out a systematic study of positronium in crossed fields as a function of field strength and pseudomomentum. By a direct numerical solution of the 3D Schr€ odinger equation, we obtained the complete energy spectrum and corresponding wave functions. We also developed accurate approximation techniques for the low field regime. Our results indicate that the bound states of positronium that reside in the OW are stable against direct annihilation due to the near zero probability for positron–electron overlap. Radiative decay from an OW state to a CW state is also suppressed because the OW and CW wave functions are separated spatially by the barrier. Even at laboratory field strengths, it should be possible to create long-lived positronium. This suggests a mechanism for storing energy using antimatter.