Combined Zeeman and Motional Stark Effects in the First Excited State of Positronium

Calculations are presented of the combined Zeeman- and Stark-effect level shifts in the $n=2\mathrm{}$ excited states of positronium, for positronium moving perpendicular to an applied magnetic field. Lifetimes of the Zeeman- and Stark-mixed $n=2\mathrm{}$ states are also calculated. The electric field results from the Lorentz transformation of the magnetic field to the rest frame of the positronium and is perpendicular to the magnetic field. The level shifts and lifetimes are calculated by diagonalizing the 16×16 Hamiltonian matrix for positronium in crossed electric and magnetic fields. The unperturbed energy eigenvalues calculated by Fulton and Martin are used as the diagonal elements of the Hamiltonian.