Radiative widths and splitting of cyclotron lines in superstrong magnetic fields

We calculate the radiative line widths of the Landau levels in a superstrong magnetic field and give simple analytic expressions and fits for these which are valid over a wide range of the principal quantum number and the magnetic field strength. If one does not allow for QED corrections, all levels but the first are doubly degenerate, corresponding to the two possible spin projections. However, the interaction with the QED vacuum removes this degeneracy, leading to an energy splitting of each level which exceeds the radiative line width for low Landau levels if the magnetic field is not too large (B ≲ 10¹³ G). We present estimations of the splitting in various limits as a function of field strength and Landau number. The possibility of observing this splitting in accreting X-ray pulsars and in gamma-ray bursters is discussed.