Energy levels and oscillator strengths for the two-body problem in magnetic fields

The magnetic field dependence of the physical properties derived from the solution of the two-body problem for an electron and a proton in a magnetic field is investigated. The scaling properties of the general problem of two charged particles in a magnetic field are discussed, and it is shown that the continuous magnetic field dependence of physical properties including energies and dipole matrix elements can be approximated by low-degree polynomials. The continuous magnetic field dependence of the lowest energy levels and corresponding oscillator strengths of the hydrogen atom in the limit of infinite proton mass are then examined in detail for magnetic fields from 0 to 4.7 x 10 to the 13th gauss. It is noted that the results have important applications for the hydrogen atom with a finite proton mass, positronium and the complete isoelectronic series of hydrogen in magnetic fields of intensities up to those characteristic of neutron stars.