Effect of closed classical orbits on quantum spectra: Ionization of atoms in a magnetic field. II. Derivation of formulas

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Abstract
A formula is derived for oscillations in the near-threshold absorption spectrum of an atom in a magnetic field. Three approximations are used. (1) Near the atomic nucleus, the diamagnetic field is negligible. (2) Far from the nucleus, the waves propagate semiclassically. (3) Returning waves are similar to (cylindrically modified) Coulomb-scattering waves. With use of these approximations, together with the physical picture described in the accompanying paper, an algorithm is specified for calculation of the spectrum.