A simple analytic formula for the photodetachment cross section of H in an electric field is derived. The formula becomes identical to a formula derived many years ago in the vanishing-field limit. Three special features appear in the cross section in the presence of an electric field: a quantum tunneling effect, a new threshold law, and oscillations. These appear when the photon energy is, respectively, less than, equal to, or greater than the binding energy of H . Enough information is provided in this paper so that one can calculate the cross section quickly.

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This is the first of two papers that develop the theory of oscillatory spectra. When an atom is placed in a magnetic field, and the absorption spectrum into states close to the ionization threshold is measured at finite resolution, so that individual energy levels are not resolved, it is found that the absorption as a function of energy is a superposition of sinusoidal oscillations. These papers present a quantitative theory of this phenomenon. In this first paper, we describe the physical ideas underlying the theory in the simplest possible way, and we present our first calculations based upon the theory. In the second paper, the theory is developed in full detail, proofs of all of the assertions are given, and we describe the algorithm that was used to make the calculations.