Systematic theoretical study of the Stark spectrum of atomic hydrogen. I. Density of continuum states

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Abstract
An exact method which allows the authors to obtain normalised wavefunctions for a hydrogen-like atom in the presence of a uniform electric field is reported. An unambiguous classification of the Stark states is presented which correlates a given Stark state to a unique zero-field state; this classification is valid for any Stark states-resonant or non-resonant-and at any energy smaller or greater than E0 the ionisation limit of the unperturbed atom. From the supersymmetry in the hydrogen spectrum, states with different values for m, the magnetic quantum number, or for n1, the generalised parabolic quantum number, can be considered independently. A parabolic critical energy can be defined for any state m, n1; for sufficiently high value of n1 the critical energy is greater than E0. A systematic study of the positions and widths of the resonance in a broad energy range below E0 is presented.