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

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 E 0 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 n 1 , the generalised parabolic quantum number, can be considered independently. A parabolic critical energy can be defined for any state m, n 1 ; for sufficiently high value of n 1 the critical energy is greater than E 0 . A systematic study of the positions and widths of the resonance in a broad energy range below E 0 is presented.