The hydrogen atom in an external DC electric field: the discretization approach

We propose a finite element approach to treat the problem of the hydrogen atom in a static electric field. We show the efficiency of a L2 basis set, i.e. B-spline functions. Particular attention is placed on the problem of the delta(E - E') normalization in the context of parabolic coordinates. The method is applied to the study of hydrogen photoionization from the fundamental (1s) and excited (n = 2, 3, 4) states in a weal; external DC electric field. Oscillator strengths have been calculated in the region of the field-fret atomic threshold. The pertinence of the finite element approach is also discussed for the study of Stark energies of hydrogen. The results are compared with other accurate calculations when available.