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 a tom 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 th e delta(E - E') normalization in the context of parabolic coordinates. The method is applied to the study of hydrogen photoionization from the fundame ntal (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 al so discussed for the study of Stark energies of hydrogen. The results are c ompared with other accurate calculations when available.