Analytical S-matrix derivation in the theory of the nonhydrogenic Stark effect

An analytical scattering matrix is found for Rydberg atoms in external electrica#13; field at negative energies. The exact relation between the Coulomb sphericala#13; and parabolic irregular solutions is obtained, which is then used to find thea#13; physical solution of the Stark problem bounded at infinity and satisfying thea#13; quantum-defect boundary condition within the region next to the ion core wherea#13; the external field does not mix the states with definite orbital momentum. Thea#13; S matrix thus found can be used for interpreting various experimental data,a#13; such as positions and widths of lines in the photo-absorption spectra,a#13; photoionization cross-section, and ionization microscopy.