We propose a finite-element approach with prolate spheroidal
coordinates to calculate, for one-electron diatomic molecules,
ac Stark shifts and multiphoton ionization cross-sections in
lowest-order perturbation theory. We use B-spline expansions to
represent both angular and radial parts of the wavefunctions.
The method takes advantage of the fact that the Schrödinger equation is
separable with prolate spheroidal coordinates. The effective
completeness of the basis set leads to an accurate
representation of the molecular spectrum. Partial
cross-sections, associated with each open continuum, are
calculated. Particular attention is placed on the problem of
the normalization of the discretized continua. We show that the
proper normalization is simply obtained from a density of
states, thus the explicit evaluation of the continua at large
distances is not necessary. Accurate values of energies,
shifts, one-, four- and six-photon ionization cross-sections
are obtained in lowest-order perturbation theory and they are
compared with other calculations when available.