Dynamic hyperpolarizability and two-photon detachment in the presence of astrong static electric field: Application to H- - art. no. 023417

Our recent analysis [J. Phys. B 33, R141 (2000)] of the problem of H- in bo th laser and strong static electric fields, which treated effects that are linear in the laser intensity I (e.g., the dynamic polarizability and the s ingle-photon detachment cross section), is extended here to treat effects o f higher order (similar toI(2)) in the laser intensity (e.g., the dynamic h yperpolarizability, the two-photon detachment cross section, the linear in I corrections to the single-photon detachment rate, etc). We introduce the concept of the dynamic hyperpolarizability of an atom in the presence of a strong electric field based on the complex quasienergy approach with proper ly normalized, quasistationary quasienergy wave functions. Our analysis of the general structure of the dynamic hyperpolarizability tensor of an atom in a nondegenerate (S-) state is performed for arbitrary field geometries a nd laser polarizations. The connection of the hyperpolarizability gamma (F; omega) to the complex quasienergy and to atomic ionization rates is establ ished. Analytic results (in terms of Airy functions) are obtained for five irreducible components of a hyperpolarizability tensor (that are independen t of the laser polarization and the field geometry) for the case of a weakl y bound electron in a three-dimensional, zero-range potential. These result s are used for the analysis of the frequency, field geometry, and laser pol arization dependence of the two-photon detachment rate as well as of the li near in laser intensity corrections to the single-photon detachment rate. I t is shown that the oscillatory behavior of the frequency dependence of bot h the real and the imaginary parts of gamma (F; omega) exists for both the coplanar and orthogonal field geometries, and that this behavior is qualita tively different for frequencies below and above the single-photon detachme nt threshold. The threshold behavior of the two-photon detachment rate is a nalyzed in detail and the static electric-field-induced modification of Wig ner's threshold law for a short-range potential is discussed.