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Journal of Physics B Atomic and Molecular Physics

Multiphoton transitions. IV. Bound-free transition integrals in compact forms

Farhad H. M. Faisal

Published Mar 1, 1973• 9 citations
Publisher

Abstract

For pt. III see abstr. A11153 of 1973. The basic integrals appearing in the N-photon T-matrix for ionization of neutral atoms and electron detachment of negative ions are obtained in compact forms both for circular polarization as well as for linear polarization of incident radiation. The present results circumvent the often lengthy procedure of summing the partial amplitudes and provide a basis for investigating physically interesting limits of multiphoton transitions, analytically.

DOI
10.1088/0022-3700/6/3/023

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For pt. III see abstr. A11153 of 1973. The basic integrals appearing in the N-photon T-matrix for ionization of neutral atoms and electron detachment of negative ions are obtained in compact forms both for circular polarization as well as for linear polarization of incident radiation. The present results circumvent the often lengthy procedure of summing the partial amplitudes and provide a basis for investigating physically interesting limits of multiphoton transitions, analytically.
The theory of multiphoton ionization for an atomic system of arbitrary complexity is developed using a density matrix formalism. An expression is obtained which determines the differential N-photon ionization cross section as a function of the polarization states of the target atom and the incident radiation. The parameters which characterize the photo-electron angular distribution are related to the general reduced matrix elements for the N-photon transition. Two-photon ionization of unpolarized atoms is treated as an illustration of the use of the theory. The dependence of the multiphoton ionization cross section on the polarization state of the incident radiation, which has been observed in two- and three-photon ionization of Cs, is accounted for by the theory. Finally, the photoelectron spin polarization produced by the multiphoton ionization of unpolarized atoms, like the analogous polarization resulting from single-photon ionization, is found to depend on the circular polarization of the incident radiation.
The infinite summations over the complete set of unperturbed atomic states appearing in the NNNth-order perturbation theory for multiphoton ionization are performed using the Dalgarno-Lewis method. The relevant transition matrix elements are written in a closed integral form exhibiting all the analytic properties of the amplitude as a function of incident photon energy. The cross sections for two- and three-photon ionization for atomic hydrogen are calculated for both linearly and circularly polarized light with a wide range of photon energy spectrum including the near resonance, and numerical comparison is made with the values obtained by different methods.
In the first part of this thesis, a new variational principle is presented for the calculation of perturbative transition amplitudes of any order but free from any singularities. Applications are made to the multiphoton ionization and harmonic generation for atomic hydrogen. Its formulations in hyperspherical coordinates as well as in Hartree-Fock representation are also presented. In the second part of this thesis, theories for multiphoton detachment in a static electric or magnetic field are developed. They are based on the analytic solutions of an electron in the combined field of a laser and a static electric or magnetic field, and, therefore, are nonperturbative in both the laser intensity and the static electric or magnetic field strength. Heretofore unexpected cyclotron resonances, which are due to the infinite range character of the electron-photon coupling induced by the external magnetic field, are shown to exist under certain conditions.