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 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.

Journal of Physics B Atomic and Molecular PhysicsAug 1, 197328 citations

One- and two-photon ionization of model atoms

Giovanni P. Arrighini, Carla Guidotti, N. Durante

Il Nuovo Cimento DApr 1, 198610 citations

Quantitative Theory of the Two-Photon Ionization of the Alkali Atoms

H. Barry Bebb

The theory of two-photon ionization of the alkali atoms is developed from the well-known perturbation formula for the second-order transition rate. Quantum defect Coulomb functions are used for both the negative and positive energy states. Spin-orbit splitting of the intermediate $p$ states is taken into account. The results are presented as dispersion curves of the transition rate for photon energies between the two-photon and one-photon thresholds. Cesium is of particular interest because the photon energy for the second harmonic of ruby laser light falls very near the $10{p}^{2}{P}_{\frac{3}{2}}$ level. For a photon energy of 3.57 eV, the transition rate (in cgs units) is found to be 2.6\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}49}$\ifmmode\times\else\texttimes\fi{} ${(\mathrm{photon}\mathrm{flux})}^{2}$ .The theory of two-photon ionization of the alkali atoms is developed from the well-known perturbation formula for the second-order transition rate. Quantum defect Coulomb functions are used for both the negative and positive energy states. Spin-orbit splitting of the intermediate $p$ states is taken into account. The results are presented as dispersion curves of the transition rate for photon energies between the two-photon and one-photon thresholds. Cesium is of particular interest because the photon energy for the second harmonic of ruby laser light falls very near the $10{p}^{2}{P}_{\frac{3}{2}}$ level. For a photon energy of 3.57 eV, the transition rate (in cgs units) is found to be 2.6\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}49}$\ifmmode\times\else\texttimes\fi{}${(\mathrm{photon}\mathrm{flux})}^{2}$.

Physical ReviewSep 9, 1966139 citations

Theory of Three-Photon Ionization of the Alkali Atoms

H. Barry Bebb

Three-photon ionization transition rates are calculated for the alkali atoms (except Li) using quantum defect Coulomb functions to evaluate the well-known perturbation formula. Several corrections of previous work are mentioned. The often-used approximation of keeping only a small number of intermediate states is investigated. The predicted three-photon ionization rate (in cgs units) of the alkalis for the ruby photon energy of 1.78 eV is of the order of ${10}^{\ensuremath{-}77}$ \ifmmode\times\else\texttimes\fi{} ${(\mathrm{photon}\mathrm{flux})}^{3}$ . Detailed results are presented as dispersion curves of the transition rate for photon energies between the three-photon and two-photon thresholds.Three-photon ionization transition rates are calculated for the alkali atoms (except Li) using quantum defect Coulomb functions to evaluate the well-known perturbation formula. Several corrections of previous work are mentioned. The often-used approximation of keeping only a small number of intermediate states is investigated. The predicted three-photon ionization rate (in cgs units) of the alkalis for the ruby photon energy of 1.78 eV is of the order of ${10}^{\ensuremath{-}77}$ \ifmmode\times\else\texttimes\fi{} ${(\mathrm{photon}\mathrm{flux})}^{3}$. Detailed results are presented as dispersion curves of the transition rate for photon energies between the three-photon and two-photon thresholds.

Physical ReviewJan 5, 196772 citations

Multiphoton Transitions in the Ionization Continuum of Atoms

Pierre Agostini, G. Petite

Springer eBooksJan 1, 19843 citations

p

states is taken into account. The results are presented as dispersion curves of the transition rate for photon energies between the two-photon and one-photon thresholds. Cesium is of particular interest because the photon energy for the second harmonic of ruby laser light falls very near the

10{p}^{2}{P}_{\frac{3}{2}}

level. For a photon energy of 3.57 eV, the transition rate (in cgs units) is found to be 2.6\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}49}$\ifmmode\times\else\texttimes\fi{}

{(\mathrm{photon}\mathrm{flux})}^{2}

{(\mathrm{photon}\mathrm{flux})}^{3}

. Detailed results are presented as dispersion curves of the transition rate for photon energies between the three-photon and two-photon thresholds.