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
10p2P23 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{}
(photonflux)2.
A perturbation theory of the ionization of atoms by simultaneous absorption of several photons, each of whose energy is less than the ionization potential, is developed from the evolution-operator formalism. A precise computation is made for the hydrogen atom, giving transition rates as a function of photon energy for two- through twelve-photon photoionization. The eighth-order ionization rate (in cgs units) at the 1.78-eV ruby-laser line is found to be \ensuremath{\sim}${10}^{\ensuremath{-}244}$\ifmmode\times\else\texttimes\fi{}
(photonflux)8 and should be observable using available techniques. Good agreement is obtained with Zernik's exact calculation of the two-photon ionization rate of metastable
2S hydrogen. Approximate calculations are made for the rare gases. Assuming "typical" experimental conditions of a gas density of \ensuremath{\sim}
1020 atoms ${\mathrm{cm}}^{\ensuremath{-}3}$ and a ruby laser focused into a volume of \ensuremath{\sim}${10}^{\ensuremath{-}8}$
cm3, we find that the flux required to liberate one electron during a 10-nsec pulse is \ensuremath{\sim}
1029 ${\mathrm{cm}}^{\ensuremath{-}2}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ for Xe, Kr, and Ar and \ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}
1030 photons ${\mathrm{cm}}^{\ensuremath{-}2}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ for Ne and He. These gases ionize with the simultaneous absorption of 7, 8, 9, 13, and 14 photons, respectively. The predicted rate for Xe is found to be in excellent agreement with the recent direct measurements of Voronov and Delone. We conclude that multiphoton ionization provides the initial electrons required for the optical breakdown of gases, though it does not account for the over-all growth of the discharge except possibly at very low pressures. Impurity atoms (particularly heavy rare gases) may be the source of "initiating" electrons in Ne and He.
Orer a small range of light intensity the three-photon ionization rate of caesium atoms by ruby laser light decreases when the incident photon flux is increased. This result may be quantitatively explained by an induced energy shift of the 913 levels of the caesium atom proportional to the square of the light intensity. Thus perturbations of bound electron states by an intense light beam can be of importance in determining the multiphoton ionization rate. In this paper the functional dependence of the ionization rate on the photon flux is calculated for caesium, using a perturbation theory somewhat different from that usually employed.
A theoretical method previously developed for the two-photon ionization of alkali-metal atoms is extended to the spin-orbit coupling scheme. We have obtained the Green's function of this problem in the framework of quantum-defect theory and so we have been able to perform the infinite summations related to perturbation theory. The generalized transition probability rates are calculated in the off-resonant and resonant regions, respectively, for polarized incident radiation. Destructive interference effects between the unperturbed atomic states in the infinite summations producing a finite deep minimum in the off-resonant region, are predicted by our theory, both for linearly and circularly polarized incident radiation. A detailed calculation of electron-spin polarization is given. Comparisons of values predicted by the present work with experiment and other theoretical calculations are made for the case of atomic cesium initially in the ground
6S state.
Single mode ruby laser radiation (694 nm) and an atomic beam apparatus have been used in the study of the three photon ionization of Na, K, Rb, and Cs atoms. The process in all cases is nonresonant, the observations being consistent with a rate given by W3F3 where F is the photon flux. The values obtained for W3l (linear polarization) and W3C (circular polarization) and the ratio W3c/W3l are discussed in relation to recently calculated results and the few other experimental results available. Discrepancies well beyond the assigned errors exist between experimental and calculated results.
The dynamical process of photoexcitation and photoionization of alkali atoms is studied with three-step laser pulses, focusing on the similarities and differences between Li and Cs atoms on their properties by making a comparison of them. Based on several excitation schemes, the present work not only establishes the rate equations of atom population for all related transition states, but also obtains the analytical solutions of photoexcitation and photoionization process. The mathematical solutions are simplified significantly by restricting the most general case to the several special cases, either designed or selected carefully, in order to highlight the main factors and obtain the physical insight underlying the complicated mathematical expressions. With self-programming, the possible impact of time configuration of laser pulses on the three-step laser excitation process of the photoexcitation and photoionization is calculated and studied systematically. Variation of the ionization efficiency with the laser parameters is investigated and discussed. With the same time configuration of laser pulses, the dependences of atom population for all the related transition states on the two different excitation paths are compared and analyzed, reflecting the impact of changing the atomic parameters. Under the similar excitation conditions, the differences of ionization efficiency between Li and Cs atoms are explored. Finally, based on the present study, several means for optimizing ionization efficiency are proposed.