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.
The development of methods of generation of ultrashort pulses (USP) of femto- and attosecond duration ranges with controlled parameters necessitates the theoretical study of features of their interaction with a matter [1]. Among such features that do not exist in case of “long” pulses should first of all be the nonlinear dependence of the photoprocess probability W on the USP duration (τ) [2] as well as the dependence on the carrier phase with respect to the pulse envelope (φ) [3-4]. It should be noted that if the dependence of the probability W on the phase φ manifests itself either only for very short pulses, when ωτ < 1 (ω is carrier frequency of the pulse), or in case of a nonlinear photoprocess [3], the function W(τ) can differ from a linear function in the limit ωτ> 1 too for fields of moderate strength, when the perturbation theory is applicable [2].
Theoretical pseudopotentials and dispersion potentials are used to study ground-state hyperfine splitting frequencies of alkali-metal atoms (Li, Na, K, Rb, and Cs) in noble gases (He, Ne, Ar, Kr, and Xe) in all combinations. With a single fitting parameter, calculations based on first-order perturbation theory qualitatively present each temperature dependence of the measured frequency shift. With this parameter and excitation energies of alkali-metal and noble-gas atoms, the hyperfine splitting frequency of alkali-metal atoms is suitable for investigating the properties of noble-gas atoms, such as the s-wave scattering length of electrons, the electric-dipole polarizability, and the van der Waals radius. This study suggests the possibility of improving excitation energies and van der Waals potentials of colliding pairs.