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Physical Review

Multiphoton Ionization of Atomic Hydrogen in the Ground State

Yves Gontier, M. Trahin

Published Aug 5, 1968• 133 citations
Publisher

Abstract

The general theory of multiphoton ionization of hydrogen atoms by simultaneous absorption of several photons is discussed. In the nonrelativistic dipole approximation, the calculations lead to a recursion relationship concerning angular functions and involve radial matrix elements containing many summations over intermediate states. A general method for exactly evaluating several sums is described in detail and applied to the photo-ionization of atomic hydrogen in the ground state. Numerical results are presented as dispersion curves of the transition rate $\frac{{\ensuremath{\sigma}}_{n}}{{I}^{N\ensuremath{-}1}}$ for a range of wavelengths from 1000 up to 7200 \AA{}.

DOI
10.1103/physrev.172.83

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Physical Review A•Feb 1, 1988•52 citations
The general theory of multiphoton ionization of hydrogen atoms by simultaneous absorption of several photons is discussed. In the nonrelativistic dipole approximation, the calculations lead to a recursion relationship concerning angular functions and involve radial matrix elements containing many summations over intermediate states. A general method for exactly evaluating several sums is described in detail and applied to the photo-ionization of atomic hydrogen in the ground state. Numerical results are presented as dispersion curves of the transition rate \ensuremathσnIN\ensuremath−1\frac{{\ensuremath{\sigma}}_{n}}{{I}^{N\ensuremath{-}1}}IN\ensuremath−1\ensuremathσn​​ for a range of wavelengths from 1000 up to 7200 \AA{}.
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.
This paper illustrates the study on asymmetry of the angular distribution of the ejected electrons in a multiphoton process from the ground state of a hydrogen atom. General expressions for the multiphoton ionization rates have been derived based on a variation of the Dalgarno–Lewis method for the evaluation of matrix elements in higher order perturbation theory. In addition, these analytical expressions for the various multiphoton transition rates and their variation as a function of polarization, phase, frequency and intensity of the incident radiation have been studied extensively. The general expression obtained can be used to analyse any number of incident beams with arbitrary polarization, phase and intensity.
The general expression for the amplitude of the probability of ionisation by a multiphoton absorption process is derived. Its non-relativistic limit is taken and the bipolar approximation is used for calculating the ionisation cross-section of hydrogen-like atoms. This latter involves the summation over intermediate virtual states by means of: a) a recursion relationship concerning angular functions, b) a particular technique which when applied to radial functions makes it possible to solve a system of inhomogeneous first-order differential equations. (authors) [French] On etablit l'expression generale de l'amplitude de probabilite d'ionisation par un processus d'absorption multiphotonique. On en prend la limite non-relativiste et l'on utilise l'approximation dipolaire avant de calculer la section efficace d'ionisation d'atomes hydrogenoides. Cette derniere fait intervenir des sommations sur des etats virtuels intermediaires effectuees a l'aide: a) d'une relation de recurrence qui concerne les fonctions angulaires, b) d'une technique particuliere qui, appliquee aux fonctions radiales, conduit a resoudre un systeme d'equations differentielles inhomogenes du premier ordre. (auteur)
In this paper, we have presented the analytical and numerical calculations of the ionization rate (σ/I in units of cm4∙W−1) for the hydrogen atom in the ground state. The summation over infinite intermediate states, discrete plus continuous, has been carried out using our modified technique based on Bebb and Gold's concept of average frequency. Our method improves the results of Bebb and Gold at all frequencies, and the results obtained are in good agreement with the results of Gontier and Trahin, Chan and Tang, and Klarsfeld.
The strong-field multiphoton ionization of atoms is considered and a theoretical approach dealing nonperturbatively with the radiation field formulated. The general computational scheme is the conventional perturbation theory, but the intermediate states are dressed by the field. We present in detail a method to dress the continuum states and to study the dipole transitions within the continuum. In the high-frequency domain, the proposed procedure rapidly converges over a wide range of field intensity and offers an interesting framework for calculating ionization rates for arbitrary numbers of absorbed (above-threshold) photons and field polarization.
Multiphoton ionization of hydrogen atoms by a strong multimode field when several final continuum states are populated is treated theoretically within a model based on the S-matrix formalism. The field is taken in dipole approximation, with zero bandwidth. Field-dressed Coulomb wave functions are used for the electron final states. Ionization rates are calculated for different numbers of photons absorbed in excess of the minimum number required to go into the continuum. In general, the calculated quantities are in good qualitative agreement with the corresponding experimental observations.