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Journal of Physics B Atomic and Molecular Physics

The role of the wavelength in a statistical description of multiphoton ionisation

Michele Crance

Published Oct 14, 1984• 7 citations
Publisher

Abstract

The authors derive an approximate formula for multiphoton ionisation cross sections valid for complex atoms when processes are not resonant. They show that the dependence of the frequency and the order of the process is fully contained in an atomic quantity similar to a cross section. For optical field excitation the variation range of the latter quantity is rather small. The trend of experimental results are well reproduced by the author's calculation.

DOI
10.1088/0022-3700/17/19/003

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Journal of Physics B Atomic and Molecular Physics•Nov 14, 1984•21 citations
The authors derive an approximate formula for multiphoton ionisation cross sections valid for complex atoms when processes are not resonant. They show that the dependence of the frequency and the order of the process is fully contained in an atomic quantity similar to a cross section. For optical field excitation the variation range of the latter quantity is rather small. The trend of experimental results are well reproduced by the author's calculation.
Perturbation theory of multiphoton ionisation due to a classical electromagnetic field is modified to allow for intermediate resonances with bound states. Complex energies, generally associated with resonances, do not enter into this formalism. For a monochromatic field of frequency u, a constant ionisation rate can then be defined unambiguously and only such continuum states are excited which correspond to the absorption of energy in integral multiples of hu. As an application, differential and total cross sections for the two-photon ionisation of hydrogen, for frequencies below the n = 3 resonance region, are obtained in closed form. Existing data for generalised cross sections, calculated numerically using the complex coordinate method, are in good agreement with the present results. Finally, the mean fractional ionisation resulting from a pulse of finite duration is estimated on the basis of the associated power spectrum. For short pulses, the time dependence of ionisation exhibits a departure from that expected of a time-independent rate.
Four-photon ionisation of caesium requires strong electromagnetic fields and the usual interpretation in terms of generalised cross sections has to be questioned. A theoretical calculation in the experimental conditions of a recent measurement provides a new interpretation of the results of Morellec and Normand (1979): the effect of light shifts masks the effect of saturation and leads one to overestimate the multiphoton ionisation cross section. The expected overestimation is only 25 per cent for the quoted experiment, but could be larger in some other physical cases.
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 a recent experiment involving multiphoton ionisation of Xe it was found that the photoelectron spectrum contained peaks which corresponded to absorption of more than the minimum number of photons required ionise. The effective orders of nonlinearity, furthermore, showed a striking uniformity. The authors investigated these effects with a model approximation consisting of a single bound state and m continua. Simple analytic expressions are obtained for the quantity measured in the experiment and the limit m to infinity is obtained. The results show good qualitative agreement with experiment.