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Journal of Physics B Atomic and Molecular Physics

Multiphoton ionisation cross sections: a correlation function approach

Giovanni P. Arrighini, F Biondi, Carla Guidotti

Published May 14, 1986• 8 citations
Publisher

Abstract

N-photon ionisation cross sections obtained by perturbation theory treatments are expressed in terms of Fourier transforms of appropriate autocorrelation functions. As expected, the N=1 case is related to the well known electric dipole-dipole autocorrelation function, while correlation of increasingly complicated operators is involved as N=1, 2, 3, . . .. A simple application of the formalism to the evaluation of one- and two-photon cross sections for a schematic model of the negative ion H - is presented.

DOI
10.1088/0022-3700/19/9/012

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Journal of Physics B Atomic and Molecular Physics•Oct 14, 1979•6 citations
N-photon ionisation cross sections obtained by perturbation theory treatments are expressed in terms of Fourier transforms of appropriate autocorrelation functions. As expected, the N=1 case is related to the well known electric dipole-dipole autocorrelation function, while correlation of increasingly complicated operators is involved as N=1, 2, 3, . . .. A simple application of the formalism to the evaluation of one- and two-photon cross sections for a schematic model of the negative ion H - is presented.
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.
A theory of two-photon ionisation of atomic systems is developed incorporating into the treatment details of the laser spectrum. A general expression for the time-integrated two-photon ionisation probability is obtained together with general expressions for the induced shifts and widths of the atomic levels. These expressions are valid near resonance, when in the ordinary perturbation treatment the energy denominators vanish. The general expressions are then evaluated for the special case of a Lorentzian laser spectrum, when simple analytic results are obtained. The treatment is not confined to the two-level atom or the rotating-wave approximation.
The infinite summations over the complete set of unperturbed atomic states appearing in the Nth-order time-dependent perturbation theory are performed using the Green's function formalism. In order to test the method extended calculations of the cross section for two- and three-photon ionization for atomic hydrogen are made and numerical comparison is shown with the values obtained by different methods. The resonant character of the process is made evident since the poles of the radial part of the Green's function represent the actual energy spectrum of the atom. The relevant transition matrix elements are written in closed form and then computed exactly without averaging over the intermediate states. The cross sections vanish for circularly polarized light near some energies which explains the form of the cross sections for circularly and linearly polarized light.