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Journal of Physics B Atomic and Molecular Physics

Multiphoton ionization of hydrogenic atoms and the breakdown of perturbative calculations at high intensities

Farhad H. M. Faisal

Published Oct 1, 1972• 11 citations
Publisher

Abstract

A non-perturbative method is used to obtain an analytic expression for the rate of multiphoton ionization of hydrogenic atoms as a function of the incident radiation. The result shows that at low intensities the ionization rate is similar to that obtained in the usual perturbative calculations. With increasing intensities, however, the perturbative result is violated and the ionization rate is found to depend not only on the Nth power of intensity but on higher powers as well.

DOI
10.1088/0022-3700/5/10/002

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An Introduction to Multiphoton Ionization and Study of Ionization Rate of Hydrogen Atom

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Himalayan Physics•Dec 26, 2012•1 citation
A non-perturbative method is used to obtain an analytic expression for the rate of multiphoton ionization of hydrogenic atoms as a function of the incident radiation. The result shows that at low intensities the ionization rate is similar to that obtained in the usual perturbative calculations. With increasing intensities, however, the perturbative result is violated and the ionization rate is found to depend not only on the Nth power of intensity but on higher powers as well.
An approximate non-perturbative theory of multiphoton ionization of a hydrogen atom by two strong radiation fields is outlined. The special case is then considered for when one of the fields is of low intensity and high frequency and the other field is of high intensity and low frequency. A set of representative calculations has been performed for this case; that is, (a) angular distributions for given numbers of absorbed and emitted low-frequency photons and different geometries; (b) total cross-sections versus the strong-field intensity; (c) angular distributions summed over all the low-frequency photon exchanges, showing a fourfold symmetry in a geometry in which each ionization channel exhibits, instead, only a twofold symmetry; (d) the average energy gained by the ejected electrons. Calculations are performed for a strong low-frequency field of arbitrary polarization. In many respects, the present calculations are expected to complement those of single-field multiphoton ionization. It is hoped that the results of the calculations reported here may prompt systematic measurements also in this new class of processes, as the predictions are well within the state of the art of present multiphoton-ionization experiments.
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 work reports multiphoton ionization and dissociation of molecular hydrogen under the influence of laser radiation at 0.53 $\ensuremath{\mu}$. The six-photon ionization probability of hydrogen atoms is derived for laser radiation acting upon atomic hydrogen from a molecular hydrogen beam which is up to 80% dissociated by radio-frequency power. The experimental six-photon ionization probability of atomic hydrogen has been found to be in good agreement with the corresponding probability calculated using time-dependent perturbation theory if the statistical properties of the incident light are taken into account.
We have discussed the problems of non linear interaction between electromagnetic radiations with atoms from semi-classical point of view. Time dependent Schrödinger equation for single electron system is solved by using perturbative technique to obtain transition probability. Higher order perturbation is also discussed which is used in multiple processes, in which two or more quanta are emitted instead of a single photon. The theory is based on assumption that the perturbation is small. From this transition probability ionization rate and absorption cross-section of hydrogen atom is calculated. Its variation with photon energy and field strength is analyzed which agrees very well with experimental observations.The Himalayan PhysicsVol. 3, No. 32012Page : 40-43