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Physical Review A

Above-threshold ionization in the x-ray regime

Hari R. Varma, Marcelo F. Ciappina, Nina Rohringer, Robin Santra

Published Nov 30, 2009• 31 citations

Abstract

Two-photon above-threshold ionization processes in the x-ray regime are studied using atomic hydrogen as a model system. Within the minimal-coupling formalism of nonrelativistic quantum electrodynamics, two distinct interactions---$\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{A}}\ensuremath{\cdot}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{p}}$ in second order and ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{A}}}^{2}$ in first order---contribute to the two-photon absorption amplitude. The relative importance of these two interactions is assessed. It is found that above a photon energy of 6.8 keV, the contribution from ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{A}}}^{2}$ to the total two-photon absorption cross section dominates. In this high-energy regime, above-threshold ionization is a nonsequential purely nondipole process. Rate equations are employed to calculate the probabilities of ionization by Compton scattering, one-photon absorption, and two-photon absorption.

DOI: 10.1103/physreva.80.053424

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Two-photon above-threshold ionization processes in the x-ray regime are studied using atomic hydrogen as a model system. Within the minimal-coupling formalism of nonrelativistic quantum electrodynamics, two distinct interactions---

\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{A}}\ensuremath{\cdot}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{p}}

in second order and

{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{A}}}^{2}

in first order---contribute to the two-photon absorption amplitude. The relative importance of these two interactions is assessed. It is found that above a photon energy of 6.8 keV, the contribution from

{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{A}}}^{2}

to the total two-photon absorption cross section dominates. In this high-energy regime, above-threshold ionization is a nonsequential purely nondipole process. Rate equations are employed to calculate the probabilities of ionization by Compton scattering, one-photon absorption, and two-photon absorption.

We investigate the absorption of two identical photons from the ground state of hydrogen-like atoms over an energy range that extends beyond that explored up to now. Our approach is based on a hybrid formula, valid in second-order perturbation theory, in which the

{\mathbf{A}}^{2}

contribution from the nonrelativistic Hamiltonian is treated exactly, while the $\mathbf{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{P}$ contribution is calculated in dipole approximation. We find that, at least up to 50 keV, the nonrelativistic dipole approximation, based only on the $\mathbf{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{P}$ contribution, determines the values of the total cross section. Our numerical results, covering photon energies from 90 nm (13.7 eV) to 0.0248 nm (50 keV) are in very good agreement with most previous theoretical works. Differences with recent results are discussed.

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

We present accurate cross sections for two-photon double ionization of helium at photon energies above and below the threshold for sequential double ionization. Above this threshold

{\mathbf{A}}^{2}

, sequential ionization competes with nonsequential ionization. Remarkably, even below

54.4\phantom{\rule{0.3em}{0ex}}\mathrm{eV}

, sequential ionization leaves a clear signature in the magnitude and shape of both the total and energy-sharing cross sections---even though at these energies it is only a virtual process.

Two-color two-photon photoionization of hydrogen and alkali atoms is presented. The method based on a perturbation expansion is valid for low to moderately intense radiation fields. Three processes are considered leading to the photoionization. For the first process both photons are below threshold, and for the second process one photon is above the threshold with an energy less than the final energy of the photoelectron. The last process is identical to the continuum Raman (Compton) scattering where the first photon is absorbed high in the continuum and the second low energy photon is scattered. Photoionization cross sections of hydrogen and the alkali atoms are given as functions of the first photon energy and the photoelectron energy.

The advent of the laser has brought about a revolution in the kinds of experimental phenomena that can be investigated. In particular, ultra-high power monochromatic, collimated sources have intensities of sufficient magnitude to enable studies to be carried out in the regime where 'non-linear' effects are important, even dominant. Important among these are processes which are characterised by the simultaneous absorption of two or more optical photons. While multiple photon processes are not completely new, those in the optical part of the spectrum, like Raman scattering, have, until the advent of the laser, been thought of as linear in the incident intensity, or, like the two-quantum decay of the metastable 2s states of hydrogen-like atoms and ions, been confined to theory. Of the multiple photon, non-linear optical processes, multiquantum ionization is one of the more fruitful for detailed, quantitative measurements, and for comparison with theory, since (1) one does not require precise coincidence between the laser light and an absorption line (2) the ionizations can be detected unambiguously with 100% efficiency (3) atomic wave functions are simple, and sufficiently accurate to enable one to make reasonable precise calculations.