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Physical Review A

Electron-impact excitation of atoms in the presence of a nearly resonant laser field

P. Francken, C. J. Joachain

Published Apr 1, 1990• 22 citations

Abstract

We have studied the electron-impact excitation of an atom, in the presence of a laser field whose photon energy is tuned close to the energy difference between two excited final states. Both the laser-projectile and the laser-target interactions are treated nonperturbatively, while the electron-atom interaction is treated within the first Born approximation. As an application, we have analyzed the resonant laser-assisted excitation of the ${2}^{1}$S and ${2}^{1}$P states of helium. The agreement between the present nonperturbative results and previous perturbative ones is excellent, except for very small detunings. The present nonperturbative treatment also shows that the results given by perturbation theory on both sides of the resonance, when plotted as a function of the laser frequency, correspond to the excitation of different Floquet pseudostates. This is related to the presence of avoided crossings in the diagram of the Floquet pseudoenergies, as a function of the laser frequency.

DOI: 10.1103/physreva.41.3770

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Journal of Physics B Atomic and Molecular Physics•Feb 14, 1985•7 citations

We have studied the electron-impact excitation of an atom, in the presence of a laser field whose photon energy is tuned close to the energy difference between two excited final states. Both the laser-projectile and the laser-target interactions are treated nonperturbatively, while the electron-atom interaction is treated within the first Born approximation. As an application, we have analyzed the resonant laser-assisted excitation of the

{2}^{1}

S and

{2}^{1}

P states of helium. The agreement between the present nonperturbative results and previous perturbative ones is excellent, except for very small detunings. The present nonperturbative treatment also shows that the results given by perturbation theory on both sides of the resonance, when plotted as a function of the laser frequency, correspond to the excitation of different Floquet pseudostates. This is related to the presence of avoided crossings in the diagram of the Floquet pseudoenergies, as a function of the laser frequency.

Dressed states of an atom in a classical laser field of frequency close to an atomic transition frequency are obtained, which are a considerable improvement over the usual two-level rotating-wave approximation. These wave functions are used in a calculation of the cross section for elastic electron-atom scattering in a laser field. Numerical calculations for electron-hydrogen scattering demonstrate that scattering involving absorption or emission of photons can be strongly influenced by coupling to the nonresonant states, regardless of the field strength. Inclusion of the counter-rotating terms in the calculation is shown to be essential for extending the applicability of the theory to scattering in nonresonant fields, where a first-order perturbation-theoretic treatment of the atom-field interaction would be expected to be quite justified.

A modified perturbation theory is developed for the calculation of the time-dependent wave function describing the propagation of an atom in a two-mode laser field. With the mode frequencies nearly equal, a first approximation is obtained that reproduces and extends known results, for both resonant and nonresonant transitions. This lowest-order solution sums terms that describe the absorption of a photon from one mode and emission into the other, leaving the total number of photons unchanged and shifting the momentum of the atom accordingly. Corrections are generated by expansion of a resolvent from which the nearly degenerate states have been projected out. These approximate solutions are used to construct asymptotic states in a formulation of atom-atom scattering in the two-mode field. In close analogy with the soft-photon approximation, a ``soft-pair'' approximation is developed based on the dominance of those asymptotic interactions in which the transfer of energy from the field to the atom is small, allowing one to relate the scattering amplitude in the presence of the field to the field-free amplitude. When the atomic ground state and an excited state are closely coupled by the field, the asymptotic wave function can have mixed parity allowing for long-range contributions to the effective potential. In addition to an enhancement of forward-scattering probabilities, this leads to a threshold anomaly that is analyzed here, in the resonant case, with the aid of a modified effective-range theory.

Electron-impact excitation of the hydrogen metastable 2s state to the 3s, 4s, 3d, and 4d states is studied in the presence of a resonant laser field using the rotating-wave approximation. The frequency of the circularly polarized laser field is chosen to match the 2s-3p transition frequency in the hydrogen atom. The role of the laser field in individual magnetic substate (

{\mathit{m}}_{\mathit{f}}

=0,\ifmmode\pm\else\textpm\fi{}1,\ifmmode\pm\else\textpm\fi{}2) excitation is analyzed. It is found that for these optically forbidden transitions (s-s, s-d), a significant increase in the excitation cross sections is obtained through joint collisions with electrons and photons.

When an atom is driven by a laser field with a photon energy that is nearly resonant with an atomic transition, it can undergo periodic population transfers between the ground and excited state, known as Rabi oscillations [1], [2]. The aim of this work is to study photoionization from atoms for parameters accessible to a free-electron laser (FEL) [3]. Using time dependent perturbation theory to model photoionization from a Rabi oscillating atom, we have shown that in addition to the expected pathway of ionization from the excited state, non-resonant two-photon ionization will have a comparable amplitude at intensities on the order of 1013W/cm2[3].