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Physical Review A

Cross sections for the multiphoton ionization of sodium in a linearly polarized radiation field

Milan Blaha, Jack Davis

Published Mar 1, 1995• 10 citations
Publisher

Abstract

A calculation of the N-photon ionization cross sections with N=2,3,4,5 in the frequency interval 0.0980.165 (atomic units) for sodium has been performed using a procedure described by Pan [J. Mod. Opt. 36, 877 (1989)]. The final-state wave function represents the Volkov-like continuum, distorted by the atomic potential, while the initial state is described by the rotating-wave approximation with the inclusion of the ground-state 3s and two excited p states. The cross sections were calculated for two kinds of initial conditions: instantaneous and adiabatic switching of radiation. The results of the calculation with the distorted continuum wave functions representing the final state were compared to those obtained from Coulomb and plane-wave functions.

DOI
10.1103/physreva.51.2308

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A calculation of the N-photon ionization cross sections with N=2,3,4,5 in the frequency interval 0.0980.165 (atomic units) for sodium has been performed using a procedure described by Pan [J. Mod. Opt. 36, 877 (1989)]. The final-state wave function represents the Volkov-like continuum, distorted by the atomic potential, while the initial state is described by the rotating-wave approximation with the inclusion of the ground-state 3s and two excited p states. The cross sections were calculated for two kinds of initial conditions: instantaneous and adiabatic switching of radiation. The results of the calculation with the distorted continuum wave functions representing the final state were compared to those obtained from Coulomb and plane-wave functions.
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 theory of multiphoton ionization for an atomic system of arbitrary complexity is developed using a density matrix formalism. An expression is obtained which determines the differential N-photon ionization cross section as a function of the polarization states of the target atom and the incident radiation. The parameters which characterize the photo-electron angular distribution are related to the general reduced matrix elements for the N-photon transition. Two-photon ionization of unpolarized atoms is treated as an illustration of the use of the theory. The dependence of the multiphoton ionization cross section on the polarization state of the incident radiation, which has been observed in two- and three-photon ionization of Cs, is accounted for by the theory. Finally, the photoelectron spin polarization produced by the multiphoton ionization of unpolarized atoms, like the analogous polarization resulting from single-photon ionization, is found to depend on the circular polarization of the incident radiation.
Sodium atoms are excited to either the 32P323^{2}P_{\frac{3}{2}}32P23​​ or 32P123^{2}P_{\frac{1}{2}}32P21​​ state using a linearly polarized dye-laser beam and are subsequently ionized using a linearly polarized nitrogen-laser beam. Angular distributions of the ejected electron have been both measured and calculated for several relative orientations of the photon polarization vectors. The difference between the sss- and ddd-continuum partial-wave phase shifts ${\ensuremath{\delta}}_{s}\ensuremath{-}{\ensuremath{\delta}}_{d}$ and the ratio of the radial dipole matrix elements (dsdd\frac{{d}_{s}}{{d}_{d}}dd​ds​​) are obtained.
Formal time-independent scattering theory is applied to multiphoton ionization of atoms in intense electromagnetic fields. The quantized-field version of the Volkov solution makes this approach possible. With the electron-photon interaction in a monochromatic photon field, it is found that, in the nonrelativistic and large-photon-number limits, the final scattering state exists only in the special case in which the ponderomotive potential per unit photon energy is an integer; otherwise the final state vanishes. In the integer case the corresponding wave function reduces to a single Volkov function, multiplied by an overlap factor. A simple interpretation of this result is given, and some other consequences of this work are discussed.
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.
Multiphoton ionization of hydrogen atoms by a strong multimode field when several final continuum states are populated is treated theoretically within a model based on the S-matrix formalism. The field is taken in dipole approximation, with zero bandwidth. Field-dressed Coulomb wave functions are used for the electron final states. Ionization rates are calculated for different numbers of photons absorbed in excess of the minimum number required to go into the continuum. In general, the calculated quantities are in good qualitative agreement with the corresponding experimental observations.