Two-photon Ionization Cross Sections Research Articles

Far-infrared multiphoton ionization of lithium Rydberg atoms bypassing a Cooper minimum.

Multiphoton excitation and ionization studies of the Li $23s$ state by 20 ps far-infrared laser pulses originating from the free-electron laser FELIX are presented. The two-photon ionization cross section of highly excited Rydberg $s$ states is small, due to a newly discovered Cooper minimum in the bound-bound $ns\ensuremath{-}{n}^{\ensuremath{'}}p$ transitions. Instead of this lowest-order process, ionization proceeds via a remarkable multiphoton bypass starting with stimulated emission to a lower-lying state. The measurements are interpreted with calculations of the Cooper minimum and a Floquet analysis of the states involved in the bypass.

Calculation of the differential two-photon ionization cross section of H2S

Differential cross section of nonresonant two-photon ionization of the outer valence shell of H2S is computed using ab initio methods for several choices of photon polarization and experimental setup. The theoretical model employed is based on the second-order perturbation theory in the dipole and vertical transition approximations and the calculations are performed adopting a large basis set of L2 integrable functions. The excitations to intermediate states are described in the random phase approximation, while the final states are described in the static-exchange approximation adopting for the continuum orbitals a K-matrix technique that allows a proper description of the angular distribution of the emitted electrons.

Multiphoton dissociative ionization of O2: Competition between dissociation and ionization in excited states

A mass and energy resolved photoion spectrum of O2 induced by 12 ns 193 nm radiation with an intensity of 1010–1011 W/cm2 is presented. The analysis of the spectrum gives (1) the two-photon ionization cross section (≊1.1×10−54 cm4 s) of the X 3Σ−g of O2 and (2) the intensity dependent branching ratios between photoionization and predissociation of the B 3Σ−u state of O2. The two-photon ionization cross section of O2 is linked to our ab initio calculation of the three-photon ionization cross section (≊7.5×10−84 cm6 s2) of atomic oxygen.

Two-photon ionization cross sections for the free ion production of naphthacene and fluoranthene in hexane

Naphthacene and fluoranthene in hexane showed photoconductivity signals upon excitation by 458-nm irradiation (200 mW) with a continuous-wave argon ion laser. The signals were quadratically proportional to the laser power and linearly proportional to the solute concentration, indicating a two-photon excitation-ionization. By evaluation of the signal intensity and laser beam parameters, two-photon ionization cross sections for the production of the free ions separating from geminate ion-electron pairs have been determined absolutely to be 2.2×10 -52 and 2.5×10 -54 cm 4 s/(molecule photon) for naphthacene and fluoranthene, resistively, at an electric field of 5000 V/cm. The former cross section of the ionization via a real state was about 100 times larger than the latter via a virtual state

Three-photon ionization cross section calculations of Be

Three-photon perturbative photoionization cross sections from the ground state of beryllium have been calculated employing B-spline basis functions. Two-photon ionization cross sections are also calculated and compared to other L2 basis set calculations. Various approximations for the 1s2 core are discussed, calculations are performed in velocity and length gauges including electron correlations.

Calculation of multiphoton-ionization Green's functions using the Wentzel-Kramers-Brillouin approximation. II.

Recently, a technique [M. Edwards, Phys. Rev. A 45, 409 (1992)] was presented for calculating multiphoton-ionization Green's functions based on the Wentzel-Kramers-Brillouin (WKB) approximation. In that paper it was shown that the ability of this method to produce accurate cross sections and angular distributions depended critically on the single-particle potential for the valence electron that was used in the calculation. In this work we present a supporting technique for determining the optimal potential for use with this method in low-Z alkali-metal atoms. The technique produces the parameter values for a parametric model potential whose WKB Green's function has poles that coincide with the measured energy levels of the atom. We have determined the parameter values for a specific model potential in Li and Na. For these cases, only two parameters are needed to produce a potential whose WKB energy levels match all of the measured ones to within 165 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. We have calculated cross sections for two-photon ionization of Li and Na for a range of laser-photon energies using this model potential and present comparisons with previous work.

R-matrix theory of two-photon absorption: application of beryllium and carbon

An R-matrix theory of two-photon absorption is presented for a general atom within the confines of lowest-order perturbation theory. The theory has been used in extending the R-matrix general atom codes to calculate two-photon processes where neither photon has individually sufficient energy to ionize the atom. The extended codes have been employed in calculating the two-photon excitation of the closed-shell ground state of beryllium and also the two-photon ionization cross section for this state. Good agreement is obtained with results of recent calculations performed using a different method although the new method reaches higher energies. Contact is established with experimental results on two-photon absorption by beryllium. In addition, the two-photon ionization cross section of a ground-state open-shell atom-carbon-is calculated for the first time.

Transformed Coulomb Green function Sturmian expansion

Two Coulomb Green function Sturmian expansions are presented. Both of them are used to derive the transformed Coulomb Green function Sturmian expansion. The new Coulomb Green function representation is tested for calculating two-photon above-threshold ionization cross sections for atomic hydrogen. The new representation may be useful also in the case of more excess photons as well as for calculating free-free transitions.

Theoretical methods for the calculation of the multiphoton ionisation cross-section of atoms and molecules

Some of the available theoretical methods to compute the two-photon ionisation cross-section of many-electron systems are reviewed. In particular the problems concerning the computation of (i) reliable approximations for the transition matrix elements and the excitation energies; and (ii) accurate results pertaining to the electronic continuum by the use of L2 basis functions are considered.

Two-photon ionization of the Ar atom and detachment of the F- ion.

Theoretical calculations of the two-photon ionization cross section of argon and of the two-photon detachment cross section of the negative fluorine ion are presented for the energy region from threshold to the single-photon ionization or detachment threshold. Detailed analyses are presented of the effects of various kinds of electron correlations, whose contributions to the two-photon transition amplitudes are evaluated using variationally stable procedures to sum implicitly over intermediate states. These variationally stable procedures enable us to give much more reliable predictions in the region of the first few intermediate-state resonances in argon than were provided by previous calculations of one of us [A.F. Starace and T. F. Jiang, Phys. Rev. A 36, 1705 (1987)]. In addition, we show here for both argon and ${\mathrm{F}}^{\mathrm{\ensuremath{-}}}$ the large corrections to the p${(}^{1}$S) final-state channel cross sections provided by certain intermediate-state shake-up interactions, which we show to be essential for obtaining good agreement of dipole length and velocity cross sections. We provide detailed comparisons of our results with those of previous workers; in particular, our results for the negative fluorine ion are in excellent agreement with the recent absolute measurement of Kwon et al. [Phys. Rev. A 40, 676 (1989)].

Variational methods for high-order multiphoton processes

Methods for applying the variationally stable procedure for Nth-order perturbative transition matrix elements of Gao and Starace [ Phys. Rev. Lett.61, 404 ( 1988);Phys. Rev. A39, 4550 ( 1989)] to multiphoton processes involving systems other than atomic H are presented. Three specific cases are discussed: one-electron ions or atoms in which the electron-ion interaction is described by a central potential; two-electron ions or atoms in which the electronic states are described by the adiabatic hyperspherical representation; and closed–shell ions or atoms in which the electronic states are described by the multiconfiguration Hartree–Fock representation. Applications are made to the dynamic polarizability of He and the two-photon ionization cross section of Ar.

Atomic magnesium: Discrete and continuum spectrum properties from a valence-shell L2 configuration-interaction calculation with polarization potential.

The discrete and continuous spectrum of atomic magnesium below the 3p${\mathrm{}}^{2}$${\mathit{P}}^{\mathrm{o}}$ ionization threshold has been investigated by a valence-shell frozen-core ${\mathit{L}}^{2}$ configuration-interaction calculation with a phenomenological polarization potential. The results presented include positions of bound and autoionizing levels, oscillator strengths and radiative lifetimes, the ground-state one- and two-photon ionization cross sections, and several observables of interest for long-range interaction and Zeeman-effect studies. In particular, the two-photon ionization cross section is discussed in the near-threshold region, where one experimental result is available for comparison

Quantum-defect parametrization of perturbative two-photon ionization cross sections.

A multichannel quantum-defect theory (MQDT) parametrization of two-photon ionization (2PI) of atoms, suitable for use with ab initio calculations of perturbative 2PI amplitudes in the presence of intermediate- and/or final-state Rydberg resonances is developed. The rapid energy variation of such amplitudes is extracted in terms of elementary functions of energy and a set of MQDT parameters, which are ``smooth'' functions of energy. As an example, results of numerical computations of MQDT parameters for 2PI of atomic hydrogen (1s, 2s, and 3s) by circularly polarized light are presented. MQDT parameters for the many-channel case are derived, and an analysis of their energy dependence across Rydberg thresholds is given. The two-channel case is analyzed using phase-shifted Coulomb functions, and simple analytic formulas are given for the energy dependence of the amplitude as a function of a small set of physical parameters.

Two-photon ionization calculations. Results for H 2O

The two-photon first ionization cross section of H 2O was computed in the vertical transition approximation. The K-matrix method was employed, adopting a basis set of L 2 functions and an interpolation procedure, to obtain the final continuous orbitals needed to calculate the two-photon oscillator strength density. The results for the integral two-photon ionization cross section refer to the case of a single photon beam either linearly or circularly polarized. The static-exchange approximation was used to describe both intermediate and final states.

Two-photon ionization cross section calculation for H2O

The two-photon first ionization cross section was computed for H2O in the vertical transition approximation. A Stieltjes imaging technique was used to obtain from the results of a L2 basis set calculation, the two-photon oscillator strength density in the continuum. The calculations were performed in the independent particle static-exchange approximation for the final states. The ground-intermediate state transition matrix elements and excitation energies were computed by adopting the single channel static-exchange approximation or the multichannel random phase approximation; in the last case the intermediate-final state transition matrix elements were obtained by the equation of motion method. The calculated cross sections refer to the case of single beam of linearly or circularly polarized photons.

Atomic magnesium: III. Two-photon transition probabilities and ionisation cross sections: A valence-shell L2 CI calculation

For pt.II see ibid., pp.1133-43 (1988). A frozen-core valence-shell L2 CI has been employed to compute the following ground-state properties: electric dipole polarisability, C6 (van der Waals) coefficient, two-photon transition properties to the lowest 2Se and 1De levels and the two-photon ionisation cross section.

Linear and nonlinear screening effects in two-photon ionization of xenon.

We apply the random-phase approximation to two-photon ionization. We develop a formalism which, by means of screened electron-photon interactions, includes the nonlinear response and, in particular, double-excitation processes. The theory is illustrated by numerical calculations of the two-photon ionization cross section of the external (5p and 5s) shell of xenon, over a large energy range: from the two-photon ionization threshold, in the discrete resonance region, and above the one-photon ionization threshold. We show the influence of different many-electron effects, for example, ground-state and final-state correlation, and linear and nonlinear screening. Compared with an independent-electron picture, screening effects lead to a large reduction of the ionization cross section at low photon energy and in contrast, to an important enhancement at higher photon energy, due to the influence of double-excitation and -ionization processes.

One- and two-photon ionization of model atoms: The sphericalδ-shell potential

One- and two-photon ionization cross sections for the negative hydrogen ion ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ are evaluated by using a one-electron model where the effective intra-atomic potential energy is assumed to be of a very-short-range character and approximated by a ``spherical \ensuremath{\delta} shell.'' The adjustment of the two parameters involved in the model potential so as to reproduce either the photodetachment energy or the behavior of the one-photon ionization cross section over a substantial range of frequencies beyond the ionization threshold leads to conjecture of a reasonable estimate of the two-photon ionization cross section over the proper range of frequencies of the ionizing field.

Two-photon one-electron ionisation cross section of the 5p shell of xenon including screening effects

The authors present calculations of the two-photon one-electron ionisation of the 5p shell of xenon including non-linear response. Screening effects are described within the random-phase approximation (RPA). The authors use both a local-density approximation (LDA) and a Hartree-Fock average basis set. They describe a large energy region from the two-photon ionisation threshold to above the one-photon ionisation threshold ('above-threshold-ionisation' process, ATI). They demonstrate the importance of many-electron screening effects; and in particular point out the role of double excitation mechanisms.

Electron Correlation Effects in Nonresonant Multiphoton Ionization Processes

The role of electron correlations in nonresonant multiphoton processes of atoms is presented. The evidence for the validity of a lowest order perturbation theory (LOPT) approach for the laser field in the case of nonresonant processes is sketched. The growing consensus for a LOPT interpretation of even the multiply-charged ion spectra obtained with high intensity lasers is reviewed. Finally, a review of those specific electron correlation processes within LOPT that are important for the quantitative prediction of two-photon ionization cross sections is presented and some of their effects on calculated generalized cross sections are exhibited.