Two-photon Ionization Cross Sections Research Articles

Two-photon ionization in solar opacity experiments

The discrepancies between theoretical and experimental opacities reported by experiments performed at the Sandia National Laboratory Z-pinch relevant to the solar interior remain unexplained. The suggestion that two-photon ionization could help resolve the discrepancies was recently examined and found not to account for the higher than predicted measured opacities. That test, however, was limited in scope and is now extended to include excited configurations and different charge states of several elements. Comparisons of one- and two-photon ionization cross-sections show that the latter fail to resolve the aforementioned discrepancies.

Photoelectron Angular Distributions of Nonresonant Two-Photon Atomic Ionization Near Nonlinear Cooper Minima

Photoelectron angular distributions of the two-photon ionization of neutral atoms are theoretically investigated. Numerical calculations of two-photon ionization cross sections and asymmetry parameters are carried out within the independent-particle approximation and relativistic second-order perturbation theory. The dependence of the asymmetry parameters on the polarization and energy of the incident light as well as on the angular momentum properties of the ionized electron are investigated. While dynamic variations of the angular distributions at photon energies near intermediate level resonances are expected, we demonstrate that equally strong variations occur near the nonlinear Cooper minimum. The described phenomena is demonstrated on the example of two-photon ionization of magnesium atom.

Auger-like correlations in the two-photon above threshold ionization of Ar

The two-photon above-threshold 3p-ionization of argon for the photon energies exceeding the 3p-ionization threshold is studied using the correlation function technique. Generalized two-photon ionization cross sections were calculated taking into account many-electron correlations. The calculations demonstrate that the two-photon ionization of Ar at the 3p4 threshold is almost entirely a collective process. The decisive contribution in the above-threshold two-photon 3p-ionization at the exciting-photon energies corresponding to the 3p→ed giant resonance comes from the Auger-like many-electron correlations of e′ de″d − 3pef type.

Role of intermediate continuum states in exterior complex scaling calculations of two-photon ionization cross sections

The calculation of partial two-photon ionization cross sections in the above-threshold energy region is discussed in the framework of exterior complex scaling. It is shown that with a minor modification of the usual procedure, which is based on the calculation of the outgoing partial waves of the second-order scattering wave function, reliable partial ionization amplitudes can be obtained. The modified procedure relies on a few-term least-squares fit of radial functions pertaining to different partial waves. To test the procedure, partial and total two-photon ionization cross sections of the helium atom have been calculated for a broad range of incident photon energies. The calculated cross sections may be seen to agree well with the results found in the literature. Furthermore, it is shown that, using a similar approach, partial photoionization cross sections of an atom in an autoionizing (resonance) state may be calculated in a relatively straightforward way. Such photoionization cross sections may find their use in enhanced few-parameter models describing the atom-light interaction in cases where a direct solution of the time-dependent Schroedinger equation becomes too resource-intensive.

Floquet calculations for H2+ photoionization

We present results of calculations of rates for ionization of the lowest electronic state of the H2+ ion by a continuous-wave laser field. We solve the coupled-channel Floquet equations in both length and velocity gauges using a pseudospectral method. We employ a complex absorbing potential to obtain Siegert-type solutions resulting in resonance positions and widths. We calculate generalized cross sections for one-, two-, and three-photon ionizations for various internuclear separations of the ion with intensity of I = 1.76 × 1012 W/cm2. This is the first time the Floquet technique combined with the complex absorbing potential has been employed for photoionization cross sections of the ion. We report on ionization rates of the ion for different internuclear distances with intensity of I = 5 × 1013 W/cm2. We also present two-photon ionization cross section for different internuclear distances with intensities of I = 1.76 × 1013 and 1.76 × 1014 W/cm2. We compare our findings from calculations carried out in both gauges with those of previous calculations.

Relativistic, correlation, and polarization effects in two-photon photoionization of Xe

Two-photon ionization of xenon was investigated theoretically for exciting-photon energies from 6.7 to 11.5 eV, which results in the ionization of Xe between $5{p}_{1/2}$ (13.43 eV) and $5s$ (23.40 eV) thresholds. We describe the extension of a previously developed computational technique for the inclusion of relativistic effects to calculate energies of intermediate resonance state and cross sections for two-photon ionization. Reasonable consistency of cross sections calculated in length and velocity form was obtained only after considering many-electron correlations. Agreement between calculated and measured resonance energies is found when core polarization was additionally included in the calculations. The presently computed two-photon photoionization cross sections of Xe are compared with Ar cross sections in our previous work. Photoelectron angular distribution parameters calculated here indicate that intermediated resonances strongly influence photoelectron angular distribution of Xe.

Towards XUV pump-probe experiments in the femtosecond to sub-femtosecond regime: New measurement of the helium two-photon ionization cross-section

Non-linear photoionization of molecules in the 10–50eV range is a prerequisite for pump-probe measurements with sub-femtosecond resolution, but hitherto has been limited to femtosecond resolution, low repetition rate and high photon flux laser systems. We demonstrate two-photon single ionization of helium atoms using 100pJ, 1.34fs pulses (main peak FWHM=680 as) at 1kHz repetition rate with a central photon energy of 19.6eV. We obtained an exponent of 2.27±0.21 for the intensity dependence of the signal and a two-photon ionization cross-section of 5.0±0.5×10−50cm4s. Our work opens the possibility of attosecond pump-probe measurements of ultrafast molecular processes.

Time-dependent configuration-interaction-singles calculation of the 5p -subshell two-photon ionization cross section in xenon

The $5p$ two-photon ionization cross section of xenon in the photon-energy range below the one-photon ionization threshold is calculated within the time-dependent configuration-interaction-singles (TDCIS) method. The TDCIS calculations are compared to random-phase-approximation (RPA) calculations [Wendin \textit{et al.}, J. Opt. Soc. Am. B \textbf{4}, 833 (1987)] and are found to reproduce the energy positions of the intermediate Rydberg states reasonably well. The effect of interchannel coupling is also investigated and found to change the cross section of the $5p$ shell only slightly compared to the intrachannel case.

Relativistic calculations of the nonresonant two-photon ionization of neutral atoms

The non-resonant two-photon one-electron ionization of neutral atoms is studied theoretically in the framework of relativistic second-order perturbation theory and independent particle approximation. In particular, the importance of relativistic and screening effects in the total two-photon ionization cross section is investigated. Detailed computations have been carried out for the K-shell ionization of neutral Ne, Ge, Xe, and U atoms. The relativistic effects significantly decrease the total cross section, for the case of U, for example, they reduce the total cross section by a factor of two. Moreover, we have found that the account for the screening effects of the remaining electrons leads to occurrence of an unexpected minimum in the total cross section at the total photon energies equal to the ionization threshold, for the case of Ne, for example, the cross section drops there by a factor of three.

Ion and electron spectroscopy of strontium in the vicinity of the two-photon-excited5p2 1S0state

Two-photon ionization of ground-state strontium is investigated experimentally in the 360--370-nm spectral range with dye laser pulses of long (\ensuremath{\sim}ns) duration and low $(\ensuremath{\sim}10{}^{10}W\mathrm{ cm}{}^{\ensuremath{-}2}$) intensity. The ${\mathrm{Sr}}^{+}$ spectra recorded with linear laser polarization are dominated by the presence of the highly correlated $5{p}^{2}$ ${}^{1}{S}_{0}$ state and by the even parity $[4d$$6d]$]${}_{J}$${}_{=0,2}$ autoionizing states. The partial $J=0$ and $J=2$ two-photon ionization cross sections are recovered from these data along with the spectra obtained with circular polarization. For linear polarization, the observed wavelength dependence of ${\mathrm{Sr}}^{+}$ production is compared with earlier theoretical work based on the $R$-matrix--multichannel-quantum-defect-theory approach and the agreement is generally found to be quite satisfactory. There are, however, a few, albeit noticeable, discrepancies. The latter motivated us to proceed to a more comprehensive experimental characterization of the examined energy range, by also measuring the kinetic energy and angular distribution of the ejected photoelectrons under linear laser polarization. The shapes of the angular distributions vary rapidly in the neighborhood of each resonance, while these distributions are found to be almost spherically symmetric on the maxima of the sharp $[4d$$6d]$]${}_{J}$${}_{=0}$ lines. On these, and only these, maxima, electron energy spectra reveal the absorption of a third photon, resulting in production of ${\mathrm{Sr}}^{+}$ into its excited $4{d}_{j}$ and $5{p}_{j}$ states. The non-negligible $5{p}_{j}$ branching ratio reflects the mixing between the $[4d$$6d]$]${}_{J}$${}_{=0}$ states and the $5{p}^{2}$ ${}^{1}{S}_{0}$ perturber, found to be rather underestimated by the aforementioned theoretical work. Thus, the presently acquired ion and electron spectra as well as the asymmetry parameters obtained by fitting the photoelectron angular distributions provide a stringent test of future theoretical efforts, addressing structure as well as excitation and ionization issues in an improved manner.

Time-dependentR-matrix theory applied to two-photon double ionization of He

We introduce a time-dependent R-matrix theory generalised to describe double ionization processes. The method is used to investigate two-photon double ionization of He by intense XUV laser radiation. We combine a detailed B-spline-based wavefunction description in a extended inner region with a single-electron outer region containing channels representing both single ionization and double ionization. A comparison of wavefunction densities for different box sizes demonstrates that the flow between the two regions is described with excellent accuracy. The obtained two-photon double ionization cross sections are in excellent agreement with other cross sections available. Compared to calculations fully contained within a finite inner region, the present calculations can be propagated over the time it takes the slowest electron to reach the boundary.

Time-resolved resonant photoionization of He using a time-dependent Feshbach method with ultrashort laser pulses

We study the resonant photoionization of the Helium atom subject to ultrashort laser pulses by using a Feshbach formalism in the time domain. We solve the projected time-dependent Schrodinger equation in terms of a configuration interaction spectral method, with a total wave function expanded with configurations defined within bound-like () and scattering-like () halfspaces. The method allows for accurate descriptions of both the atomic structure (energy positions and widths) as well as for the resonant photodynamics using ultrashort laser pulses. Special attention is given to the temporal formation of Fano profiles in the one- and two-photon ionization cross sections.

Time-resolved resonant photoionization of He using a time-dependent Feshbach method with ultrashort laser pulses

We study the photoionization and autoionization of the helium atom subject to ultrashort laser pulses by using a Feshbach formalism in the time domain. We solve the time-dependent Schrödinger equation in terms of a configuration interaction (CI) spectral method, in which the total wavefunction is expanded with configurations defined within bound-like () and scattering-like () halfspaces. The method allows one to provide accurate descriptions of both the atomic structure (energy positions and widths) and the photodynamics. We illustrate our approach by (i) calculating the time-resolved one-photon ionization below the He+ (n = 2) ionization threshold, from 11Se and 21Po initial states, then reaching the lowest autoionizing states of 1Se, 1Po and 1De final symmetries, (ii) studying the temporal formation of the Fano profile of 1Po resonances and (iii) showing its performance in obtaining the perturbative long-time limit of one- and two-photon ionization cross sections using ultrashort laser pulses following a recently developed procedure in Palacios et al (2008 Phys. Rev. A 77 032716).

Detection of Atmospheric Pollutant NO With the Method of Resonant-Enhanced Multiphoton Ionization

NO is one of the key substances of air pollution. This paper presents the use of the technique of resonant enhanced multi-photon ionization (REMPI) for NO ambient detection. NO is ionized by absorbing four photons and via A2Σ intermediate resonant state when use 452.4nm laser as radiation source. A physical model concerning the ionization process is presented. It is shown that the ion signal depends on laser character and the dynamic parameters of NO. Two-photon absorption and ionization cross section about the resonant state are obtained from the ion decay curve and the model. The detection limit of this work, which can reach 1.4 ppm, is determined by measuring the variation of the ion signal with the concentration of NO.

Enhanced nonlinear response of Ne8+to intense ultrafast x rays

We investigate the possible reasons for the discrepancy between the theoretical two-photon ionization cross section, $\sim 10^{-56}$ $\text{cm}^4 \text{s}$, of Ne$^{8+}$ obtained within the perturbative nonrelativistic framework for monochromatic light [J. Phys. B {\bf 34}, 4857 (2001)] and the experimental value, $7 \times 10^{-54}$ $\text{cm}^4 \text{s}$, reported in [Phys. Rev. Lett. {\bf 106}, 083002 (2011)] at a photon energy of 1110 eV. To this end, we consider Ne$^{8+}$ exposed to deterministic and chaotic ensembles of intense x-ray pulses. The time-dependent configuration-interaction singles (TDCIS) method is used to quantitatively describe nonlinear ionization of Ne$^{8+}$ induced by coherent intense ultrashort x-ray laser pulses. The impact of the bandwidth of a chaotic ensemble of x-ray pulses on the effective two-photon ionization cross section is studied within the lowest nonvanishing order of perturbation theory. We find that, at a bandwidth of 11 eV, the effective two-photon ionization cross section of Ne$^{8+}$ at a photon energy of 1110 eV amounts to $5 \times 10^{-57}$ and $1.6 \times 10^{-55}$ $\text{cm}^4 \text{s}$ for a deterministic ensemble and a chaotic ensemble, respectively. We show that the enhancement obtained for a chaotic ensemble of pulses originates from the presence of the one-photon 1$s^2$--1$s4p$ resonance located at 1127 eV. Using the TDCIS approach, we also show that, for currently available radiation intensities, two-photon ionization of a 1$s$ electron in neutral neon remains less probable than one-photon ionization of a valence electron.

Alignment effects in two-photon double ionization of H2in femtosecond xuv laser pulses

Triple-differential cross sections for two-photon double ionization of the aligned hydrogen molecule at the equilibrium distance are presented for a central photon energy of 30 eV. The temporal response of the laser-driven molecule is investigated by solving the time-dependent Schr\"odinger equation in full dimensionality using two-center elliptical coordinates and a finite-element discrete-variable-representation approach. The molecular orientation is found to have a strong effect on the emission modes of the two correlated photoelectrons. This molecular effect is most noticeable when the molecular axis and the laser polarization vector are oriented parallel to each other. For intermediate cases between the parallel and perpendicular geometries, the dominant emission modes for two-electron ejection oscillate between those for the two extreme cases. The contributions from different ionization channels are also analyzed in detail. Depending on the emission direction of the reference electron, the interference contributions from the various channels can be constructive or destructive at small alignment angles, while they always contribute constructively to the triple-differential cross sections near the perpendicular geometry.

Determination of the absolute two-photon ionization cross section of He by an XUV free electron laser

The resonant and non-resonant two-photon single ionization processes of He were investigated using intense free electron laser light in the extreme ultraviolet (XUV) region (53.4–61.4 nm) covering the 1s–2p and 1s–3p resonant transitions of He. On the basis of the dependences of the yield of He+ on the XUV light-field intensity at 53.4, 58.4, 56.0 and 61.4 nm, the absolute values of the two-photon ionization cross sections of He at the four different wavelengths and their dependence on the light-field intensity were determined for the first time.

Nonlinear Atomic Response to Intense Ultrashort X Rays

The nonlinear absorption mechanisms of neon atoms to intense, femtosecond kilovolt x rays are investigated. The production of Ne(9+) is observed at x-ray frequencies below the Ne(8+), 1s(2) absorption edge and demonstrates a clear quadratic dependence on fluence. Theoretical analysis shows that the production is a combination of the two-photon ionization of Ne(8+) ground state and a high-order sequential process involving single-photon production and ionization of transient excited states on a time scale faster than the Auger decay. We find that the nonlinear direct two-photon ionization cross section is orders of magnitude higher than expected from previous calculations.

Two-photon double ionization ofH2in intense femtosecond laser pulses

Triple-differential cross sections for two-photon double ionization of molecular hydrogen are presented for a central photon energy of 30 eV. The calculations are based on a fully {\it ab initio}, nonperturbative, approach to the time-dependent Schroedinger equation in prolate spheroidal coordinates, discretized by a finite-element discrete-variable-representation. The wave function is propagated in time for a few femtoseconds using the short, iterative Lanczos method to study the correlated response of the two photoelectrons to short, intense laser radiation. The current results often lie in between those of Colgan {\it et al} [J. Phys. B {\bf 41} (2008) 121002] and Morales {\it et al} [J. Phys. B {\bf 41} (2009) 134013]. However, we argue that these individual predictions should not be compared directly to each other, but preferably to experimental data generated under well-defined conditions.

Two photon double ionization of H2 using exterior complex scaling

We report converged calculations of fully, singly differential and total cross sections for two-photon double ionization of the hydrogen molecule in the range of 26–30 eV. These results have been obtained by using the method of exterior complex scaling combined with the use of DVR basis set.