haber_2009

L. H. Haber, B. Doughty and S. R. Leone, “Photoelectron Angular Distributions and Cross Section Ratios of Two-Color Two-Photon Above Threshold Ionization of Argon”, J. Phys. Chem. A 113, 13152-13158 (2009)

Source record · Catalogue · Review register

DOI: 10.1021/jp903231n

Source kind: measurement

Recorded technique: Velocity map imaging of the photoelectrons of argon (skimmed effusive beam) ionised by one selected high-order harmonic of 800 nm (the 13th or the 15th, chosen by a home-built EUV monochromator; HH generated in a pulsed argon jet) with a delayed 800 nm dressing pulse (Ti:sapphire, 50 fs, 2.4 mJ, 1 kHz, split 50:50) crossing it at about 1.5 deg. Estimated intensities about 5 x 10^10 W/cm2 (IR) and 1 x 10^4 W/cm2 (EUV). Both beams linearly polarised, the polarisations collinear and parallel to the detector face. EUV-only and EUV+IR images alternated at 1 min intervals by a beam block over about one day per harmonic; images inverted with pBASEX (P2 and P4) after subtracting 0-100 % of the EUV-only image (85 % for the quoted values); the EUV-IR cross-correlation FWHM about 100 fs (pp. 13153-13154).

Materials in structured entries: None recorded.

Dataset quantities: None recorded.

Contents: 0 datasets; 0 formulas.

Curation notes

Context only, no datasets. Identity checked on the first page (PDF p. 1): Haber, Doughty and Leone, J. Phys. Chem. A 113, 13152-13158 (2009), published on the web 07/17/2009, part of the Robert W. Field Festschrift; seven pages, PDF page n = journal page 13151 + n. The version in the library carries the ‘Note Added after ASAP Publication’ (p. 13158): the text after eq 3 and three lines below eq 5 were corrected on 3 August 2009, so this is the corrected version. Every number below was read on the rendered pages (pp. 13154-13157) and Table 1’s image.

WHAT THE PAPER MEASURES. Two-colour two-photon above-threshold ionisation of argon 3p: the sidebands one 800 nm photon above (+, EUV + IR, both photons absorbed) and below (-, EUV - IR, the IR photon emitted) the single-photon (SPI) line of one harmonic. The harmonic photon energies are inferred from the SPI photoelectrons: ‘consistent with photon energies of 20.1 and 23.2 eV for the 13th and 15th harmonics’ (p. 13155), from SPI peaks at 4.30 +- 0.08 eV (FWHM 0.65 eV) and 7.42 +- 0.10 eV (FWHM 0.91 eV). The sideband peaks: 13th, 5.86 +- 0.09 (+) and 2.73 +- 0.06 eV (-); 15th, 8.95 +- 0.11 (+) and 5.84 +- 0.09 eV (-); no ponderomotive shift seen. The energy axis is the photoelectron kinetic energy; the paper does not say which threshold it subtracted, but 20.1 - 4.30 and 23.2 - 7.42 give 15.8 eV, the 2P3/2 threshold (15.7596 eV, data/external/nist_asd/ionization_energies.csv). The two ionic cores 2P3/2 and 2P1/2 (0.18 eV apart, p. 13155) are not resolved: every value is summed over both, over the final magnetic sublevels and over the final partial waves, which for a 3p electron after two photons are p and f (‘The sideband photoelectrons are composed of partial waves of p and f symmetry’, p. 13156), not s and d.

The numbers (Table 1, p. 13157; the same in the text, pp. 13155-13157): - sigma(+)/sigma(-), the ratio of the sidebands’ angle-integrated cross sections: experiment 1.39 +- 0.04 (13th HH + 800 nm) and 1.27 +- 0.05 (15th); second-order perturbation theory (SOPT) 1.42 and 1.28; soft-photon approximation (SPA) 1.78 and 1.27. - beta_2 and beta_4 of each sideband, I(theta) = sigma/(4 pi) [1 + beta_2 P_2(cos theta) + beta_4 P_4(cos theta)] (eq 1), theta from the common polarisation axis. 13th: experiment beta_2(-) 1.52 +- 0.05, beta_4(-) 0.21 +- 0.05, beta_2(+) 2.37 +- 0.10, beta_4(+) 0.63 +- 0.04; SOPT 1.97, 0.40, 1.68, 0.54; SPA 2.27, 0.35, 2.59, 0.79. 15th: experiment 1.63 +- 0.12, 0.54 +- 0.15, 2.48 +- 0.06, 0.69 +- 0.05; SOPT 1.69, 0.40, 1.28, 0.45; SPA 2.59, 0.79, 2.69, 0.92. - single-photon beta_2 and beta_4 of argon at the two harmonics (unconstrained fit): 0.86 +- 0.01 and 0.00 +- 0.01 (13th), 1.32 +- 0.01 and 0.00 +- 0.01 (15th), p. 13155. The uncertainty’s level is not stated.

The definition of sigma (p. 13156): ‘In the low-intensity limit, the cross section of the ATI sideband is expressed as sigma = sum_ij |F1 F2 M_ij|^2’, F1 and F2 the EUV and IR fields and M the complex two-photon matrix element (SOPT, Toma and Muller), so sigma(+)/sigma(-) = sum |M(+)|^2 / sum |M(-)|^2 (eq 2), independent of the fields. The measured ratio is the ratio of the difference spectra’s areas over each sideband’s FWHM, ‘Because the positive EUV+IR and negative EUV-IR sidebands are produced concurrently under the same experimental conditions and photon fluxes’ (p. 13155). It is constant from 0 to about 90 % background subtraction (Fig. 4). No absolute cross section, rate or amplitude is given, and no gauge is named. The SOPT values were computed by the authors from Toma and Muller’s tabulated matrix elements and phase shifts (ref. 18; a one-electron model potential without spin-orbit coupling, p. 13156); the SPA values from eqs 4-5 with Henke et al.’s SPI cross sections (37.6, 37.0 and 34.9 Mb at 18.6, 21.7 and 24.9 eV, ref. 28) and Taylor’s beta_2(0) (about 0.4, 1.1 and 1.4 at 2.7, 5.8 and 9.0 eV, ref. 26).

AN INCONSISTENCY. The SOPT beta_2(-) for the 15th harmonic is 1.69 in Table 1 but ‘beta_2(-) = 1.63’ in the text (p. 13156, right column, checked on the rendered page), which calls the agreement with the measured 1.63 +- 0.12 ‘fortuitous’. Which is the misprint the paper does not show; both agree with the measurement within its uncertainty. Also printed (p. 13156) and model-only: the SOPT partial cross-section ratios sigma_pz/sigma_px,y of 2.19 (+) and 2.62 (-) for the 13th and 2.57 (+) and 2.99 (-) for the 15th harmonic.

WHY NOTHING IS TAKEN. multiphoton_ionization_cross_section is an absolute generalised cross section; the paper gives only ratios, and its - sideband is absorption plus stimulated emission, not two-photon absorption. A sideband cross-section ratio and photoelectron anisotropy parameters have no quantity: NOT TAKEN (awaiting vocabulary): Table 1 (6 rows x 5 columns) and the SPI beta_2, beta_4 of p. 13155 (a candidate quantity, not yet in the vocabulary). Also not taken: the background anisotropy parameters at the sideband energies (p. 13155), which ‘result from small deviations from ideal velocity map imaging configurations’; the SOPT partial ratios above (model quantities, not observables); Figs. 2-6 (raster images; Figs. 4-6 show the Table 1 values against the subtracted percentage, Figs. 2-3 the photoelectron spectra in arbitrary units).

FOR OEP 8 (section 4.2, Q6) AND OEP 6 (Q9). The + sideband is a nondegenerate two-photon amplitude M(Omega, omega) with Omega = 20.1 or 23.2 eV and omega the 800 nm photon: total energies about 21.6 and 24.7 eV and a half-separation nu = (Omega - omega)/2 of about 9.3 and 10.8 eV. The harmonic alone ionises argon (Omega above 15.76 eV and far above the first intermediate resonance, 3p5 4s[3/2]1 at 11.62 eV, NIST Ar_I_levels.tsv), so the harmonic-first time order passes through the continuum on shell and the amplitude is complex; the IR-first order sits 10 eV below 4s. Like mccann_1988’s xenon pair, these splits lie past every bound intermediate pole and test nothing at small splits; the - sideband carries the E^-E^+ terms OEP 8’s kernel omits. Both are channel-summed ratios, not channel-resolved amplitudes.

Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets

No datasets are recorded.

Formulas

No formulas are recorded.

Corrections

No dataset errata are recorded in this source record.

Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.