lhuillier_1989#
A. L’Huillier, X. Tang and P. Lambropoulos, “Multiphoton ionization of rare gases using multichannel-quantum-defect theory”, Phys. Rev. A 39, 1112-1122 (1989)
Source record · Catalogue · Review register
Source kind: theory
Recorded technique: Multichannel quantum-defect theory (Fano’s eigenchannel formulation; Lu-Fano plots and the Robaux-Aymar program) for the J = 0, 2 even-parity and J = 1, 3 odd-parity Rydberg series of Xe and Kr, the parameters (mu_alpha, U_i_alpha) fitted to experimental energy levels, with jj-coupled channels converging to the 2P3/2 and 2P1/2 limits; bound-bound and bound-free dipole matrix elements of the MQDT wave functions outside the core (Burgess-Seaton cutoff, Eq. 28), with fitted one-photon oscillator strengths. N-photon generalised cross sections in lowest-order perturbation theory (Eqs. 29-30), linear polarisation (p. 1116), the sum over intermediate states truncated to the discrete spectrum, about 25 Rydberg states (p. 1117).
Materials in structured entries: Kr, Xe
Dataset quantities: multiphoton_ionization_cross_section
Contents: 7 datasets; 0 formulas.
Curation notes#
Journal pp. 1112-1122 = PDF pages 1-11 (a scan: each page one 1-bit image, 5169 x 7129 pixels, 600 dpi; no text layer is used). Identity checked on the first page (Physical Review A, volume 39, number 3, 1 February 1989; A. L’Huillier, X. Tang and P. Lambropoulos, University of Southern California; received 11 August 1988) on 2026-10-08.
THE DEFINITION (Eq. 29, p. 1116): sigma_N = 2 pi (alpha c / a0) (omega / F0)^N sum_J sum_alpha |D_alpha^N|^2, in cm^2N s^(N-1), F0 = 3.22e34 photons/cm2 s, omega the photon energy (a.u.); the rate is sigma_N F^N with F the photon flux. D_alpha^N (Eq. 30) is the N-photon amplitude with the dipole operator epsilon . r (Eq. 27, the length form), epsilon linear. The truncation of the intermediate sum to the discrete spectrum ‘should yield reasonable cross sections in this energy range’ (between the two limits and slightly above the second, p. 1117); the authors expect it to become worse as the number of photons increases (p. 1121).
THE ENERGY AXES (Figs. 6 and 10): ‘Energy (10^3 cm^-1)’, the TOTAL energy of the two-photon final state above the ground state, not the photon energy: Fig. 6’s ranges, 115 000-116 500 cm^-1 in Kr and 103 000-106 000 cm^-1 in Xe, lie between the 2P3/2 and 2P1/2 limits (p. 1118), and Fig. 10 is ‘above the second ionization threshold, up to about 130 000 cm^-1 in Xe, and 140 000 cm^-1 in Kr’ (p. 1120). The resonance positions are those of the MQDT fit to experimental levels (J-resolved, jj-coupled channels; the primes mark series converging to 2P1/2); no shift or scaling was applied. DECISION (recorded in the register): the data files’ x is the PHOTON wavenumber (cm-1, vacuum), half the total energy read on the axis; each value’s printed cell keeps the total energy and the pixel it was read at.
EXTRACTED (tools/extract/lhuillier_1989.py), by data rule 8 (TC-699): the two-photon cross sections are in figures only, read from the page images at their native resolution. Each panel’s frame lines are fitted to the image and the shear of the scan (up to 0.013 pixel per row) corrected; every tick mark is found in the image where the script writes it (within 2 pixels) and lies on the fitted scale: Fig. 6 within 3.8 pixels (x; y within 2.4: the inner x ticks sit 2-5 pixels off the line through the frame lines, so the total energy is uncertain by about 5 cm^-1 in Kr and 10 cm^-1 in Xe), Fig. 10 within 6.2 pixels (its minor ticks are hand-placed; 1 pixel = 0.43 %). The frame and ticks are erased and the ink split into connected pieces; the solid line is the pieces at least 150 pixels long, Fig. 6’s J = 0 dashes the smaller pieces in the band near zero. A curve is read at a column only where its ink is one run no taller than 12 pixels (the lines are 6-8 pixels wide): the resonances’ steep flanks and narrow peaks, and the off-scale tops of the f’ resonances, are left out by that rule. Gaps between dashes are bridged by linear interpolation within 25 pixels; a J = 0 dash touching the frame line (values below about 0.07e-50) is not read. The overlays of every value on the page images were inspected (2026-10-08): all lie on their lines.
FIG. 6 (p. 1119, fig_31bfc6fa4487): sigma_2 in 1e-50 cm4 s, linear axes, (a) Kr, (b) Xe. Solid: the total cross section; dashed: the partial cross section to J = 0 final states, ‘much smaller (by about a factor of 30) than that of the J = 2 states, except, of course, in the vicinity of the J = 0 resonances’ (p. 1118). Linear polarisation from the J = 0 ground state reaches J = 0 and J = 2 final states, so the total is J = 0 plus J = 2. The J = 0 curve is read only on its low background (0.12-0.26e-50) and a few points near its peaks; its peaks (Xe: 2.3e-50 at 104.62, 1.3e-50 at 105.71; Kr: about 0.3e-50) are steep and not read.
MISPRINT IN THE TEXT (not an erratum of a value): p. 1118 says ‘the cross in Fig. 6(a) indicates the experimental measurement ... by McCown et al.’; the cross is drawn in Fig. 6(b), the Xe panel (at a total energy of 103.62e3 cm^-1), and McCown et al. measured Xe. The caption spells the name ‘McCowen’.
CHECK AGAINST McCOWN (mccown_1982): the script finds the cross’s centre at 103.617e3 cm^-1 total and 5.70e-50 cm4 s, on the solid line (5.67e-50 there; the paper: ‘in good agreement with the present calculation’). It is drawn at twice the photon wavenumber of 193 nm (103.627e3), not at twice McCown et al.’s ArF line centre (103 466 cm^-1, their p. 3321). FINDING: its height is 1.39 times McCown et al.’s printed alpha = 4e-32 cm4 W-1 converted as sigma = alpha hbar omega (4.12e-50 cm4 s at 193 nm, the conversion of mccown_1982’s notes); the conversion the authors used is not stated. The script fails if the cross moves off the line or the ratio leaves 1.30-1.42.
FIG. 10 (p. 1120, fig_2942ab283ba9): sigma_2 in cm4 s, logarithmic axes, (a) Xe 110-130 and (b) Kr 120-140 (1e3 cm^-1, total). Only the solid line is this paper’s; overlaid and NOT TAKEN: Gangopadhyay et al.’s MQDT crosses (Ref. 18), McGuire’s independent-electron dashed line (Ref. 34, mcguire_1981 in the library), and L’Huillier and Wendin’s RPAE dot-dashed and linear-RPAE short-dashed lines (Ref. 8: lhuillier_1987 and J. Phys. B 20, L37 (1987)). Xe: read from 110.5 to 129.5 except at 129.0, where Gangopadhyay et al.’s cross lies on the line; Kr: 120.5 to 139.5. The labels 10^-49 and 10^-50 of panel (a) are centred on the ticks at rows 3576.5 and 4122.5 (the ‘10’ glyphs); a dash of McGuire’s line meets the frame 33 pixels higher.
STATED IN THE TEXT (p. 1121): three-photon ionisation above the second limit, ‘within 20% of those obtained by McGuire. For example, at 266 nm, we have sigma_3 = 6 x 10^-82 cm6 s2. The result of McGuire is 5 x 10^-82 cm6 s2. Perry and Landen have measured sigma_3 = 1.2 x 10^-82 cm6 s2. Kulander calculates a cross section equal to 2.5 x 10^-82 cm6 s2.’ The sentence does not name the gas; it is Xe: three 266 nm photons (112.8e3 cm^-1) lie above Xe’s second limit (below 110e3, where Fig. 10(a) starts) and below Kr’s (above 116.5e3, the top of Fig. 6(a), which is still between Kr’s limits). Taken: this paper’s value. NOT TAKEN: McGuire’s 5e-82 (mcguire_1981 holds McGuire’s own values), Perry and Landen’s 1.2e-82 (unpublished, Ref. 35) and Kulander’s 2.5e-82 (Ref. 7, not in the library; partly unpublished).
NOT TAKEN: Tables I-III (p. 1116), the MQDT parameters (mu_alpha^0, mu_alpha^1 and U_i_alpha) of the J = 0 and J = 2 even-parity series of Xe and Kr and the J = 3 odd-parity series of Xe: no quantity holds quantum-defect parameters. Figs. 2-3 (Lu-Fano plots), Figs. 4(a) and 5(a) (one-photon oscillator-strength density and cross section), Figs. 4(b) and 5(b) (three-photon autoionisation spectra, the scope of a later round), Fig. 7 (three-photon spectra against experiment, arbitrary units) and Figs. 8-9 (angular distributions).
THE PRINTED FIG. 2 CAPTION is from another paper: on p. 1117 the Kr Lu-Fano plot (panels ‘Kr J=2’ and ‘Kr J=0’) is printed above ‘FIG. 2. Three stages of the plasma-vacuum interface development under the influence of the Rayleigh-Taylor instability ...’, a caption unrelated to this paper; the library copies it. Fig. 3’s caption is the Xe Lu-Fano plot’s. Nothing taken depends on Fig. 2.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
lhuillier_1989/fig6_total_Kr#
{
"id": "fig6_total_Kr",
"material": "Kr",
"file": "Kr/lhuillier_1989__fig6_total_Kr.csv",
"table": "fig_31bfc6fa4487",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"scale": 1e-50,
"abscissa_unit": "cm-1",
"use": "check",
"uncertainty": {
"absolute": 0.1,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"channel": "total (J = 0 and J = 2 final states)",
"method": "MQDT (eigenchannel, parameters fitted to experimental levels), lowest-order perturbation theory, intermediate sum over about 25 discrete Rydberg states",
"definition": "sigma_2 = 2 pi (alpha c / a0) (omega / F0)^2 sum_J sum_alpha |D_alpha^2|^2 (Eq. 29), F0 = 3.22e34 photons/cm2 s; the rate is sigma_2 F^2, F the photon flux in photons/cm2 s",
"gauge": "length (dipole operator epsilon . r, Eq. 27)",
"abscissa_definition": "photon wavenumber = half the total two-photon energy on the figure's axis (the record's decision)"
}
}
Fig. 6(a) (p. 1119), solid line: the total two-photon ionisation cross section of Kr between its 2P3/2 and 2P1/2 limits, 1e-50 cm4 s, against the photon wavenumber (half the total energy, 115.01 to 116.49e3 cm^-1 total, every 10 cm^-1 where readable). Autoionising resonances 6f’, 7f’ (off scale, not read), 9p2’, 9p’, 10p2’, 10p0’ (peaks not read). Read from the image (the record’s notes). 0.1e-50: 4 pixels of line half-width and calibration (0.011e-50 per pixel), and the x uncertainty on the sloping stretches; the paper states none.
lhuillier_1989/fig6_J0_Kr#
{
"id": "fig6_J0_Kr",
"material": "Kr",
"file": "Kr/lhuillier_1989__fig6_J0_Kr.csv",
"table": "fig_31bfc6fa4487",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"scale": 1e-50,
"abscissa_unit": "cm-1",
"use": "check",
"uncertainty": {
"absolute": 0.05,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"channel": "J = 0 final states (partial)",
"method": "MQDT (eigenchannel, parameters fitted to experimental levels), lowest-order perturbation theory, intermediate sum over about 25 discrete Rydberg states",
"definition": "the J = 0 term of sigma_2 = 2 pi (alpha c / a0) (omega / F0)^2 sum_J sum_alpha |D_alpha^2|^2 (Eq. 29), F0 = 3.22e34 photons/cm2 s",
"gauge": "length (dipole operator epsilon . r, Eq. 27)",
"abscissa_definition": "photon wavenumber = half the total two-photon energy on the figure's axis (the record's decision)"
}
}
Fig. 6(a) (p. 1119), dashed line: the partial two-photon cross section of Kr to J = 0 final states, 1e-50 cm4 s, against the photon wavenumber (half the total energy). Read only where the dashes stand clear of the frame line: 115.01-115.61 and near 116.26e3 cm^-1 total; between, the line lies on the frame (below about 0.07e-50). 0.05e-50: the dash half-width (3 pixels) and calibration.
lhuillier_1989/fig6_total_Xe#
{
"id": "fig6_total_Xe",
"material": "Xe",
"file": "Xe/lhuillier_1989__fig6_total_Xe.csv",
"table": "fig_31bfc6fa4487",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"scale": 1e-50,
"abscissa_unit": "cm-1",
"use": "check",
"uncertainty": {
"absolute": 0.15,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"channel": "total (J = 0 and J = 2 final states)",
"method": "MQDT (eigenchannel, parameters fitted to experimental levels), lowest-order perturbation theory, intermediate sum over about 25 discrete Rydberg states",
"definition": "sigma_2 = 2 pi (alpha c / a0) (omega / F0)^2 sum_J sum_alpha |D_alpha^2|^2 (Eq. 29), F0 = 3.22e34 photons/cm2 s; the rate is sigma_2 F^2, F the photon flux in photons/cm2 s",
"gauge": "length (dipole operator epsilon . r, Eq. 27)",
"abscissa_definition": "photon wavenumber = half the total two-photon energy on the figure's axis (the record's decision)"
}
}
Fig. 6(b) (p. 1119), solid line: the total two-photon ionisation cross section of Xe between its 2P3/2 and 2P1/2 limits, 1e-50 cm4 s, against the photon wavenumber (half the total energy, 103.02 to 105.98e3 cm^-1 total, every 20 cm^-1 where readable; 103.56-103.68 left out under McCown et al.’s cross, which lies on the line at 5.70e-50). Resonances 5f’, 6f’ (off scale), 9p2, 9p0’, 10p2’, 10p0’ (peaks not read). 0.15e-50: 4 pixels of line half-width and calibration (0.017e-50 per pixel), and the x uncertainty on the sloping stretches.
lhuillier_1989/fig6_J0_Xe#
{
"id": "fig6_J0_Xe",
"material": "Xe",
"file": "Xe/lhuillier_1989__fig6_J0_Xe.csv",
"table": "fig_31bfc6fa4487",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"scale": 1e-50,
"abscissa_unit": "cm-1",
"use": "check",
"uncertainty": {
"absolute": 0.08,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"channel": "J = 0 final states (partial)",
"method": "MQDT (eigenchannel, parameters fitted to experimental levels), lowest-order perturbation theory, intermediate sum over about 25 discrete Rydberg states",
"definition": "the J = 0 term of sigma_2 = 2 pi (alpha c / a0) (omega / F0)^2 sum_J sum_alpha |D_alpha^2|^2 (Eq. 29), F0 = 3.22e34 photons/cm2 s",
"gauge": "length (dipole operator epsilon . r, Eq. 27)",
"abscissa_definition": "photon wavenumber = half the total two-photon energy on the figure's axis (the record's decision)"
}
}
Fig. 6(b) (p. 1119), dashed line: the partial two-photon cross section of Xe to J = 0 final states, 1e-50 cm4 s, against the photon wavenumber (half the total energy). Read on its background, 103.02-103.82e3 cm^-1 total (0.13-0.24e-50), and a few points on the flanks of the 9p0’ and 10p0’ peaks; elsewhere the dashes lie on the frame line or are steep (the peaks, 2.3e-50 at 104.62 and 1.3e-50 at 105.71, are not read). 0.08e-50: the dash half-width (3 pixels) and calibration.
lhuillier_1989/fig10_total_Xe#
{
"id": "fig10_total_Xe",
"material": "Xe",
"file": "Xe/lhuillier_1989__fig10_total_Xe.csv",
"table": "fig_2942ab283ba9",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "cm-1",
"use": "check",
"uncertainty": {
"relative": 0.03,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"channel": "total",
"method": "MQDT (eigenchannel, parameters fitted to experimental levels, fitted one-photon oscillator strengths), lowest-order perturbation theory, intermediate sum over about 25 discrete Rydberg states",
"definition": "sigma_2 = 2 pi (alpha c / a0) (omega / F0)^2 sum_J sum_alpha |D_alpha^2|^2 (Eq. 29), F0 = 3.22e34 photons/cm2 s; the rate is sigma_2 F^2, F the photon flux in photons/cm2 s",
"gauge": "length (dipole operator epsilon . r, Eq. 27)",
"abscissa_definition": "photon wavenumber = half the total two-photon energy on the figure's axis (the record's decision)"
}
}
Fig. 10(a) (p. 1120), solid line (‘present work’): the two-photon ionisation cross section of Xe above the 2P1/2 limit, cm4 s, against the photon wavenumber (half the total energy, 110.5 to 129.5e3 cm^-1 total every 500 cm^-1, without 129.0 under Gangopadhyay et al.’s cross). Smooth: 3.0e-50 at 110.5, a minimum of 1.65e-50 near 124, rising to 2.1e-50. 3 %: 4 pixels of line half-width and the ticks’ scatter (up to 6.2 pixels; 0.43 % per pixel).
lhuillier_1989/fig10_total_Kr#
{
"id": "fig10_total_Kr",
"material": "Kr",
"file": "Kr/lhuillier_1989__fig10_total_Kr.csv",
"table": "fig_2942ab283ba9",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "cm-1",
"use": "check",
"uncertainty": {
"relative": 0.03,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"channel": "total",
"method": "MQDT (eigenchannel, parameters fitted to experimental levels, fitted one-photon oscillator strengths), lowest-order perturbation theory, intermediate sum over about 25 discrete Rydberg states",
"definition": "sigma_2 = 2 pi (alpha c / a0) (omega / F0)^2 sum_J sum_alpha |D_alpha^2|^2 (Eq. 29), F0 = 3.22e34 photons/cm2 s; the rate is sigma_2 F^2, F the photon flux in photons/cm2 s",
"gauge": "length (dipole operator epsilon . r, Eq. 27)",
"abscissa_definition": "photon wavenumber = half the total two-photon energy on the figure's axis (the record's decision)"
}
}
Fig. 10(b) (p. 1120), solid line (‘present work’): the two-photon ionisation cross section of Kr above the 2P1/2 limit, cm4 s, against the photon wavenumber (half the total energy, 120.5 to 139.5e3 cm^-1 total every 500 cm^-1). Falls from 1.3e-50 at 120.5 to 1.8e-51 at 139.5. 3 % (as for Xe).
lhuillier_1989/text_sigma3_Xe#
{
"id": "text_sigma3_Xe",
"material": "Xe",
"table": "text",
"scale": 1e-82,
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm6 s2",
"abscissa_unit": "nm",
"use": "check",
"uncertainty": {
"level": "not stated"
},
"parameters": {
"photons": 3,
"wavelength_nm": 266,
"polarization": "linear",
"method": "MQDT (eigenchannel, parameters fitted to experimental levels), lowest-order perturbation theory, intermediate sums over the discrete spectrum",
"definition": "sigma_3 = 2 pi (alpha c / a0) (omega / F0)^3 sum_J sum_alpha |D_alpha^3|^2 (Eq. 29), F0 = 3.22e34 photons/cm2 s; the rate is sigma_3 F^3, F the photon flux in photons/cm2 s",
"gauge": "length (dipole operator epsilon . r, Eq. 27)"
}
}
1 inline points in the source record.
p. 1121: ‘at 266 nm, we have sigma_3 = 6 x 10^-82 cm6 s2’, three-photon ionisation above the second limit; the gas is Xe by the energies (the record’s notes). One significant figure; ‘within 20% of those obtained by McGuire’, and the truncated intermediate sum ‘may become worse as the number of photons increases’. The wavelength medium is not stated.
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.