lhuillier_1987#
A. L’Huillier and G. Wendin, “Linear and nonlinear screening effects in two-photon ionization of xenon”, Phys. Rev. A 36, 4747-4758 (1987)
Source record · Catalogue · Review register
Source kind: theory
Recorded technique: Diagrammatic many-body perturbation theory of two-photon ionisation of the Xe 5p (and 5s) shell in the zero-intensity limit, with screened electron-photon interactions r(omega) from the random-phase approximation with exchange (RPAE): ‘nonlinear screening’ screens both electron-photon interactions (Eq. 4, Fig. 1(c)), which brings in double excitations. Hartree-Fock basis (V^N potential; ten discrete states up to 14d or 15s, the continuum from 0.002 to 20 Ry in 90 points, the rest interpolated) or local-density basis (LDRPA; continuum states only, about 70); the two-photon amplitude by the perturbed-orbital method (Eqs. 9-11). Nonrelativistic: the spin-orbit splitting of the 5p^5 core is neglected (p. 4753).
Materials in structured entries: Xe
Dataset quantities: multiphoton_ionization_cross_section
Contents: 6 datasets; 0 formulas.
Curation notes#
Journal pp. 4747-4758 = PDF pages 1-12 (a scan: each page one 1-bit image, 5169 x 7129 pixels, 600 dpi). Identity checked on the first page (Physical Review A, volume 36, number 10, 15 November 1987; Anne L’Huillier, CEN Saclay, and Goran Wendin, Chalmers University of Technology; received 9 February 1987, revised 15 June 1987) on 2026-10-08.
THE DEFINITION (Eq. 8, p. 4751): ‘The two-photon 5p-shell ionization generalized cross section sigma_2 expressed in cm4 s’ is sigma_2 = 2 pi (alpha c / a0) (1 / F F0)^2 sum_l |t_eps_i(omega)|^2, F the laser flux in photons/cm2 s, F0 = 3.22e34 photons/cm2 s, summed over the electrons of the 5p shell and the final eps p and eps f channels; t (Eq. 9) is built from the dipole operator r or its screened form r(omega) (the length form). Linearly polarised light (p. 4753).
THE ENERGY AXES: the PHOTON energy in Ry, as printed (not the total energy). Fig. 6 runs ‘from the two-photon HF ionization threshold (0.46 Ry) up to 0.86 Ry’ and Fig. 7 ‘from 0.98 Ry to 1.40 Ry’ (p. 4753); the script finds the frame lines of both at those values within 0.001 Ry. The thresholds and resonance positions are the calculation’s own, nonrelativistic and spin-orbit-averaged, not experimental: the HF 5p threshold is 0.92 Ry (two photons of 0.46), the LD 5p ionisation energy 0.62 Ry with no bound excited states (p. 4753), and the experimental limits 0.89 and 0.99 Ry (2P3/2, 2P1/2; p. 4753). The resonances drawn are the calculated ones: the HF 6s spike lies at 0.660 Ry and the RPAE 6s resonance at 0.675 Ry (read), while the experimental 5p5(2P3/2)6s 1P1 energy is 0.62 Ry (p. 4754); ‘the RPAE screening leads to an important shift of the 5p^-1 nd resonances towards higher energies’ (p. 4753). No shift or scaling was applied, and none is applied here. Two-photon autoionisation between the real limits (‘below 0.5 Ry in Fig. 6’) is not described by the calculation (p. 4753).
EXTRACTED (tools/extract/lhuillier_1987.py), by data rule 8 (TC-699): the cross sections are in figures only, read from the page image (PDF page 7) at its native resolution. The frame lines are fitted to the image; every tick mark (x every 0.05 Ry; y every decade) is found where the script writes it (within 2 pixels) and lies on the fitted scale within 2 pixels. The frame, ticks, lettering (boxes written in the script), McCown et al.’s cross and Fig. 6’s 13 filled markers (squares of McGuire, circles of Gangopadhyay et al., found by a morphological opening and counted) are erased; the remaining ink is split into connected pieces: at least 150 pixels long, the solid line; at most 10 pixels, a dot; between, a dash. A curve is read at a column only where its ink is one run no taller than 12 pixels (steep flanks and resonance peaks are not read), gaps of the dashes and dots bridged within 25 pixels, and a value is kept only if a neighbouring grid point was read and agrees with it within the steepest slope the rule lets through. Above 0.79 Ry (HF) and 0.765 Ry (RPAE) the 5d-8s resonances of the solid and dashed lines overlap and are not read. One pixel is 1.33 % (Fig. 6) or 1.30 % (Fig. 7) in sigma_2; the lines are 4-7 pixels wide. The overlays of every value on the page image were inspected (2026-10-08): all lie on their lines. Where the dashed and dotted lines run together (Fig. 6, 0.49-0.53 Ry; Fig. 7, 1.25-1.40 Ry) a value may include pixels of the other line: the 8 % of those datasets covers it.
CHECK AGAINST McCOWN (mccown_1982): Fig. 6’s cross (‘experimental point at 193 nm by McCown et al.’, ‘0.47 Ry’) is found at 0.4719 Ry (193 nm is 0.4722 Ry) and 0.408e-49 cm4 s, 0.99 times McCown et al.’s alpha = 4e-32 cm4 W-1 converted as sigma = alpha hbar omega (0.412e-49 at 193 nm). FINDING: lhuillier_1989’s Fig. 6(b) draws the same measurement at 5.70e-50 cm4 s, 1.39 times as high (that record’s notes).
CHECK OF THE TEXT (p. 4753): above the threshold (Fig. 7) the RPAE result is ‘enhanced compared to the independent-electron result, by more than one order of magnitude’: the readings give RPAE / HF = 34 at 0.985 Ry, 23 at 1.0, 9 at 1.1 and 7-7.5 from 1.2 to 1.4 Ry, so the statement holds below about 1.1 Ry. In the threshold region the RPAE and LDRPA results lie a factor 5-70 below HF (readings: HF 1.41, RPAE 0.257, LDRPA 0.31 at 0.462-0.464 Ry; HF 4.29, RPAE 0.093, LDRPA 0.063 at 0.60 Ry, 1e-49 cm4 s).
NOT TAKEN: the overlays of Fig. 6, McGuire’s independent-electron squares (Ref. 34, mcguire_1981 holds McGuire’s own values), Gangopadhyay et al.’s MQDT circles (Ref. 35, not in the library) and McCown et al.’s cross (mccown_1982); Fig. 9 (the 5p + 5s total and 5p partial cross sections, HF and RPAE, 0.98-1.40 Ry), Fig. 10 (near-threshold region: RPAE nonlinear and linear screening, TDAE without ground-state correlation, and screening at 2 omega) and Fig. 11 (the same four in the ATI region), all two-photon cross sections in figures only, left for a later round; Fig. 12 (the ratio sigma_2 F / sigma_1, no quantity), Fig. 5 (the effective field) and Table I (the algebraic intrachannel interaction terms, no numbers).
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_1987/fig6_hf_Xe#
{
"id": "fig6_hf_Xe",
"material": "Xe",
"file": "Xe/lhuillier_1987__fig6_hf_Xe.csv",
"table": "fig_1027dbe08272",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"scale": 1e-49,
"abscissa_unit": "rydberg",
"use": "check",
"uncertainty": {
"relative": 0.05,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"channel": "5p shell (5p -> eps p, eps f)",
"method": "Hartree-Fock independent-electron approximation (V^N HF basis), lowest-order perturbation theory, nonrelativistic (no spin-orbit splitting of the core)",
"definition": "sigma_2 = 2 pi (alpha c / a0) (1 / F F0)^2 sum_l |t_eps_i(omega)|^2 (Eq. 8), F the photon flux in photons/cm2 s, F0 = 3.22e34 photons/cm2 s; the rate is sigma_2 F^2",
"gauge": "length (dipole operator r, Eq. 9)"
}
}
Fig. 6 (p. 4753), solid line: the Hartree-Fock (independent-electron) two-photon cross section of the Xe 5p shell, 1e-49 cm4 s, against the photon energy, read every 0.002 Ry from 0.462 to 0.762 Ry where readable (the 6s spike at 0.660 Ry, the steep 5d hump’s top and the overlapping resonances above 0.79 Ry not read). Calculated, nonrelativistic resonance positions (the record’s notes). 5 %: 3 pixels of line half-width and calibration at 1.33 % per pixel.
lhuillier_1987/fig6_rpae_Xe#
{
"id": "fig6_rpae_Xe",
"material": "Xe",
"file": "Xe/lhuillier_1987__fig6_rpae_Xe.csv",
"table": "fig_1027dbe08272",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"scale": 1e-49,
"abscissa_unit": "rydberg",
"use": "check",
"uncertainty": {
"relative": 0.08,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"channel": "5p shell (5p -> eps p, eps f)",
"method": "RPAE with nonlinear screening (both electron-photon interactions screened, Eq. 4), HF basis, nonrelativistic",
"definition": "sigma_2 = 2 pi (alpha c / a0) (1 / F F0)^2 sum_l |t_eps_i(omega)|^2 (Eq. 8), F the photon flux in photons/cm2 s, F0 = 3.22e34 photons/cm2 s; the rate is sigma_2 F^2",
"gauge": "length (screened dipole operator r(omega), Eqs. 4 and 9)"
}
}
Fig. 6 (p. 4753), dashed line: the RPAE two-photon cross section of the Xe 5p shell with nonlinear screening (Eq. 4, Fig. 1(c)), 1e-49 cm4 s, against the photon energy, read every 0.002 Ry from 0.462 to 0.762 Ry where readable (the 6s resonance’s peak near 0.675 Ry and the steep flanks not read; the antiresonance minimum near 0.72 Ry is read). 8 %: line half-width and calibration, and where the dashed and dotted lines run together (0.49-0.53 Ry) a value may include the dots.
lhuillier_1987/fig6_ldrpa_Xe#
{
"id": "fig6_ldrpa_Xe",
"material": "Xe",
"file": "Xe/lhuillier_1987__fig6_ldrpa_Xe.csv",
"table": "fig_1027dbe08272",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"scale": 1e-49,
"abscissa_unit": "rydberg",
"use": "check",
"uncertainty": {
"relative": 0.08,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"channel": "5p shell (5p -> eps p, eps f)",
"method": "LDRPA (RPA on a local-density basis, continuum states only) with nonlinear screening, nonrelativistic; LD 5p ionisation energy 0.62 Ry",
"definition": "sigma_2 = 2 pi (alpha c / a0) (1 / F F0)^2 sum_l |t_eps_i(omega)|^2 (Eq. 8), F the photon flux in photons/cm2 s, F0 = 3.22e34 photons/cm2 s; the rate is sigma_2 F^2",
"gauge": "length (screened dipole operator r(omega), Eqs. 4 and 9)"
}
}
Fig. 6 (p. 4753), dotted line: the LDRPA two-photon cross section of the Xe 5p shell with nonlinear screening (local-density basis, no bound excited states: ‘an average description of the real two-photon ionization spectrum’, p. 4753), 1e-49 cm4 s, against the photon energy, read every 0.002 Ry from 0.464 to 0.844 Ry where readable. Smooth: a minimum of 0.063 near 0.60 Ry, 0.99 near 0.74 Ry. 8 % (as for the dashed line).
lhuillier_1987/fig7_hf_Xe#
{
"id": "fig7_hf_Xe",
"material": "Xe",
"file": "Xe/lhuillier_1987__fig7_hf_Xe.csv",
"table": "fig_39a6b612098f",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"scale": 1e-49,
"abscissa_unit": "rydberg",
"use": "check",
"uncertainty": {
"relative": 0.05,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"channel": "5p shell (5p -> eps p, eps f)",
"method": "Hartree-Fock independent-electron approximation (V^N HF basis), lowest-order perturbation theory, nonrelativistic (no spin-orbit splitting of the core)",
"definition": "sigma_2 = 2 pi (alpha c / a0) (1 / F F0)^2 sum_l |t_eps_i(omega)|^2 (Eq. 8), F the photon flux in photons/cm2 s, F0 = 3.22e34 photons/cm2 s; the rate is sigma_2 F^2",
"gauge": "length (dipole operator r, Eq. 9)"
}
}
Fig. 7 (p. 4753), solid line: the Hartree-Fock two-photon cross section of the Xe 5p shell above the one-photon threshold (above-threshold ionisation), 1e-49 cm4 s, against the photon energy, every 0.005 Ry from 0.985 to 1.395 Ry: 0.032 at 0.985, a maximum of 0.071 near 1.15, 0.036 at 1.395. 5 % (as in Fig. 6; 1.30 % per pixel).
lhuillier_1987/fig7_rpae_Xe#
{
"id": "fig7_rpae_Xe",
"material": "Xe",
"file": "Xe/lhuillier_1987__fig7_rpae_Xe.csv",
"table": "fig_39a6b612098f",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"scale": 1e-49,
"abscissa_unit": "rydberg",
"use": "check",
"uncertainty": {
"relative": 0.08,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"channel": "5p shell (5p -> eps p, eps f)",
"method": "RPAE with nonlinear screening (both electron-photon interactions screened, Eq. 4), HF basis, nonrelativistic",
"definition": "sigma_2 = 2 pi (alpha c / a0) (1 / F F0)^2 sum_l |t_eps_i(omega)|^2 (Eq. 8), F the photon flux in photons/cm2 s, F0 = 3.22e34 photons/cm2 s; the rate is sigma_2 F^2",
"gauge": "length (screened dipole operator r(omega), Eqs. 4 and 9)"
}
}
Fig. 7 (p. 4753), dashed line: the RPAE two-photon cross section of the Xe 5p shell with nonlinear screening in the above-threshold region, 1e-49 cm4 s, against the photon energy, every 0.005 Ry from 0.985 to 1.39 Ry where readable: 1.11 at 0.985 falling to 0.27 at 1.39. The same calculation is the 5p partial cross section of Fig. 9 (not taken). 8 %: from 1.25 Ry the dashed and dotted lines run together.
lhuillier_1987/fig7_ldrpa_Xe#
{
"id": "fig7_ldrpa_Xe",
"material": "Xe",
"file": "Xe/lhuillier_1987__fig7_ldrpa_Xe.csv",
"table": "fig_39a6b612098f",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"scale": 1e-49,
"abscissa_unit": "rydberg",
"use": "check",
"uncertainty": {
"relative": 0.08,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"channel": "5p shell (5p -> eps p, eps f)",
"method": "LDRPA (RPA on a local-density basis, continuum states only) with nonlinear screening, nonrelativistic",
"definition": "sigma_2 = 2 pi (alpha c / a0) (1 / F F0)^2 sum_l |t_eps_i(omega)|^2 (Eq. 8), F the photon flux in photons/cm2 s, F0 = 3.22e34 photons/cm2 s; the rate is sigma_2 F^2",
"gauge": "length (screened dipole operator r(omega), Eqs. 4 and 9)"
}
}
Fig. 7 (p. 4753), dotted line: the LDRPA two-photon cross section of the Xe 5p shell with nonlinear screening in the above-threshold region, 1e-49 cm4 s, against the photon energy, every 0.005 Ry from 0.985 to 1.39 Ry where readable: 0.75 at 0.985, 0.31-0.35 from 1.13 Ry. 8 % (as for the dashed line).
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.