pan_1990b#
C. Pan, B. Gao and A. F. Starace, “Two-photon ionization of the Ar atom and detachment of the F- ion”, Phys. Rev. A 41, 6271-6286 (1990)
Source record · Catalogue · Review register
Source kind: theory
Recorded technique: Lowest-order (two-photon) perturbation theory for the Ar 3p subshell below the one-photon threshold, with electron correlations added process by process (Table I) and every sum over intermediate states done implicitly by variationally stable procedures (Sec. II): (1) HF (lowest order; 3p and, in lowest order, 3s and inner subshells); (2) intermediate-state interchannel interactions, to infinite order by a projection PHP onto singly excited states; (3) ground-state correlations; (4) intermediate-state shake-up; (5) intermediate-state electron scattering; (6) final-state electron scattering, with exact angular factors (Pauli principle) rather than the RPA ones. Final states 3p5(2P) epsilon-p 1S, epsilon-p 1D, epsilon-f 1D (Eq. 49); frozen-core HF orbitals; continuum HF orbitals in the LS-dependent nonlocal potential; Slater-orbital expansions of 40-50 terms, amplitudes converged ‘to better than 1 part in 10^3’ (p. 8/6278). Dipole length and velocity forms.
Materials in structured entries: Ar
Dataset quantities: multiphoton_ionization_cross_section
Contents: 16 datasets; 0 formulas.
Curation notes#
Journal pp. 6271-6286 = PDF pages 1-16; journal page = PDF page + 6270. Identity checked on the first page (PDF p. 1: ‘PHYSICAL REVIEW A VOLUME 41, NUMBER 11 1 JUNE 1990’; Cheng Pan, Bo Gao and Anthony F. Starace, Nebraska; received 5 February 1990) on 2026-10-09. The record id is pan_1990b: pan_1990 is Pan, Taylor and Clark’s 1990 paper on harmonic generation. The PDF is a scan: every page is one embedded image, 5060 x 6898 pixels (about 595 dpi).
THE CROSS SECTION (p. 9/6279): ‘W = sigma_N I^N’ (Eq. 52), ‘W is usually measured in units of ions/sec, sigma_N in units of cm^2N sec^N-1, and I in units of photons /(cm^2 sec)’; ‘sigma_2^q = 8 pi^3 omega^2 / c^2 |T|^2 f_q (a.u.)’ (Eq. 53), T the reduced transition amplitude and f_q a geometrical factor of the polarisation q and the final term (Table II: linear q = 0, 1/9 for 1S and 2/45 for 1D; circular q = +-1, 0 for 1S and 1/15 for 1D); ‘L^4 T (a.u.) = 1.8967 x 10^-50 cm^4 sec’ (Eq. 54; a0^4 t0 in CODATA 2018 is 1.89679e-50). So the linear total is the sum of the three channels and the circular total is 3/2 the linear 1D channels’ sum, with no 1S part (p. 11/6281).
ENERGY AXIS (p. 8/6278): the abscissa of every figure is the photon energy, eV. ‘we have replaced the HF 3p orbital binding energy of 16.08 eV by the experimental 3p subshell binding energy of 15.76 eV’, in every singly excited intermediate-state Green’s function, and ‘the kinetic energy of the photoelectron is related to the photon energy by k^2/2 = 2 omega - 15.76 eV’; ‘it is not possible to shift the positions of intermediate-state resonances into exact agreement with experiment’. In process (6) one of the two 3p energies is replaced by half the experimental double ionisation energy, 43.4 eV (Eq. 51). The resonances are thus at the calculation’s own positions (‘HF level energies but experimental binding energies’, p. 12/6282): the 4s 1P rise begins near 11.4 eV and the peak stands near 11.9-12.1 eV in Figs. 1-5, the 3d/5s 1P near 14 eV and 4d/6s 1P near 15 eV (p. 9/6279, unresolved). LS coupling. No shift was applied to the drawn curves.
EXTRACTED (tools/extract/pan_1990b.py), by data rule 8 (TC-699): the paper prints its Ar cross sections only in figures, and no number of them in the text but the shake-up’s ‘approximately 0.1 x 10^-50 cm^4 sec’ (p. 12/6282). Fig. 1(b) (p. 9/6279): the p 1S channel, linear, length and velocity, with all processes and without the shake-up (4); Fig. 2 and Fig. 3 (p. 10/6280): the p 1D and f 1D channels, linear, length, all processes; Fig. 4 (p. 10/6280): the linear total, length and velocity, HF (a), without the shake-up (b) and with all processes (c); Fig. 5 (p. 11/6281): the circular total, length and velocity, HF and all processes. Each read from the page image at its native resolution: the axes calibrated from the tick marks (each found in the image and checked; the frame lines at the labelled corners added as ticks; every side’s ticks on one linear scale within 4.5 pixels, the worst residual 3.9), the photon energy interpolated between the bottom and top ticks’ scales and the value between the left and right ones (the scan is rotated by about 0.2 degrees); each curve traced column by column from a seed pixel and its line style checked from the trace (solid: no gap; dashed: gaps with nothing in them; dash-dot: one dot per gap; dash-double-dot: two), which tells the curves apart; samples every 0.1 eV where the line is clear: no other dark pixel within 6 pixels (about one line width) of it within 10 columns either side, no steeper than 3 pixels per column, away from the tick marks; across a gap of the dashes, interpolated between the nearest clear columns (at most 40 pixels apart). Where another curve comes closer the samples are left out, and where two curves of a figure are read within 7 pixels of each other (Fig. 5 at 9.2 and 10.5-10.8 eV) both are left out, since the reading cannot tell whose line it is: the script lists both kinds and fails if they change. Each value’s pixel is in its printed cell. One pixel is 0.0045 to 0.0047 eV in x; in y 0.0097e-51 cm4 s (Figs. 1-3), 0.0019e-50 (Fig. 4) and 0.0033e-50 (Fig. 5); the lines are 5 to 8 pixels wide. The overlays of the values on the page images were inspected (2026-10-09).
DIGITISING UNCERTAINTY: 5 pixels in y (the tick residuals, up to 3.9 pixels, and the centring on a line 5 to 8 pixels wide): 0.05e-51 cm4 s in Figs. 1-3, 0.010e-50 in Fig. 4, 0.017e-50 in Fig. 5. On the steep stretches (the rises into the resonances) add the slope times 0.02 eV (the x reading). The paper states no uncertainty of its calculation.
THE CHECKS (the script fails if one is missed): (1) Fig. 4(c) length against Figs. 1(b) + 2 + 3 (the total is the sum of the channels, Eq. 49): 0.983 to 0.997 (8.4-9.3 eV, 10 samples; Fig. 2 is read only to 9.6 eV). (2) Fig. 5’s all-process length curve against 3/2 times Figs. 2 + 3 (Table II): 1.000 to 1.003 (8.4-9.1 eV, 4 samples). (3) Fig. 6(a)’s solid curve (the same result drawn again beside the other calculations, read for this check only) against Fig. 4(c): 0.981 to 1.015 (8.4-13.8 eV, 32 samples). (4) Table II’s f_q give the 3/2 and no circular 1S. (5) Eq. 54 against CODATA, 5e-5. Reported: the shake-up lowers the length p 1S channel by 1.4e-51 to 2.5e-51 cm4 s (Fig. 1(b), 8.3-10.9 eV) and the length total by 1.3e-51 to 3.0e-51 (Fig. 4(b) - 4(c), 8.4-11.1 eV), against the text’s ‘approximately 0.1 x 10^-50 cm^4 sec’; it raises the velocity forms by 1.4e-51 to 3.3e-51. Length over velocity of the total below the 4s rise: HF 2.05 to 2.83, without the shake-up 1.52 to 2.04, all processes 0.93 to 1.11 (8.1-11.1 eV): the text’s agreement of the two forms (p. 11/6281).
COMPARISONS (Fig. 4(c), this paper over the other, at the samples read nearest 8, 9, 10 and 11 eV, and the range 8.4-11.1 eV): length form against McKenna and van der Hart 2004 (mckenna_2004/fig5_sigma2_Ar, TC-856; R-matrix Floquet): 0.78 (8.4 eV), 0.74 (9.0), 0.69 (10.1), 0.63 (11.0); range 0.62-0.78. Against Petrov et al. 2016 (petrov_2016, TC-877) corr + CP length (fig10_corrcp_L): 0.85, 0.81, 0.75, 0.60 (0.55-0.85); against their corr length without core polarisation (fig10_corr_L): 0.96, 0.94, 0.92, 0.88 (0.88-0.96). Against Starace and Jiang 1987’s ESI total (starace_1987/fig7_esi_linear_Ar, TC-878): 0.90, 0.89, 0.86, 0.84. The velocity form against McKenna: 0.69 (8.1 eV), 0.71, 0.71, 0.67. McKenna and van der Hart quote this paper as ‘within 20% of 0.85 x 10^-50 cm4 s’ (mckenna_2004 notes): the length total read here runs from 0.98e-50 (8.4 eV) to 0.71e-50 (11.0 eV), within 0.85e-50 +- 16 %; and about 30 % below theirs, as they say: 22-38 % here. Petrov et al. (petrov_2016 notes) quote it as ‘approximately 12% smaller than our G2PICS’ in the length form, 8-11.5 eV: 4-12 % below their corr curve, 15-45 % below their final corr + CP curve as read here.
ERRATA: none found in the values; Fig. 2’s caption ‘Ar 3p6 + 2 gamma’ omits the (1S) the other captions give, without effect.
NOT TAKEN: (a) the F- two-photon detachment cross sections (Sec. IV, Figs. 7-11): no material of the registry. (b) Fig. 1(a) (the p 1S channel, HF and processes (1)-(3), length and velocity), Fig. 2’s HF length curve (dashed), Fig. 3’s HF (dash-dot) and processes (1)-(3) (dashed) curves, and Fig. 4(a)’s processes (1)-(3) curves (dash-dot, dash-double-dot): intermediate approximations, not read; the HF totals (Fig. 4(a), Fig. 5) and the totals without the shake-up (Fig. 4(b)) are taken to show how the correlations move the result. (c) Fig. 6: the other authors’ curves, which are theirs: Starace and Jiang 1987 (starace_1987, TC-878), Moccia, Rahman and Rizzo 1983 (moccia_1983), Pindzola and Kelly 1975 (pindzola_1975), McGuire 1981 (mcguire_1981, TC-879); this paper’s own curve in Fig. 6(a) is read only for check (3), and Fig. 6(b)’s is Fig. 5’s again (not read). (d) Table I (the processes) and Table II (f_q): no quantity. (e) Ranges of the curves not read: where another curve runs within about a line width, along the axis near zero, at the frame’s tick marks, and the steep rises into and the peaks of the resonances (the datasets list what is read).
TWO-PHOTON REFERENCES the paper cites (data not in this record): Ar: Pindzola and Kelly 1975 (pindzola_1975), Moccia et al. 1983 (moccia_1983), McGuire 1981 (mcguire_1981), Starace and Jiang 1987 (starace_1987); Xe: A. L’Huillier and G. Wendin, J. Phys. B 20, L37 (1987) and Phys. Rev. A 36, 4747 (1987) (lhuillier_1987, TC-883); P. Gangopadhyay, X. Tang, P. Lambropoulos and R. Shakeshaft, Phys. Rev. A 34, 2998 (1986); A. L’Huillier, X. Tang and P. Lambropoulos, Phys. Rev. A 39, 1112 (1989) (lhuillier_1989, TC-882); K. C. Kulander, Phys. Rev. A 36, 2726 (1987) and 38, 778 (1988); He: G. A. Victor, Proc. Phys. Soc. London 91, 825 (1967); B. Ritchie, Phys. Rev. A 16, 2080 (1977); A. L’Huillier, L. Jonsson and G. Wendin, Phys. Rev. A 33, 3938 (1986); H-: M. Crance and M. Aymar, J. Phys. B 18, 3529 (1985); M. G. J. Fink and P. Zoller, J. Phys. B 18, L373 (1985); F-: E. J. Robinson and S. Geltman, Phys. Rev. 153, 4 (1967); M. Crance, J. Phys. B 20, 6553 (1987) and 21, 3559 (1988); N. Kwon, P. S. Armstrong, T. Olsson, R. Trainham and D. J. Larson, Phys. Rev. A 40, 676 (1989) (measured).
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
pan_1990b/fig1b_all_L_p1S_Ar#
{
"id": "fig1b_all_L_p1S_Ar",
"material": "Ar",
"file": "Ar/pan_1990b__fig1b_all_L_p1S_Ar.csv",
"table": "fig_41ffe3dfe10f",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 5e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "variationally stable perturbation theory (implicit sums over intermediate states, Slater-orbital expansions), frozen-core HF orbitals, continuum HF orbitals in the LS-dependent nonlocal potential, experimental 3p binding energy 15.76 eV in the intermediate-state Green's functions and the photoelectron energy (k^2/2 = 2 omega - 15.76 eV), half the experimental double-ionisation energy (43.4 eV) in process (6) (Eq. 51); all processes of Table I, (1)-(6), including the intermediate-state shake-up (4)",
"definition": "sigma_2 = W / I^2 (Eq. 52), W the ionisation rate in s^-1 and I the photon flux in photons cm^-2 s^-1; computed as sigma_2^q = (8 pi^3 omega^2 / c^2) |T|^2 f_q in atomic units (Eq. 53, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 54)",
"channel": "3p5(2P) epsilon-p 1S"
}
}
Fig. 1(b) (p. 9/6279), solid curve: the partial (3p5(2P) epsilon-p 1S channel) generalised two-photon cross section of Ar, linear polarisation, dipole length form, all processes of Table I, cm4 s against the photon energy, read from the scanned image every 0.1 eV, 8.1 to 10.9 eV (from 11.0 eV it meets the dashed velocity curve and rises into the 4s resonance). +-5.0e-53 cm4 s: the reading (5 pixels; the record’s notes); the paper states none.
pan_1990b/fig1b_all_V_p1S_Ar#
{
"id": "fig1b_all_V_p1S_Ar",
"material": "Ar",
"file": "Ar/pan_1990b__fig1b_all_V_p1S_Ar.csv",
"table": "fig_41ffe3dfe10f",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 5e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "velocity",
"method": "variationally stable perturbation theory (implicit sums over intermediate states, Slater-orbital expansions), frozen-core HF orbitals, continuum HF orbitals in the LS-dependent nonlocal potential, experimental 3p binding energy 15.76 eV in the intermediate-state Green's functions and the photoelectron energy (k^2/2 = 2 omega - 15.76 eV), half the experimental double-ionisation energy (43.4 eV) in process (6) (Eq. 51); all processes of Table I, (1)-(6), including the intermediate-state shake-up (4)",
"definition": "sigma_2 = W / I^2 (Eq. 52), W the ionisation rate in s^-1 and I the photon flux in photons cm^-2 s^-1; computed as sigma_2^q = (8 pi^3 omega^2 / c^2) |T|^2 f_q in atomic units (Eq. 53, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 54)",
"channel": "3p5(2P) epsilon-p 1S"
}
}
Fig. 1(b) (p. 9/6279), dashed curve: the partial (3p5(2P) epsilon-p 1S channel) generalised two-photon cross section of Ar, linear polarisation, dipole velocity form, all processes of Table I, cm4 s against the photon energy, read from the scanned image every 0.1 eV, 8.2 to 11.0 eV. +-5.0e-53 cm4 s: the reading (5 pixels; the record’s notes); the paper states none.
pan_1990b/fig1b_noshakeup_L_p1S_Ar#
{
"id": "fig1b_noshakeup_L_p1S_Ar",
"material": "Ar",
"file": "Ar/pan_1990b__fig1b_noshakeup_L_p1S_Ar.csv",
"table": "fig_41ffe3dfe10f",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 5e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "variationally stable perturbation theory (implicit sums over intermediate states, Slater-orbital expansions), frozen-core HF orbitals, continuum HF orbitals in the LS-dependent nonlocal potential, experimental 3p binding energy 15.76 eV in the intermediate-state Green's functions and the photoelectron energy (k^2/2 = 2 omega - 15.76 eV), half the experimental double-ionisation energy (43.4 eV) in process (6) (Eq. 51); processes (1)-(3), (5) and (6) of Table I: all but the intermediate-state shake-up (4)",
"definition": "sigma_2 = W / I^2 (Eq. 52), W the ionisation rate in s^-1 and I the photon flux in photons cm^-2 s^-1; computed as sigma_2^q = (8 pi^3 omega^2 / c^2) |T|^2 f_q in atomic units (Eq. 53, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 54)",
"channel": "3p5(2P) epsilon-p 1S"
}
}
Fig. 1(b) (p. 9/6279), dash-dot curve: the partial (3p5(2P) epsilon-p 1S channel) generalised two-photon cross section of Ar, linear polarisation, dipole length form, all processes but the intermediate-state shake-up (4), cm4 s against the photon energy, read from the scanned image every 0.1 eV, 8.3 to 10.4 and 10.7 to 11.3 eV (10.5-10.6: the tip of the label’s arrow touches it). +-5.0e-53 cm4 s: the reading (5 pixels; the record’s notes); the paper states none.
pan_1990b/fig1b_noshakeup_V_p1S_Ar#
{
"id": "fig1b_noshakeup_V_p1S_Ar",
"material": "Ar",
"file": "Ar/pan_1990b__fig1b_noshakeup_V_p1S_Ar.csv",
"table": "fig_41ffe3dfe10f",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 5e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "velocity",
"method": "variationally stable perturbation theory (implicit sums over intermediate states, Slater-orbital expansions), frozen-core HF orbitals, continuum HF orbitals in the LS-dependent nonlocal potential, experimental 3p binding energy 15.76 eV in the intermediate-state Green's functions and the photoelectron energy (k^2/2 = 2 omega - 15.76 eV), half the experimental double-ionisation energy (43.4 eV) in process (6) (Eq. 51); processes (1)-(3), (5) and (6) of Table I: all but the intermediate-state shake-up (4)",
"definition": "sigma_2 = W / I^2 (Eq. 52), W the ionisation rate in s^-1 and I the photon flux in photons cm^-2 s^-1; computed as sigma_2^q = (8 pi^3 omega^2 / c^2) |T|^2 f_q in atomic units (Eq. 53, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 54)",
"channel": "3p5(2P) epsilon-p 1S"
}
}
Fig. 1(b) (p. 9/6279), dash-double-dot curve: the partial (3p5(2P) epsilon-p 1S channel) generalised two-photon cross section of Ar, linear polarisation, dipole velocity form, all processes but the intermediate-state shake-up (4), cm4 s against the photon energy, read from the scanned image every 0.1 eV, 8.1 to 9.3 eV (above, it runs along the axis within a line width of zero, and the label’s arrow ends on it). +-5.0e-53 cm4 s: the reading (5 pixels; the record’s notes); the paper states none.
pan_1990b/fig2_all_L_p1D_Ar#
{
"id": "fig2_all_L_p1D_Ar",
"material": "Ar",
"file": "Ar/pan_1990b__fig2_all_L_p1D_Ar.csv",
"table": "fig_08fff07d737e",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 5e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "variationally stable perturbation theory (implicit sums over intermediate states, Slater-orbital expansions), frozen-core HF orbitals, continuum HF orbitals in the LS-dependent nonlocal potential, experimental 3p binding energy 15.76 eV in the intermediate-state Green's functions and the photoelectron energy (k^2/2 = 2 omega - 15.76 eV), half the experimental double-ionisation energy (43.4 eV) in process (6) (Eq. 51); all processes of Table I, (1)-(6), including the intermediate-state shake-up (4)",
"definition": "sigma_2 = W / I^2 (Eq. 52), W the ionisation rate in s^-1 and I the photon flux in photons cm^-2 s^-1; computed as sigma_2^q = (8 pi^3 omega^2 / c^2) |T|^2 f_q in atomic units (Eq. 53, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 54)",
"channel": "3p5(2P) epsilon-p 1D"
}
}
Fig. 2 (p. 10/6280), solid curve: the partial (3p5(2P) epsilon-p 1D channel) generalised two-photon cross section of Ar, linear polarisation, dipole length form, all processes of Table I, cm4 s against the photon energy, read from the scanned image every 0.1 eV, 8.1 and 8.4 to 9.6 eV (above 9.7 eV it runs along the axis within a line width of zero, to the 4s rise). +-5.0e-53 cm4 s: the reading (5 pixels; the record’s notes); the paper states none.
pan_1990b/fig3_all_L_f1D_Ar#
{
"id": "fig3_all_L_f1D_Ar",
"material": "Ar",
"file": "Ar/pan_1990b__fig3_all_L_f1D_Ar.csv",
"table": "fig_7ef7a8747556",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 5e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "variationally stable perturbation theory (implicit sums over intermediate states, Slater-orbital expansions), frozen-core HF orbitals, continuum HF orbitals in the LS-dependent nonlocal potential, experimental 3p binding energy 15.76 eV in the intermediate-state Green's functions and the photoelectron energy (k^2/2 = 2 omega - 15.76 eV), half the experimental double-ionisation energy (43.4 eV) in process (6) (Eq. 51); all processes of Table I, (1)-(6), including the intermediate-state shake-up (4)",
"definition": "sigma_2 = W / I^2 (Eq. 52), W the ionisation rate in s^-1 and I the photon flux in photons cm^-2 s^-1; computed as sigma_2^q = (8 pi^3 omega^2 / c^2) |T|^2 f_q in atomic units (Eq. 53, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 54)",
"channel": "3p5(2P) epsilon-f 1D"
}
}
Fig. 3 (p. 10/6280), solid curve: the partial (3p5(2P) epsilon-f 1D channel) generalised two-photon cross section of Ar, linear polarisation, dipole length form, all processes of Table I, cm4 s against the photon energy, read from the scanned image every 0.1 eV, 8.2 to 11.7 and 12.4 to 13.9 eV (the 4s window resonance between). +-5.0e-53 cm4 s: the reading (5 pixels; the record’s notes); the paper states none.
pan_1990b/fig4a_hf_L_Ar#
{
"id": "fig4a_hf_L_Ar",
"material": "Ar",
"file": "Ar/pan_1990b__fig4a_hf_L_Ar.csv",
"table": "fig_6af979c5d055",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 1e-52,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "variationally stable perturbation theory (implicit sums over intermediate states, Slater-orbital expansions), frozen-core HF orbitals, continuum HF orbitals in the LS-dependent nonlocal potential, experimental 3p binding energy 15.76 eV in the intermediate-state Green's functions and the photoelectron energy (k^2/2 = 2 omega - 15.76 eV), half the experimental double-ionisation energy (43.4 eV) in process (6) (Eq. 51); HF: process (1) of Table I (lowest order)",
"definition": "sigma_2 = W / I^2 (Eq. 52), W the ionisation rate in s^-1 and I the photon flux in photons cm^-2 s^-1; computed as sigma_2^q = (8 pi^3 omega^2 / c^2) |T|^2 f_q in atomic units (Eq. 53, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 54)",
"channel": "total (3p5 epsilon-p 1S + epsilon-p 1D + epsilon-f 1D)"
}
}
Fig. 4(a) (p. 10/6280), solid curve: the total generalised two-photon cross section of Ar, linear polarisation, dipole length form, HF (process (1)), cm4 s against the photon energy, read from the scanned image every 0.1 eV, 8.1 to 11.2 and 12.5 to 13.8 eV. +-1.0e-52 cm4 s: the reading (5 pixels; the record’s notes); the paper states none.
pan_1990b/fig4a_hf_V_Ar#
{
"id": "fig4a_hf_V_Ar",
"material": "Ar",
"file": "Ar/pan_1990b__fig4a_hf_V_Ar.csv",
"table": "fig_6af979c5d055",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 1e-52,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "velocity",
"method": "variationally stable perturbation theory (implicit sums over intermediate states, Slater-orbital expansions), frozen-core HF orbitals, continuum HF orbitals in the LS-dependent nonlocal potential, experimental 3p binding energy 15.76 eV in the intermediate-state Green's functions and the photoelectron energy (k^2/2 = 2 omega - 15.76 eV), half the experimental double-ionisation energy (43.4 eV) in process (6) (Eq. 51); HF: process (1) of Table I (lowest order)",
"definition": "sigma_2 = W / I^2 (Eq. 52), W the ionisation rate in s^-1 and I the photon flux in photons cm^-2 s^-1; computed as sigma_2^q = (8 pi^3 omega^2 / c^2) |T|^2 f_q in atomic units (Eq. 53, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 54)",
"channel": "total (3p5 epsilon-p 1S + epsilon-p 1D + epsilon-f 1D)"
}
}
Fig. 4(a) (p. 10/6280), dashed curve: the total generalised two-photon cross section of Ar, linear polarisation, dipole velocity form, HF (process (1)), cm4 s against the photon energy, read from the scanned image every 0.1 eV, 8.1 to 11.6 and 12.4 to 13.9 eV. +-1.0e-52 cm4 s: the reading (5 pixels; the record’s notes); the paper states none.
pan_1990b/fig4b_noshakeup_L_Ar#
{
"id": "fig4b_noshakeup_L_Ar",
"material": "Ar",
"file": "Ar/pan_1990b__fig4b_noshakeup_L_Ar.csv",
"table": "fig_6af979c5d055",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 1e-52,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "variationally stable perturbation theory (implicit sums over intermediate states, Slater-orbital expansions), frozen-core HF orbitals, continuum HF orbitals in the LS-dependent nonlocal potential, experimental 3p binding energy 15.76 eV in the intermediate-state Green's functions and the photoelectron energy (k^2/2 = 2 omega - 15.76 eV), half the experimental double-ionisation energy (43.4 eV) in process (6) (Eq. 51); processes (1)-(3), (5) and (6) of Table I: all but the intermediate-state shake-up (4)",
"definition": "sigma_2 = W / I^2 (Eq. 52), W the ionisation rate in s^-1 and I the photon flux in photons cm^-2 s^-1; computed as sigma_2^q = (8 pi^3 omega^2 / c^2) |T|^2 f_q in atomic units (Eq. 53, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 54)",
"channel": "total (3p5 epsilon-p 1S + epsilon-p 1D + epsilon-f 1D)"
}
}
Fig. 4(b) (p. 10/6280), solid curve: the total generalised two-photon cross section of Ar, linear polarisation, dipole length form, all processes but the intermediate-state shake-up (4), cm4 s against the photon energy, read from the scanned image every 0.1 eV, 8.1 to 11.3 and 12.9 to 13.9 eV. +-1.0e-52 cm4 s: the reading (5 pixels; the record’s notes); the paper states none.
pan_1990b/fig4b_noshakeup_V_Ar#
{
"id": "fig4b_noshakeup_V_Ar",
"material": "Ar",
"file": "Ar/pan_1990b__fig4b_noshakeup_V_Ar.csv",
"table": "fig_6af979c5d055",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 1e-52,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "velocity",
"method": "variationally stable perturbation theory (implicit sums over intermediate states, Slater-orbital expansions), frozen-core HF orbitals, continuum HF orbitals in the LS-dependent nonlocal potential, experimental 3p binding energy 15.76 eV in the intermediate-state Green's functions and the photoelectron energy (k^2/2 = 2 omega - 15.76 eV), half the experimental double-ionisation energy (43.4 eV) in process (6) (Eq. 51); processes (1)-(3), (5) and (6) of Table I: all but the intermediate-state shake-up (4)",
"definition": "sigma_2 = W / I^2 (Eq. 52), W the ionisation rate in s^-1 and I the photon flux in photons cm^-2 s^-1; computed as sigma_2^q = (8 pi^3 omega^2 / c^2) |T|^2 f_q in atomic units (Eq. 53, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 54)",
"channel": "total (3p5 epsilon-p 1S + epsilon-p 1D + epsilon-f 1D)"
}
}
Fig. 4(b) (p. 10/6280), dashed curve: the total generalised two-photon cross section of Ar, linear polarisation, dipole velocity form, all processes but the intermediate-state shake-up (4), cm4 s against the photon energy, read from the scanned image every 0.1 eV, 8.1 to 11.5 and 12.9 to 13.8 eV. +-1.0e-52 cm4 s: the reading (5 pixels; the record’s notes); the paper states none.
pan_1990b/fig4c_all_L_Ar#
{
"id": "fig4c_all_L_Ar",
"material": "Ar",
"file": "Ar/pan_1990b__fig4c_all_L_Ar.csv",
"table": "fig_6af979c5d055",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 1e-52,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "variationally stable perturbation theory (implicit sums over intermediate states, Slater-orbital expansions), frozen-core HF orbitals, continuum HF orbitals in the LS-dependent nonlocal potential, experimental 3p binding energy 15.76 eV in the intermediate-state Green's functions and the photoelectron energy (k^2/2 = 2 omega - 15.76 eV), half the experimental double-ionisation energy (43.4 eV) in process (6) (Eq. 51); all processes of Table I, (1)-(6), including the intermediate-state shake-up (4)",
"definition": "sigma_2 = W / I^2 (Eq. 52), W the ionisation rate in s^-1 and I the photon flux in photons cm^-2 s^-1; computed as sigma_2^q = (8 pi^3 omega^2 / c^2) |T|^2 f_q in atomic units (Eq. 53, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 54)",
"channel": "total (3p5 epsilon-p 1S + epsilon-p 1D + epsilon-f 1D)"
}
}
Fig. 4(c) (p. 10/6280), solid curve: the total generalised two-photon cross section of Ar, linear polarisation, dipole length form, all processes of Table I, cm4 s against the photon energy, read from the scanned image every 0.1 eV, 8.4 to 9.3, 10.1 to 11.1 and 12.8 to 13.9 eV (8.0-8.3 at the frame’s tick marks and 9.4-10.0, where the velocity curve crosses, left out). The paper’s final linear result; drawn again in Fig. 6(a), which agrees within 2 %. +-1.0e-52 cm4 s: the reading (5 pixels; the record’s notes); the paper states none.
pan_1990b/fig4c_all_V_Ar#
{
"id": "fig4c_all_V_Ar",
"material": "Ar",
"file": "Ar/pan_1990b__fig4c_all_V_Ar.csv",
"table": "fig_6af979c5d055",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 1e-52,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "velocity",
"method": "variationally stable perturbation theory (implicit sums over intermediate states, Slater-orbital expansions), frozen-core HF orbitals, continuum HF orbitals in the LS-dependent nonlocal potential, experimental 3p binding energy 15.76 eV in the intermediate-state Green's functions and the photoelectron energy (k^2/2 = 2 omega - 15.76 eV), half the experimental double-ionisation energy (43.4 eV) in process (6) (Eq. 51); all processes of Table I, (1)-(6), including the intermediate-state shake-up (4)",
"definition": "sigma_2 = W / I^2 (Eq. 52), W the ionisation rate in s^-1 and I the photon flux in photons cm^-2 s^-1; computed as sigma_2^q = (8 pi^3 omega^2 / c^2) |T|^2 f_q in atomic units (Eq. 53, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 54)",
"channel": "total (3p5 epsilon-p 1S + epsilon-p 1D + epsilon-f 1D)"
}
}
Fig. 4(c) (p. 10/6280), dashed curve: the total generalised two-photon cross section of Ar, linear polarisation, dipole velocity form, all processes of Table I, cm4 s against the photon energy, read from the scanned image every 0.1 eV, 8.1 to 9.3, 10.1 to 11.1 and 12.7 to 13.8 eV. +-1.0e-52 cm4 s: the reading (5 pixels; the record’s notes); the paper states none.
pan_1990b/fig5_hf_L_circular_Ar#
{
"id": "fig5_hf_L_circular_Ar",
"material": "Ar",
"file": "Ar/pan_1990b__fig5_hf_L_circular_Ar.csv",
"table": "fig_cc071c4e5baf",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 1.7e-52,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "circular",
"gauge": "length",
"method": "variationally stable perturbation theory (implicit sums over intermediate states, Slater-orbital expansions), frozen-core HF orbitals, continuum HF orbitals in the LS-dependent nonlocal potential, experimental 3p binding energy 15.76 eV in the intermediate-state Green's functions and the photoelectron energy (k^2/2 = 2 omega - 15.76 eV), half the experimental double-ionisation energy (43.4 eV) in process (6) (Eq. 51); HF: process (1) of Table I (lowest order)",
"definition": "sigma_2 = W / I^2 (Eq. 52), W the ionisation rate in s^-1 and I the photon flux in photons cm^-2 s^-1; computed as sigma_2^q = (8 pi^3 omega^2 / c^2) |T|^2 f_q in atomic units (Eq. 53, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 54)",
"channel": "total (3p5 epsilon-p 1D + epsilon-f 1D; no 1S for circular)"
}
}
Fig. 5 (p. 11/6281), dash-dot curve: the total generalised two-photon cross section of Ar, circular polarisation, dipole length form, HF (process (1)), cm4 s against the photon energy, read from the scanned image every 0.1 eV, 8.3 to 11.5 and 12.9 to 13.9 eV. +-1.7e-52 cm4 s: the reading (5 pixels; the record’s notes); the paper states none.
pan_1990b/fig5_hf_V_circular_Ar#
{
"id": "fig5_hf_V_circular_Ar",
"material": "Ar",
"file": "Ar/pan_1990b__fig5_hf_V_circular_Ar.csv",
"table": "fig_cc071c4e5baf",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 1.7e-52,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "circular",
"gauge": "velocity",
"method": "variationally stable perturbation theory (implicit sums over intermediate states, Slater-orbital expansions), frozen-core HF orbitals, continuum HF orbitals in the LS-dependent nonlocal potential, experimental 3p binding energy 15.76 eV in the intermediate-state Green's functions and the photoelectron energy (k^2/2 = 2 omega - 15.76 eV), half the experimental double-ionisation energy (43.4 eV) in process (6) (Eq. 51); HF: process (1) of Table I (lowest order)",
"definition": "sigma_2 = W / I^2 (Eq. 52), W the ionisation rate in s^-1 and I the photon flux in photons cm^-2 s^-1; computed as sigma_2^q = (8 pi^3 omega^2 / c^2) |T|^2 f_q in atomic units (Eq. 53, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 54)",
"channel": "total (3p5 epsilon-p 1D + epsilon-f 1D; no 1S for circular)"
}
}
Fig. 5 (p. 11/6281), dash-double-dot curve: the total generalised two-photon cross section of Ar, circular polarisation, dipole velocity form, HF (process (1)), cm4 s against the photon energy, read from the scanned image every 0.1 eV, 9.6 to 10.0 and 13.6 to 14.0 eV only (elsewhere it runs within a line width of the other curves). +-1.7e-52 cm4 s: the reading (5 pixels; the record’s notes); the paper states none.
pan_1990b/fig5_all_L_circular_Ar#
{
"id": "fig5_all_L_circular_Ar",
"material": "Ar",
"file": "Ar/pan_1990b__fig5_all_L_circular_Ar.csv",
"table": "fig_cc071c4e5baf",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 1.7e-52,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "circular",
"gauge": "length",
"method": "variationally stable perturbation theory (implicit sums over intermediate states, Slater-orbital expansions), frozen-core HF orbitals, continuum HF orbitals in the LS-dependent nonlocal potential, experimental 3p binding energy 15.76 eV in the intermediate-state Green's functions and the photoelectron energy (k^2/2 = 2 omega - 15.76 eV), half the experimental double-ionisation energy (43.4 eV) in process (6) (Eq. 51); all processes of Table I, (1)-(6), including the intermediate-state shake-up (4)",
"definition": "sigma_2 = W / I^2 (Eq. 52), W the ionisation rate in s^-1 and I the photon flux in photons cm^-2 s^-1; computed as sigma_2^q = (8 pi^3 omega^2 / c^2) |T|^2 f_q in atomic units (Eq. 53, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 54)",
"channel": "total (3p5 epsilon-p 1D + epsilon-f 1D; no 1S for circular)"
}
}
Fig. 5 (p. 11/6281), solid curve: the total generalised two-photon cross section of Ar, circular polarisation, dipole length form, all processes of Table I, cm4 s against the photon energy, read from the scanned image every 0.1 eV, 8.1 to 8.5, 9.0 to 9.1, 9.7 to 10.0 and 12.8 to 13.9 eV (the rest runs within a line width of the dashed or dash-double-dot curves). The paper’s final circular result. +-1.7e-52 cm4 s: the reading (5 pixels; the record’s notes); the paper states none.
pan_1990b/fig5_all_V_circular_Ar#
{
"id": "fig5_all_V_circular_Ar",
"material": "Ar",
"file": "Ar/pan_1990b__fig5_all_V_circular_Ar.csv",
"table": "fig_cc071c4e5baf",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 1.7e-52,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "circular",
"gauge": "velocity",
"method": "variationally stable perturbation theory (implicit sums over intermediate states, Slater-orbital expansions), frozen-core HF orbitals, continuum HF orbitals in the LS-dependent nonlocal potential, experimental 3p binding energy 15.76 eV in the intermediate-state Green's functions and the photoelectron energy (k^2/2 = 2 omega - 15.76 eV), half the experimental double-ionisation energy (43.4 eV) in process (6) (Eq. 51); all processes of Table I, (1)-(6), including the intermediate-state shake-up (4)",
"definition": "sigma_2 = W / I^2 (Eq. 52), W the ionisation rate in s^-1 and I the photon flux in photons cm^-2 s^-1; computed as sigma_2^q = (8 pi^3 omega^2 / c^2) |T|^2 f_q in atomic units (Eq. 53, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 54)",
"channel": "total (3p5 epsilon-p 1D + epsilon-f 1D; no 1S for circular)"
}
}
Fig. 5 (p. 11/6281), dashed curve: the total generalised two-photon cross section of Ar, circular polarisation, dipole velocity form, all processes of Table I, cm4 s against the photon energy, read from the scanned image every 0.1 eV, 9.7 to 11.2 and 13.5 to 14.0 eV. +-1.7e-52 cm4 s: the reading (5 pixels; the record’s notes); the paper states none.
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.