starace_1987#
A. F. Starace and T.-F. Jiang, “Transition-matrix theory for two-photon ionization of rare-gas atoms and isoelectronic ions with application to argon”, Phys. Rev. A 36, 1705-1719 (1987)
Source record · Catalogue · Review register
Source kind: theory
Recorded technique: Transition-matrix theory (Chang and Fano 1976; Starace and Shahabi 1982) of nonresonant two-photon ionisation of the Ar 3p subshell in lowest-order perturbation theory, below the one-photon threshold (Secs. II-V): the sum over intermediate states done implicitly by the Dalgarno-Lewis differential equation (Eqs. 2-4), with particle-hole (RPA-type) correlations only. Ground state: frozen-core HF 3p6 1S mixed with 3p4 3d2 and 3p4 4f2 pairs by MCHF (Froese Fischer; weights in Table I); final states 3p5(2P) epsilon-f 1D, epsilon-p 1D, epsilon-p 1S (Eq. 20), continuum orbitals in the frozen-core V^(N-1)(LS) potential, energy normalised (Eq. 21), the f 1D - p 1D final-state coupling ignored (p. 9). Four levels of approximation (p. 10): HF (first term of Eq. 10, no interchannel coupling); + ground-state correlations GSC (both terms of Eq. 10, Eqs. 13-14 without interchannel coupling); + intermediate-state interchannel coupling IIC (Eqs. 10, 13, 14 as written); + electron-scattering interactions ESI (Eq. 19, treated as L’Huillier et al. do, with the RPA-like amplitude of Eq. 13). Length form throughout the figures. ‘In solving Eqs. (13) and (14) we have used the HF value for the 3p-orbital energy ... -0.5910 a.u., where 1 a.u. = 27.2108 eV’ (p. 9).
Materials in structured entries: Ar
Dataset quantities: multiphoton_ionization_cross_section
Contents: 17 datasets; 0 formulas.
Curation notes#
Journal pp. 1705-1719 = PDF pages 1-15; journal page = PDF page + 1704. Identity checked on the first page (PDF p. 1: ‘PHYSICAL REVIEW A VOLUME 36, NUMBER 4 AUGUST 15, 1987’, p. 1705; Anthony F. Starace, Innsbruck and Nebraska, and Tsin-Fu Jiang, Nebraska; received 18 February 1986, revised 26 March 1987) on 2026-10-08. The PDF is a scan: every page is one embedded 1-bit image, 5169 x 7129 pixels (about 600 dpi).
THE CROSS SECTION (p. 9/1713): ‘W = sigma_N I^N’ (Eq. 22), ‘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. 23), T the reduced transition-matrix element (Eqs. 10, 19) 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. 24; a0^4 t0 in CODATA 2018 is 1.89679e-50). So the circular total is 3/2 the linear 1D channels’ sum and has no 1S part (p. 12/1716); the linear total is the sum of the three channels (p. 13/1717).
ENERGY AXIS (p. 11/1715): the abscissa of every figure is the photon energy, eV. ‘In our calculations, HF energies were used whenever energies were explicitly required. However, in order to facilitate comparison with both experiment and with Ref. 13, we have used the experimental 3p ionization threshold, 0.579 a.u. (15.76 eV), rather than the HF one, 0.591 a.u. (16.08 eV), to compute the generalized cross section [Eq. (23)]. Thus at any given omega in our figures, the kinetic energy we have used for our final-state wave functions is k^2/2 = 2 omega - 0.579 a.u.’ The intermediate-state resonances are thus at the calculation’s own (HF-based) positions in Figs. 2-4, 6 and 7; no shift was applied there. Only Fig. 5’s f 1D curves ‘have been shifted to give resonance profiles at the observed experimental energies’ (caption), ‘approximately’ with the techniques of Chang and Poe (p. 12/1716). The values are not given near the 4s, 5s and 3d 1P resonances: ‘the Dalgarno-Lewis procedure we use ... does not converge at energies close to these resonances’ (p. 11/1715); the curves stop short of them, and their rises begin some 0.3 to 1 eV below the experimental 4s position A (11.62 eV) in Figs. 3, 4, 6 and 7. LS coupling; the 1P labels of Table III are the jl levels 4s, 5s and 3d [1 1/2]o J = 1 of Moore (1971) (Ref. 48).
EXTRACTED (tools/extract/starace_1987.py), by data rule 8 (TC-699): the paper prints its cross sections only in figures. Figs. 2-4 (pp. 9-10/1713-1714): the linear-polarisation partial cross sections for the f 1D, p 1D and p 1S channels, each in the four approximations (HF dash-dot, GSC dash-double-dot, IIC solid, ESI dashed; Fig. 3 without GSC, ‘nearly the same as the IIC results’); Fig. 5 (p. 11/1715): f 1D, shifted IIC (solid) and ESI (dashed); Figs. 6 and 7 (pp. 12-13/1716-1717): the circular and linear totals, IIC (solid) and ESI (dashed). Each read from the page image at its native resolution: the axes calibrated from the tick marks (each found in the image and checked; every side’s ticks on one linear scale within 3.5 pixels, most within 2), 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: the frame lines drift by 4 to 5 pixels across a plot); 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 authors’ curves from the others’ and from the vertical resonance lines; 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 or a resonance line, interpolated between the nearest clear columns (at most 40 pixels apart). Where another curve comes closer, the samples are left out: the script lists them and fails if they change. Each value’s pixel is in its printed cell. One pixel is 0.0057 to 0.0050 eV in x; in y 0.0020e-50 cm4 s in Figs. 6 and 7, 0.0085e-51 (Fig. 2), 0.0029e-51 (Fig. 3), 0.0093e-51 (Fig. 4) and 0.010e-51 (Fig. 5); the lines are 4 to 8 pixels wide. The overlays of the values on the page images were inspected (2026-10-08).
DIGITISING UNCERTAINTY: 4 pixels in y (the tick residuals, up to 3.5 pixels, and the centring on a line 4 to 8 pixels wide): 0.01e-50 cm4 s in Figs. 6 and 7, 0.04e-51 in Figs. 2, 4 and 5, 0.012e-51 in Fig. 3. On the steep stretches (Fig. 3 below 9 eV, 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) the vertical lines A, B, C (experimental) and a, b, c (HF) drawn in each figure lie at Table III’s energies within 0.08 eV on the calibrated axes: within 0.045 eV everywhere except Fig. 2’s A (11.691 against 11.62); the mean over a figure’s lines is 0.00 to +0.03 eV. (2) Fig. 6 against 3/2 times Figs. 2 + 3 (p. 12/1716): IIC 0.997 to 1.010 (8.6-10.3 eV, 7 samples), ESI 0.990 to 1.006 (8.5-13.8 eV, 16). (3) Fig. 7 against Figs. 2 + 3 + 4 (p. 13/1717): IIC 0.998 to 1.010 (8.6-10.3 eV, 18 samples), ESI 0.981 to 1.010 (8.5-13.8 eV, 13). These are four independent readings of different figures, and they confirm that Figs. 6 and 7 are the sums of Figs. 2-4 (unshifted). (4) Table II’s f_q give the 3/2. (5) Eq. 24 against CODATA, 5e-5. Reported: IIC/HF of the linear total 0.88 to 0.90 below the 4s resonance (8.6-10.3 eV); the text: ‘Ground-state correlations and intermediate-state interchannel coupling correlations reduce the generalized cross section by about 15%’ (p. 10/1714); per channel 0.91-0.93 (f 1D), 0.84-0.90 (p 1S), 0.54-0.84 (p 1D, near its zero). ESI/IIC down to 0.59 (f 1D), 0.53 (p 1S): ‘by approximately a factor of 2 in some cases at certain photon energies’ (p. 10/1714). Fig. 5’s shifted IIC is 1.02 to 1.03 times Fig. 2’s unshifted IIC at 8.8-9.9 eV. No other number of the curves is printed.
COMPARISON with McKenna and van der Hart 2004 (mckenna_2004/fig5_sigma2_Ar, TC-856; R-matrix Floquet, linear, 1e12 W/cm2): Fig. 7’s IIC total is 1.02 to 1.19 times it at 8.4-10.3 eV (the larger ratios where this curve begins its rise toward the 4s resonance), the ESI total 0.82 to 0.87 times it at 8.1-9.4 eV. McKenna and van der Hart cite this paper without a number (mckenna_2004 notes); the ‘within 20% of 0.85 x 10^-50 cm4 s’ they quote is Pan, Gao and Starace, Phys. Rev. A 41, 6271 (1990), a later paper.
ERRATA: none in the values. On p. 12/1716 ‘the experimental resonance energies in Table II’ means Table III (Table II is f_q); the conversion factor of Ref. 51, 6.7734e-34, is a0^2 t0 in cm2 s (for cross sections in 10^-18 cm2 per atomic unit of flux the factor to cm4 s is 6.7734e-52 per printed unit); neither touches the data.
NOT TAKEN: (a) the other authors’ curves in Figs. 5-7, which are theirs: E. J. McGuire, Phys. Rev. A 24, 835 (1981) (mcguire_1981; central-potential model, dotted, Figs. 6, 7); M. S. Pindzola and H. P. Kelly, Phys. Rev. A 11, 1543 (1975) (MBPT, dot-dash: ‘LGI’ f 1D in Fig. 5; in Figs. 6 and 7 combined by Starace and Jiang from Pindzola and Kelly’s channels); R. Moccia, N. K. Rahman and A. Rizzo, J. Phys. B 16, 2737 (1983) (approximate RPA, dash-double-dot, Figs. 6, 7; the circular one derived from their linear total and branching ratio). (b) Table III’s resonance energies (eV; 4s 1P 11.62 experimental / 12.23 HF; 5s 1P 14.09 / 14.47; 3d 1P 14.15 / 14.55; checked cell by cell against the table image): the experimental ones are Moore’s (1971) J = 1 levels converted with 1 eV = 8065.73 cm-1 and rounded to 0.01 eV (Ref. 48; the primary is Moore), the HF ones model energies which level_energy does not hold. They are used by the script to check the drawn lines. (c) Table I (MCHF configuration weights) and Table II (f_q): no quantity. (d) Ranges of the curves not read: where another curve runs within about a line width (the record’s datasets list what is read); Fig. 2’s IIC and GSC from 13.0 to 14.0 eV, which run together within a line width to 13.85 eV and separate only in the last 0.15 eV, where which branch is which cannot be told; Fig. 4’s GSC above 13 eV (short dashes and dots among the HF and IIC lines, not traceable); Fig. 3 draws no IIC above 13 eV; Fig. 7’s ESI from 9.5 to 11 eV, where it runs among Pindzola and Kelly’s and Moccia et al.’s curves; the steep rises into the resonances and the curves’ first 0.1 to 0.4 eV above 8 eV, where they meet each other or the tick marks.
TWO-PHOTON REFERENCES the paper cites (data not in this record): Ar: Pindzola and Kelly 1975, Moccia et al. 1983, McGuire 1981 (above); Xe: A. L’Huillier and G. Wendin, J. Phys. B 20, L37 (1987) (RPA with screening; the library holds their longer Phys. Rev. A 36, 4747 (1987), lhuillier_1987); measured Xe at 193 nm: A. W. McCown, M. N. Ediger and J. G. Eden, Phys. Rev. A 26, 3318 (1982) (mccown_1982); 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. G. J. Fink and P. Zoller, J. Phys. B 18, L373 (1985); M. Crance and M. Aymar, J. Phys. B 18, 3529 (1985); HF two-photon near resonances: T. N. Chang and R. T. Poe, J. Phys. B 9, L311 (1976) and Phys. Rev. A 16, 606 (1977).
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
starace_1987/fig2_hf_f1D_linear_Ar#
{
"id": "fig2_hf_f1D_linear_Ar",
"material": "Ar",
"file": "Ar/starace_1987__fig2_hf_f1D_linear_Ar.csv",
"table": "fig_3bc749c424e4",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 4e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "transition-matrix theory, lowest-order perturbation theory (Dalgarno-Lewis implicit sum), length form, frozen-core HF orbitals, V^(N-1)(LS) continuum, experimental 3p threshold 0.579 a.u. for the photoelectron energy; HF: first term of Eq. 10, no interchannel coupling",
"definition": "sigma_2 = W / I^2 (Eq. 22), 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. 23, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 24)",
"channel": "3p5(2P) epsilon-f 1D"
}
}
Fig. 2 (p. 9/1713), HF (dash-dot curve): the f 1D channel’s generalised two-photon cross section, linear polarisation (Eq. 23; W = sigma I^2, I in photons cm^-2 s^-1), length form, cm4 s against the photon energy, read from the image every 0.1 eV, 8.5 to 12.9 and 13.3 to 14.0 eV (passing smoothly through the 4s region, as the text says; 13.0-13.2, where the ESI curve crosses, left out). +-0.04e-51 cm4 s: the reading (the record’s notes); the paper states none.
starace_1987/fig2_gsc_f1D_linear_Ar#
{
"id": "fig2_gsc_f1D_linear_Ar",
"material": "Ar",
"file": "Ar/starace_1987__fig2_gsc_f1D_linear_Ar.csv",
"table": "fig_3bc749c424e4",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 4e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "transition-matrix theory, lowest-order perturbation theory (Dalgarno-Lewis implicit sum), length form, frozen-core HF orbitals, V^(N-1)(LS) continuum, experimental 3p threshold 0.579 a.u. for the photoelectron energy; HF + ground-state correlations (3p4 3d2, 3p4 4f2 MCHF admixture): Eqs. 10, 13, 14 without interchannel coupling",
"definition": "sigma_2 = W / I^2 (Eq. 22), 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. 23, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 24)",
"channel": "3p5(2P) epsilon-f 1D"
}
}
Fig. 2 (p. 9/1713), HF + GSC (dash-double-dot curve): the f 1D channel’s generalised two-photon cross section, linear polarisation (Eq. 23; W = sigma I^2, I in photons cm^-2 s^-1), length form, cm4 s against the photon energy, read from the image every 0.1 eV, 8.5 to 13.0 eV (passing smoothly through the 4s region; above 13.0 it runs with the IIC curve within a line width, not read). +-0.04e-51 cm4 s: the reading (the record’s notes); the paper states none.
starace_1987/fig2_iic_f1D_linear_Ar#
{
"id": "fig2_iic_f1D_linear_Ar",
"material": "Ar",
"file": "Ar/starace_1987__fig2_iic_f1D_linear_Ar.csv",
"table": "fig_3bc749c424e4",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 4e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "transition-matrix theory, lowest-order perturbation theory (Dalgarno-Lewis implicit sum), length form, frozen-core HF orbitals, V^(N-1)(LS) continuum, experimental 3p threshold 0.579 a.u. for the photoelectron energy; HF + ground-state correlations + intermediate-state interchannel coupling: Eqs. 10, 13, 14",
"definition": "sigma_2 = W / I^2 (Eq. 22), 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. 23, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 24)",
"channel": "3p5(2P) epsilon-f 1D"
}
}
Fig. 2 (p. 9/1713), HF + GSC + IIC (solid curve): the f 1D channel’s generalised two-photon cross section, linear polarisation (Eq. 23; W = sigma I^2, I in photons cm^-2 s^-1), length form, cm4 s against the photon energy, read from the image every 0.1 eV, 8.6 to 11.5 eV (below 8.6 the four curves meet; it stops at 11.6; from 13.0 to 14.0 it runs with the GSC curve, not read). +-0.04e-51 cm4 s: the reading (the record’s notes); the paper states none.
starace_1987/fig2_esi_f1D_linear_Ar#
{
"id": "fig2_esi_f1D_linear_Ar",
"material": "Ar",
"file": "Ar/starace_1987__fig2_esi_f1D_linear_Ar.csv",
"table": "fig_3bc749c424e4",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 4e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "transition-matrix theory, lowest-order perturbation theory (Dalgarno-Lewis implicit sum), length form, frozen-core HF orbitals, V^(N-1)(LS) continuum, experimental 3p threshold 0.579 a.u. for the photoelectron energy; HF + ground-state correlations + intermediate-state interchannel coupling + electron-scattering interactions: Eqs. 19, 13, 14",
"definition": "sigma_2 = W / I^2 (Eq. 22), 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. 23, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 24)",
"channel": "3p5(2P) epsilon-f 1D"
}
}
Fig. 2 (p. 9/1713), HF + GSC + IIC + ESI (dashed curve): the f 1D channel’s generalised two-photon cross section, linear polarisation (Eq. 23; W = sigma I^2, I in photons cm^-2 s^-1), length form, cm4 s against the photon energy, read from the image every 0.1 eV, 8.5 to 11.5 and 13.6 to 14.0 eV (13.0-13.5: the steep fall from the 4s side and the crossing of the HF, GSC and IIC curves). +-0.04e-51 cm4 s: the reading (the record’s notes); the paper states none.
starace_1987/fig3_hf_p1D_linear_Ar#
{
"id": "fig3_hf_p1D_linear_Ar",
"material": "Ar",
"file": "Ar/starace_1987__fig3_hf_p1D_linear_Ar.csv",
"table": "fig_87f36d953f72",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 1.2e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "transition-matrix theory, lowest-order perturbation theory (Dalgarno-Lewis implicit sum), length form, frozen-core HF orbitals, V^(N-1)(LS) continuum, experimental 3p threshold 0.579 a.u. for the photoelectron energy; HF: first term of Eq. 10, no interchannel coupling",
"definition": "sigma_2 = W / I^2 (Eq. 22), 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. 23, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 24)",
"channel": "3p5(2P) epsilon-p 1D"
}
}
Fig. 3 (p. 10/1714), HF (dash-dot curve): the p 1D channel’s generalised two-photon cross section, linear polarisation (Eq. 23; W = sigma I^2, I in photons cm^-2 s^-1), length form, cm4 s against the photon energy, read from the image every 0.1 eV, 8.2 to 10.4 and 13.1 to 13.9 eV (the rise into the 4s resonance, from 10.4 eV, left out). +-0.012e-51 cm4 s: the reading (the record’s notes); the paper states none.
starace_1987/fig3_iic_p1D_linear_Ar#
{
"id": "fig3_iic_p1D_linear_Ar",
"material": "Ar",
"file": "Ar/starace_1987__fig3_iic_p1D_linear_Ar.csv",
"table": "fig_87f36d953f72",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 1.2e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "transition-matrix theory, lowest-order perturbation theory (Dalgarno-Lewis implicit sum), length form, frozen-core HF orbitals, V^(N-1)(LS) continuum, experimental 3p threshold 0.579 a.u. for the photoelectron energy; HF + ground-state correlations + intermediate-state interchannel coupling: Eqs. 10, 13, 14",
"definition": "sigma_2 = W / I^2 (Eq. 22), 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. 23, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 24)",
"channel": "3p5(2P) epsilon-p 1D"
}
}
Fig. 3 (p. 10/1714), HF + GSC + IIC (solid curve): the p 1D channel’s generalised two-photon cross section, linear polarisation (Eq. 23; W = sigma I^2, I in photons cm^-2 s^-1), length form, cm4 s against the photon energy, read from the image every 0.1 eV, 8.4 to 10.3 eV (near 10.4-10.6 eV the curves meet close to zero; no IIC curve is drawn above 13 eV). +-0.012e-51 cm4 s: the reading (the record’s notes); the paper states none.
starace_1987/fig3_esi_p1D_linear_Ar#
{
"id": "fig3_esi_p1D_linear_Ar",
"material": "Ar",
"file": "Ar/starace_1987__fig3_esi_p1D_linear_Ar.csv",
"table": "fig_87f36d953f72",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 1.2e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "transition-matrix theory, lowest-order perturbation theory (Dalgarno-Lewis implicit sum), length form, frozen-core HF orbitals, V^(N-1)(LS) continuum, experimental 3p threshold 0.579 a.u. for the photoelectron energy; HF + ground-state correlations + intermediate-state interchannel coupling + electron-scattering interactions: Eqs. 19, 13, 14",
"definition": "sigma_2 = W / I^2 (Eq. 22), 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. 23, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 24)",
"channel": "3p5(2P) epsilon-p 1D"
}
}
Fig. 3 (p. 10/1714), HF + GSC + IIC + ESI (dashed curve): the p 1D channel’s generalised two-photon cross section, linear polarisation (Eq. 23; W = sigma I^2, I in photons cm^-2 s^-1), length form, cm4 s against the photon energy, read from the image every 0.1 eV, 8.4 to 9.7 and 13.5 to 13.8 eV (near zero at 9.8-10.2 eV it touches the frame; the steep fall from 12.8 eV left out). +-0.012e-51 cm4 s: the reading (the record’s notes); the paper states none.
starace_1987/fig4_hf_p1S_linear_Ar#
{
"id": "fig4_hf_p1S_linear_Ar",
"material": "Ar",
"file": "Ar/starace_1987__fig4_hf_p1S_linear_Ar.csv",
"table": "fig_4f3d33d66e2a",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 4e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "transition-matrix theory, lowest-order perturbation theory (Dalgarno-Lewis implicit sum), length form, frozen-core HF orbitals, V^(N-1)(LS) continuum, experimental 3p threshold 0.579 a.u. for the photoelectron energy; HF: first term of Eq. 10, no interchannel coupling",
"definition": "sigma_2 = W / I^2 (Eq. 22), 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. 23, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 24)",
"channel": "3p5(2P) epsilon-p 1S"
}
}
Fig. 4 (p. 10/1714), HF (dash-dot curve): the p 1S channel’s generalised two-photon cross section, linear polarisation (Eq. 23; W = sigma I^2, I in photons cm^-2 s^-1), length form, cm4 s against the photon energy, read from the image every 0.1 eV, 8.2 to 10.7 and 13.5 to 14.0 eV. +-0.04e-51 cm4 s: the reading (the record’s notes); the paper states none.
starace_1987/fig4_gsc_p1S_linear_Ar#
{
"id": "fig4_gsc_p1S_linear_Ar",
"material": "Ar",
"file": "Ar/starace_1987__fig4_gsc_p1S_linear_Ar.csv",
"table": "fig_4f3d33d66e2a",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 4e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "transition-matrix theory, lowest-order perturbation theory (Dalgarno-Lewis implicit sum), length form, frozen-core HF orbitals, V^(N-1)(LS) continuum, experimental 3p threshold 0.579 a.u. for the photoelectron energy; HF + ground-state correlations (3p4 3d2, 3p4 4f2 MCHF admixture): Eqs. 10, 13, 14 without interchannel coupling",
"definition": "sigma_2 = W / I^2 (Eq. 22), 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. 23, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 24)",
"channel": "3p5(2P) epsilon-p 1S"
}
}
Fig. 4 (p. 10/1714), HF + GSC (dash-double-dot curve): the p 1S channel’s generalised two-photon cross section, linear polarisation (Eq. 23; W = sigma I^2, I in photons cm^-2 s^-1), length form, cm4 s against the photon energy, read from the image every 0.1 eV, 8.4 to 10.7 eV (above 13 eV: short dashes and dots among the HF and IIC lines, not read). +-0.04e-51 cm4 s: the reading (the record’s notes); the paper states none.
starace_1987/fig4_iic_p1S_linear_Ar#
{
"id": "fig4_iic_p1S_linear_Ar",
"material": "Ar",
"file": "Ar/starace_1987__fig4_iic_p1S_linear_Ar.csv",
"table": "fig_4f3d33d66e2a",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 4e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "transition-matrix theory, lowest-order perturbation theory (Dalgarno-Lewis implicit sum), length form, frozen-core HF orbitals, V^(N-1)(LS) continuum, experimental 3p threshold 0.579 a.u. for the photoelectron energy; HF + ground-state correlations + intermediate-state interchannel coupling: Eqs. 10, 13, 14",
"definition": "sigma_2 = W / I^2 (Eq. 22), 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. 23, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 24)",
"channel": "3p5(2P) epsilon-p 1S"
}
}
Fig. 4 (p. 10/1714), HF + GSC + IIC (solid curve): the p 1S channel’s generalised two-photon cross section, linear polarisation (Eq. 23; W = sigma I^2, I in photons cm^-2 s^-1), length form, cm4 s against the photon energy, read from the image every 0.1 eV, 8.4 to 10.8 and 13.6 to 14.0 eV (13.0-13.5: within about a line width of the HF and GSC curves). +-0.04e-51 cm4 s: the reading (the record’s notes); the paper states none.
starace_1987/fig4_esi_p1S_linear_Ar#
{
"id": "fig4_esi_p1S_linear_Ar",
"material": "Ar",
"file": "Ar/starace_1987__fig4_esi_p1S_linear_Ar.csv",
"table": "fig_4f3d33d66e2a",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 4e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "transition-matrix theory, lowest-order perturbation theory (Dalgarno-Lewis implicit sum), length form, frozen-core HF orbitals, V^(N-1)(LS) continuum, experimental 3p threshold 0.579 a.u. for the photoelectron energy; HF + ground-state correlations + intermediate-state interchannel coupling + electron-scattering interactions: Eqs. 19, 13, 14",
"definition": "sigma_2 = W / I^2 (Eq. 22), 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. 23, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 24)",
"channel": "3p5(2P) epsilon-p 1S"
}
}
Fig. 4 (p. 10/1714), HF + GSC + IIC + ESI (dashed curve): the p 1S channel’s generalised two-photon cross section, linear polarisation (Eq. 23; W = sigma I^2, I in photons cm^-2 s^-1), length form, cm4 s against the photon energy, read from the image every 0.1 eV, 8.4 to 11.1 and 13.6 to 14.0 eV. +-0.04e-51 cm4 s: the reading (the record’s notes); the paper states none.
starace_1987/fig5_iic_shifted_f1D_linear_Ar#
{
"id": "fig5_iic_shifted_f1D_linear_Ar",
"material": "Ar",
"file": "Ar/starace_1987__fig5_iic_shifted_f1D_linear_Ar.csv",
"table": "fig_ca863326b494",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 4e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "transition-matrix theory, lowest-order perturbation theory (Dalgarno-Lewis implicit sum), length form, frozen-core HF orbitals, V^(N-1)(LS) continuum, experimental 3p threshold 0.579 a.u. for the photoelectron energy; HF + ground-state correlations + intermediate-state interchannel coupling: Eqs. 10, 13, 14; the resonance profiles shifted approximately to the experimental 4s, 5s, 3d 1P energies (Chang and Poe's technique; Fig. 5)",
"definition": "sigma_2 = W / I^2 (Eq. 22), 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. 23, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 24)",
"channel": "3p5(2P) epsilon-f 1D"
}
}
Fig. 5 (p. 11/1715), HF + GSC + IIC (solid curve), shifted to the experimental resonance energies,: the f 1D channel’s generalised two-photon cross section, linear polarisation (Eq. 23; W = sigma I^2, I in photons cm^-2 s^-1), length form, cm4 s against the photon energy, read from the image every 0.1 eV, 8.8 to 9.9 and 11.9 to 13.4 eV (below 8.8 and from 10.0 to 11.5 eV it runs within a line width of Pindzola and Kelly’s LGI curve, as the text says, ‘essentially identical’; the resonance profiles at A and B left out). +-0.04e-51 cm4 s: the reading (the record’s notes); the paper states none.
starace_1987/fig5_esi_shifted_f1D_linear_Ar#
{
"id": "fig5_esi_shifted_f1D_linear_Ar",
"material": "Ar",
"file": "Ar/starace_1987__fig5_esi_shifted_f1D_linear_Ar.csv",
"table": "fig_ca863326b494",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 4e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "transition-matrix theory, lowest-order perturbation theory (Dalgarno-Lewis implicit sum), length form, frozen-core HF orbitals, V^(N-1)(LS) continuum, experimental 3p threshold 0.579 a.u. for the photoelectron energy; HF + ground-state correlations + intermediate-state interchannel coupling + electron-scattering interactions: Eqs. 19, 13, 14; the resonance profiles shifted approximately to the experimental 4s, 5s, 3d 1P energies (Chang and Poe's technique; Fig. 5)",
"definition": "sigma_2 = W / I^2 (Eq. 22), 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. 23, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 24)",
"channel": "3p5(2P) epsilon-f 1D"
}
}
Fig. 5 (p. 11/1715), HF + GSC + IIC + ESI (dashed curve), shifted to the experimental resonance energies,: the f 1D channel’s generalised two-photon cross section, linear polarisation (Eq. 23; W = sigma I^2, I in photons cm^-2 s^-1), length form, cm4 s against the photon energy, read from the image every 0.1 eV, 8.4 to 11.4 and 11.9 to 13.4 eV (the profiles at A and B left out). +-0.04e-51 cm4 s: the reading (the record’s notes); the paper states none.
starace_1987/fig6_iic_circular_Ar#
{
"id": "fig6_iic_circular_Ar",
"material": "Ar",
"file": "Ar/starace_1987__fig6_iic_circular_Ar.csv",
"table": "fig_ea1ce7340e25",
"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": "circular",
"gauge": "length",
"method": "transition-matrix theory, lowest-order perturbation theory (Dalgarno-Lewis implicit sum), length form, frozen-core HF orbitals, V^(N-1)(LS) continuum, experimental 3p threshold 0.579 a.u. for the photoelectron energy; HF + ground-state correlations + intermediate-state interchannel coupling: Eqs. 10, 13, 14",
"definition": "sigma_2 = W / I^2 (Eq. 22), 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. 23, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 24)"
}
}
Fig. 6 (p. 12/1716), HF + GSC + IIC (solid curve): the total generalised two-photon cross section of the Ar 3p subshell for circular polarisation (Eq. 23; W = sigma I^2, I in photons cm^-2 s^-1), length form, cm4 s against the photon energy, read from the image every 0.1 eV, 8.1 to 8.6, 9.1 to 9.5, 10.3 to 11.0 and 13.2 to 13.9 eV (8.7-9.0 and 9.6-10.2 eV: within about a line width of Pindzola and Kelly’s curve, which it crosses; ‘nearly identical’, the text says). +-0.01e-50 cm4 s: the reading (the record’s notes); the paper states none.
starace_1987/fig6_esi_circular_Ar#
{
"id": "fig6_esi_circular_Ar",
"material": "Ar",
"file": "Ar/starace_1987__fig6_esi_circular_Ar.csv",
"table": "fig_ea1ce7340e25",
"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": "circular",
"gauge": "length",
"method": "transition-matrix theory, lowest-order perturbation theory (Dalgarno-Lewis implicit sum), length form, frozen-core HF orbitals, V^(N-1)(LS) continuum, experimental 3p threshold 0.579 a.u. for the photoelectron energy; HF + ground-state correlations + intermediate-state interchannel coupling + electron-scattering interactions: Eqs. 19, 13, 14",
"definition": "sigma_2 = W / I^2 (Eq. 22), 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. 23, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 24)"
}
}
Fig. 6 (p. 12/1716), HF + GSC + IIC + ESI (dashed curve): the total generalised two-photon cross section of the Ar 3p subshell for circular polarisation (Eq. 23; W = sigma I^2, I in photons cm^-2 s^-1), length form, cm4 s against the photon energy, read from the image every 0.1 eV, 8.1 to 11.1 and 13.3 to 14.0 eV. +-0.01e-50 cm4 s: the reading (the record’s notes); the paper states none.
starace_1987/fig7_iic_linear_Ar#
{
"id": "fig7_iic_linear_Ar",
"material": "Ar",
"file": "Ar/starace_1987__fig7_iic_linear_Ar.csv",
"table": "fig_167e2294aa4c",
"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": "transition-matrix theory, lowest-order perturbation theory (Dalgarno-Lewis implicit sum), length form, frozen-core HF orbitals, V^(N-1)(LS) continuum, experimental 3p threshold 0.579 a.u. for the photoelectron energy; HF + ground-state correlations + intermediate-state interchannel coupling: Eqs. 10, 13, 14",
"definition": "sigma_2 = W / I^2 (Eq. 22), 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. 23, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 24)"
}
}
Fig. 7 (p. 13/1717), HF + GSC + IIC (solid curve): the total generalised two-photon cross section of the Ar 3p subshell for linear polarisation (Eq. 23; W = sigma I^2, I in photons cm^-2 s^-1), length form, cm4 s against the photon energy, read from the image every 0.1 eV, 8.4 to 10.8 and 13.1 to 13.9 eV. +-0.01e-50 cm4 s: the reading (the record’s notes); the paper states none.
starace_1987/fig7_esi_linear_Ar#
{
"id": "fig7_esi_linear_Ar",
"material": "Ar",
"file": "Ar/starace_1987__fig7_esi_linear_Ar.csv",
"table": "fig_167e2294aa4c",
"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": "transition-matrix theory, lowest-order perturbation theory (Dalgarno-Lewis implicit sum), length form, frozen-core HF orbitals, V^(N-1)(LS) continuum, experimental 3p threshold 0.579 a.u. for the photoelectron energy; HF + ground-state correlations + intermediate-state interchannel coupling + electron-scattering interactions: Eqs. 19, 13, 14",
"definition": "sigma_2 = W / I^2 (Eq. 22), 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. 23, f_q of Table II) and converted with L^4 T (a.u.) = 1.8967e-50 cm4 s (Eq. 24)"
}
}
Fig. 7 (p. 13/1717), HF + GSC + IIC + ESI (dashed curve): the total generalised two-photon cross section of the Ar 3p subshell for linear polarisation (Eq. 23; W = sigma I^2, I in photons cm^-2 s^-1), length form, cm4 s against the photon energy, read from the image every 0.1 eV, 8.1 to 9.4 and 13.5 to 14.0 eV (9.5-11 eV: among Pindzola and Kelly’s and Moccia et al.’s curves, not read). +-0.01e-50 cm4 s: the reading (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.