fink_1990#
M. G. J. Fink and W. R. Johnson, “Electron correlations and spin-orbit interaction in two-photon ionization of closed-shell atoms: A relativistic time-dependent Dirac-Fock approach”, Phys. Rev. A 42, 3801-3818 (1990)
Source record · Catalogue · Review register
Source kind: theory
Recorded technique: Relativistic time-dependent Dirac-Fock (TDDF) theory of the closed-shell rare-gas atoms, expanded order by order in the field (Sec. II): the first-order equation is the inhomogeneous relativistic random-phase approximation (RRPA, Eq. 2.22), the second-order one (Eq. 2.24) gives the two-photon amplitude, which is obtained without solving it under outgoing-wave conditions, as scalar products of the solutions of the homogeneous RRPA equation with the second-order inhomogeneity (Eq. 4.27), for final channels of total J = 0 and 2 (p. 3812). Relativistic (Dirac-Fock) orbitals include the spin-orbit interaction: the thresholds are the Dirac-Fock binding energies of Table I (p. 3815), and the intermediate (RRPA) resonances are J-resolved and fall at the calculation’s own positions. Lowest-order perturbation theory: the cross section has poles at the intermediate resonances (no widths). Length form of the dipole operator: ‘The results reported here are given in length form’ (p. 3814); the length and velocity forms did not agree exactly because of ‘inaccuracies of the numerically computed wave functions close to the nucleus’, and ‘We estimate these results to be numerically more accurate than 5%’ (p. 3814).
Materials in structured entries: Ar, Kr, Xe
Dataset quantities: multiphoton_ionization_cross_section
Contents: 10 datasets; 0 formulas.
Curation notes#
Journal pp. 3801-3818 = PDF pages 1-18 (journal page = PDF page + 3800). Identity checked on the first page (PDF p. 1: ‘PHYSICAL REVIEW A VOLUME 42, NUMBER 7 1 OCTOBER 1990’, footer ‘42 3801’; Michael G. J. Fink, Innsbruck, and Walter R. Johnson, Notre Dame; received 29 January 1990) on 2026-10-09. The PDF is a scan: every page one embedded 1-bit image, 5060 x 6898 pixels (about 600 dpi), with an OCR text layer that is not used.
THE CROSS SECTION (p. 3809, Eqs. 4.1-4.3): the ‘intensity-independent generalized cross section for N-photon ionization’, J_tot = F^N sigma^(N), J_tot the total photoelectron current and F = I / (hbar omega) the photon flux density, with F = E0^2 / (2 pi alpha omega) in atomic units for the field E(t) = E0 eps exp(-i omega t) + c.c. (Eqs. 4.2, 4.4). The figures give sigma^(2) in 10^-50 cm^4 s, for linear (q = 0) and circular (q = +-1) polarisation (p. 3811).
THE ENERGY AXIS: every figure (except Fig. 2, Ne) plots against ‘omega (a.u.)’, the energy of ONE photon in hartree, unshifted: the calculation’s own Dirac-Fock thresholds and RRPA resonances, no shift or scaling to experiment. Which frequencies: ‘The frequencies for 2PI are chosen such that 1PI is energetically impossible and the energy of the final 2PI state is located in the continuum, above the autoionizing range’ (p. 3812), and the paper gives ‘results for the simplest case, i.e., 2PI with final-state energies above both fine-structure components of the P threshold’ (p. 3801). The region between the 2P3/2 and 2P1/2 thresholds (two-photon autoionisation) is NOT computed: ‘We have not performed such calculations yet’ (p. 3814); Figs. 7-14 give only Lu-Fano plots for it. Near the resonances the first-order iteration ‘converges poorly’, and ‘Above the first of [sic] first few resonances, it becomes impossible to obtain convergence at all, which is the limiting factor for the frequency ranges treated’ (p. 3813): the curves end after the first few resonances. FINDING (the reading, the script’s checks): the first computed frequency of each curve lies at or just above half the EXPERIMENTAL 2P1/2 binding energy of Table I (Ar 0.2940 a.u. against 15.94/2 eV = 0.2929; Kr 0.2700 against 14.67/2 eV = 0.2696; Xe 0.2500 against 13.44/2 eV = 0.2470), and for Ar and Kr BELOW half the Dirac-Fock 2P1/2 energy that the text says is the calculation’s threshold (Ar 16.20/2 eV = 0.2977, 25 pixels further; Kr 14.74/2 eV = 0.2708, 5 pixels). Ar’s first frequency is half its Dirac-Fock 2P3/2 energy (16.00 eV, 0.2940 a.u.). The paper does not say how the frequency range was chosen beyond the sentences quoted.
THE RESONANCES drawn (the calculation’s, J-resolved): Ar, the steep rise from 0.42 a.u. into a resonance near 0.43-0.45 a.u. (11.7-12.2 eV; 3p5 4s, experimentally 11.62 and 11.83 eV), its far wing from 0.458 down to 0.505, and a pair near 0.54 (not read); Kr, the rise from 0.358 into the first resonance between 0.3655 and 0.3798 a.u. (9.95-10.33 eV; 4p5 5s, experimentally 10.03 eV), a structure from 0.380 to 0.390 and an off-scale resonance between 0.390 and 0.406, then the wing down to a minimum near 0.4325 (0.61e-50 linear) and the rise at 0.4374; Xe, the rise from 0.295 into the first resonance between 0.3080 and 0.3139 a.u. (8.38-8.54 eV; 5p5 6s, experimentally 8.437 eV), the dip from 0.314 to 0.338 and the rise to 0.3416 (9.30 eV). ‘Due to the pronounced fine structure of xenon, the TDDF approach predicts the positions of the resonances more precisely’ than L’Huillier and Wendin’s nonrelativistic RPA (p. 3813).
EXTRACTED (tools/extract/fink_1990.py), by data rule 8 (TC-699): the paper prints no table of cross sections and has no supplement; Figs. 3-6 (pp. 3813-3814) draw each computed value as a marker (Figs. 3-5: + linear, diamond circular; Fig. 6: + linear 2P3/2, x linear 2P1/2, diamond circular 2P3/2, square circular 2P1/2) joined by lines. The markers are read from the page images at native resolution: the frame lines fitted, every tick found in the image and checked on its fitted scale (x within 1 pixel, y within 3: the printed y spacing varies by a few pixels), each marker seeded at a pixel found by inspecting the image and centred by the script on its shape’s template (the + and x arms, the diamond’s and square’s sides, the arms required to end so that a steep line is not read as a +), each value’s pixel in its printed cell. A curve’s first marker on the left frame line, where the plot is clipped and only its right half is drawn, is read at the frame line’s omega from the middle of that half (Kr circular row 01, Xe Fig. 5 rows 01, Xe Fig. 6 circular 2P1/2 row 01). NOT READ: markers drawn over another curve’s in a cluster (where the two polarisations’ curves cross, Kr 0.317-0.345 a.u., and Xe 0.293-0.302 a.u., where some 30 markers of both curves merge into one blot), markers on steep stretches where the template fails, and everything above the frame (the resonance peaks are off scale). The datasets’ notes list the ranges. Where a + and a diamond are drawn exactly over each other (Ar 0.38 and 0.40 a.u., Kr 0.351 a.u., Xe Fig. 6 2P3/2 below 0.28 a.u.) both are read from the one blot. One pixel is 2.1e-4 a.u. in omega (Fig. 3), 1.5e-4 (Fig. 4), 0.8e-4 (Figs. 5, 6); in sigma^(2) 0.0035e-50 cm4 s (Fig. 3), 0.0078e-50 (Fig. 4), 0.9 % (Figs. 5, 6). The overlays of the values, mapped back through the calibration onto the page images, were inspected (2026-10-09).
UNCERTAINTY: the paper’s ‘numerically more accurate than 5%’ (p. 3814), combined with the digitising: a marker’s centre within 2 pixels (4 where two markers are drawn over each other) and the y calibration within 3: Fig. 3 +-0.015e-50, Fig. 4 +-0.03e-50 (absolute, beside the 5 % relative); Figs. 5 and 6, 4 % from the reading, 6.5 % with the paper’s 5 % in quadrature. On the steep stretches add the slope times 2 pixels in omega.
THE CHECKS (the script fails if one is missed): (1) Table I’s fine-structure splittings are the differences of its binding energies within 0.01 eV (DF Ne 0.13 printed 0.12, Ar 0.20 printed 0.21, Kr 0.74, Xe 1.43 printed 1.44; expt Ne 0.10, Ar 0.18, Kr 0.67, Xe 1.31). (2) Each curve’s first frequency at or above half the experimental 2P1/2 energy, its last below the one-photon threshold. (3) Fig. 6’s partial cross sections add up to Fig. 5’s totals at the frequencies where all are read: linear (+ and x against Fig. 5’s +) 0.989 to 1.055 (7 frequencies), circular (diamond and square against Fig. 5’s diamond) 0.989 to 1.023 (9), within 10 %. (4) Lagutin et al. 2017 redraw Fink and Johnson’s Xe totals (length form, linear and circular) as blue dashed curves in their Fig. 8 (lagutin_2017, TC-880, a vector drawing whose record does not take them): Fig. 5 against that redrawing at 6.80-8.10 and 8.70-9.28 eV is 0.84 to 0.99 (linear, 9 markers) and 0.93 to 1.03 (circular, 12), within 25 %; the redrawing begins at 6.803 eV, Fig. 5’s first frequency 0.2500 a.u. (Lagutin et al.’s text calls the two calculations in ‘close agreement’ between the 5p1/2 threshold and the 6s resonance). Lagutin et al.’s Fig. 6 draws L’Huillier and Wendin’s curves, not Fink and Johnson’s (lagutin_2017’s record). (5) Fig. 3 against Starace and Jiang’s ESI totals (starace_1987, TC-878; the text: ‘The electron scattering interaction (ESI) level results of Ref. 2 for Ar agree with the present results quantitatively within drawing accuracy’, p. 3812): 0.986 to 1.010 (linear, Fig. 7 ESI) and 0.954 to 0.971 (circular, Fig. 6 ESI) at 8.1-9.4 eV, within 15 %. Reported only: Fig. 3 linear is 0.78 to 0.89 times McKenna and van der Hart’s R-matrix Floquet Ar (mckenna_2004 fig5_sigma2_Ar, TC-856) at 8.0-10.0 eV; Fig. 4 circular is 0.22 to 0.39 times McGuire’s Kr (mcguire_1981 fig3_sigma2_Kr, TC-879) at 7.9-9.8 eV (McGuire’s is 2.6 to 4.5 times larger; Lagutin et al. find McGuire’s Xe some 4 times theirs off resonance); the two curves of a figure stand at one computed frequency (within 4 pixels) for 22 of 26 (Ar), 30 of 31 (Kr) and 16 of 18 (Xe) markers.
KRYPTON (OEP 6 Q2): the paper gives Kr two-photon ionisation cross sections ONLY as a raster figure (Fig. 4, a scanned image; no table, no vector drawing), linear and circular, total, length form, from omega = 0.2700 a.u. (7.347 eV, the first circular marker on the frame line; the first linear marker read is 0.2799 a.u., 7.617 eV) to 0.4374 a.u. (11.90 eV). Relative to Kr’s thresholds (two-photon 2P3/2 at 7.000 and 2P1/2 at 7.333 eV experimentally; 7.00 and 7.37 eV Dirac-Fock): nothing below 7.347 eV, so nothing between the thresholds; the smooth non-resonant part runs from 7.35 to 9.77 eV (0.359 a.u.), below Kr’s first resonance E1 = 10.03 eV, which the calculation puts between 9.95 and 10.33 eV; above it the values are resonant wings. sigma^(2) there falls from 2.03e-50 (linear) and 1.57e-50 (circular) at 7.6 eV to 1.22e-50 at 9.55 eV. Ratio circular/linear 0.77 at 7.6 eV, rising to 1.0 at 9.5 eV.
XENON (OEP 6 Q3): Figs. 5 and 6 begin at omega = 0.2500 a.u. (6.803 eV), above the 2P1/2 two-photon threshold (6.718 eV experimentally, 6.70 eV Dirac-Fock): nothing between Xe’s fine-structure thresholds (6.065-6.718 eV).
ERRATA: none in the values. Table I’s printed splittings differ from the differences of its printed energies by 0.01 eV for Ne, Ar and Xe (rounding of unrounded energies); not an error.
NOT TAKEN: Fig. 1 (He, solid and dashed lines without markers, 0.5-0.9 a.u.) and Fig. 2 (Ne, against the intermediate state’s effective quantum number relative to the 2P3/2 threshold, which the vocabulary has no abscissa for): raster line curves, left for a later round (He and Ne are not OEP 6’s open questions). Figs. 7-14: Lu-Fano MQDT plots of the RRPA reactance matrices against experimental levels, no quantity. Table I: the Dirac-Fock binding energies are model thresholds (orbital energies of this calculation), the experimental ones are not this paper’s measurement and their source is not named; used by the script for the checks, not taken as data. Fig. 3’s pair of resonances near 0.54 a.u. (steep, merged markers).
TWO-PHOTON REFERENCES the paper cites: P. Gangopadhyay, X. Tang, P. Lambropoulos and R. Shakeshaft, Phys. Rev. A 34, 2998 (1986) (gangopadhyay_1986); A. F. Starace and T.-F. Jiang, Phys. Rev. A 36, 1705 (1987) (starace_1987, TC-878); A. L’Huillier and G. Wendin, J. Phys. B 20, L37 (1987) (library LHuillier_1987_TwoPhotonOne); E. J. McGuire, Phys. Rev. A 24, 835 (1981) (mcguire_1981, TC-879); R. Moccia, N. K. Rahman and A. Rizzo, J. Phys. B 16, 2737 (1983) (library Moccia_1983_TwoPhotonIonisation); M. S. Pindzola and H. P. Kelly, Phys. Rev. A 11, 1543 (1975) (library Pindzola_1975_TwoPhotonIonization); A. W. McCown, M. N. Ediger and J. G. Eden, Phys. Rev. A 26, 3318 (1982) (mccown_1982); A. L’Huillier, X. Tang and P. Lambropoulos, Phys. Rev. A 39, 1112 (1989) (printed ‘1988’; lhuillier_1989); M. G. J. Fink and P. Zoller, Phys. Rev. A 39, 2933 (1989) (fink_1989); B. Gao and A. F. Starace, Phys. Rev. Lett. 61, 404 (1988), and C. Pan, B. Gao and A. F. Starace, Phys. Rev. A 41, 6271 (1990) (pan_1990). Not in the library: A. L’Huillier, L. Jonsson and G. Wendin, Phys. Rev. A 33, 3938 (1986) (He); B. Ritchie, Phys. Rev. A 16, 2080 (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#
fink_1990/fig3_linear#
{
"id": "fig3_linear",
"material": "Ar",
"file": "Ar/fink_1990__fig3_linear.csv",
"table": "fig_0567865d2622",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"scale": 1e-50,
"abscissa_unit": "hartree",
"use": "check",
"uncertainty": {
"relative": 0.05,
"absolute": 0.015,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "relativistic time-dependent Dirac-Fock (TDDF), second order in the field (inhomogeneous RRPA, Eqs. 2.22, 2.24, 4.27), J = 0 and 2 final channels, Dirac-Fock thresholds (Table I), length form, lowest-order perturbation theory",
"definition": "J_tot = F^2 sigma^(2) (Eq. 4.1), J_tot the total photoelectron current and F = I/(hbar omega) the photon flux density in photons cm^-2 s^-1; plotted in 1e-50 cm4 s"
}
}
Fig. 3 (p. 3813; the library figure’s second panel), + markers: Ar total, linear polarisation, 26 markers from 0.2942 to 0.5018 a.u. (8.01-13.66 eV): the smooth part to 0.4202, the rise to 0.4301 (1.96e-50), and the far wing from 0.4602 down to 0.5018. Not read: the first marker after 0.4301 on the steep line (0.458, the template fails), the pair of resonances near 0.54. 0.38 and 0.40 a.u. read from blots shared with the circular curve. Uncertainty: 5 % (the paper) and 0.015e-50 (the reading).
fink_1990/fig3_circular#
{
"id": "fig3_circular",
"material": "Ar",
"file": "Ar/fink_1990__fig3_circular.csv",
"table": "fig_0567865d2622",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"scale": 1e-50,
"abscissa_unit": "hartree",
"use": "check",
"uncertainty": {
"relative": 0.05,
"absolute": 0.015,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "circular",
"gauge": "length",
"method": "relativistic time-dependent Dirac-Fock (TDDF), second order in the field (inhomogeneous RRPA, Eqs. 2.22, 2.24, 4.27), J = 0 and 2 final channels, Dirac-Fock thresholds (Table I), length form, lowest-order perturbation theory",
"definition": "J_tot = F^2 sigma^(2) (Eq. 4.1), J_tot the total photoelectron current and F = I/(hbar omega) the photon flux density in photons cm^-2 s^-1; plotted in 1e-50 cm4 s"
}
}
Fig. 3 (p. 3813; the library figure’s second panel), diamond markers: Ar total, circular polarisation, 26 markers from 0.2939 to 0.5053 a.u. (8.00-13.75 eV): the smooth part to 0.4203, the rise to 0.4303 (2.72e-50), and the far wing from 0.4582 (4.01e-50) down to 0.5053. Not read: the markers near the minimum beyond 0.505 (merged with the linear curve’s) and the pair of resonances near 0.54. Uncertainty: 5 % (the paper) and 0.015e-50 (the reading).
fink_1990/fig4_linear#
{
"id": "fig4_linear",
"material": "Kr",
"file": "Kr/fink_1990__fig4_linear.csv",
"table": "fig_607b97ca1f36",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"scale": 1e-50,
"abscissa_unit": "hartree",
"use": "check",
"uncertainty": {
"relative": 0.05,
"absolute": 0.03,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "relativistic time-dependent Dirac-Fock (TDDF), second order in the field (inhomogeneous RRPA, Eqs. 2.22, 2.24, 4.27), J = 0 and 2 final channels, Dirac-Fock thresholds (Table I), length form, lowest-order perturbation theory",
"definition": "J_tot = F^2 sigma^(2) (Eq. 4.1), J_tot the total photoelectron current and F = I/(hbar omega) the photon flux density in photons cm^-2 s^-1; plotted in 1e-50 cm4 s"
}
}
Fig. 4 (p. 3813), + markers: Kr total, linear polarisation, 31 markers from 0.2799 to 0.4374 a.u. (7.62-11.90 eV): the smooth part to 0.3599 (7.62-9.79 eV, 2.03e-50 falling to 1.22e-50 at 0.351), then 0.3655 (5.11e-50) on the rise into the first resonance, 0.3798, 0.3831 and 0.3885 between the resonances, and the wing from 0.4062 down to 0.4325 (0.61e-50) and up at 0.4374. Not read: the first marker (0.270, on the frame line where the 2.0 tick merges with it), 0.317 and 0.344 (merged with circular markers), 0.435 (the template fails on the line), and everything off scale. 0.351 a.u. read from a blot shared with the circular curve. Raster only: no table or vector drawing of Kr exists in the paper (OEP 6 Q2). Uncertainty: 5 % (the paper) and 0.03e-50 (the reading).
fink_1990/fig4_circular#
{
"id": "fig4_circular",
"material": "Kr",
"file": "Kr/fink_1990__fig4_circular.csv",
"table": "fig_607b97ca1f36",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"scale": 1e-50,
"abscissa_unit": "hartree",
"use": "check",
"uncertainty": {
"relative": 0.05,
"absolute": 0.03,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "circular",
"gauge": "length",
"method": "relativistic time-dependent Dirac-Fock (TDDF), second order in the field (inhomogeneous RRPA, Eqs. 2.22, 2.24, 4.27), J = 0 and 2 final channels, Dirac-Fock thresholds (Table I), length form, lowest-order perturbation theory",
"definition": "J_tot = F^2 sigma^(2) (Eq. 4.1), J_tot the total photoelectron current and F = I/(hbar omega) the photon flux density in photons cm^-2 s^-1; plotted in 1e-50 cm4 s"
}
}
Fig. 4 (p. 3813), diamond markers: Kr total, circular polarisation, 35 markers from 0.2700 to 0.4374 a.u. (7.35-11.90 eV): row 01 the first computed frequency, on the frame line (read from the half drawn inside it, 1.56e-50), the smooth part to 0.3599 (1.57e-50 at 7.6 eV, 1.20e-50 at 0.344), 0.3654 (5.73e-50) on the rise into the first resonance, 0.3799 to 0.3898 between the resonances, and the wing from 0.4063 down to 0.4350 (0.82e-50) and up at 0.4374. Not read: 0.339 (merged with linear markers) and everything off scale. Raster only: no table or vector drawing of Kr exists in the paper (OEP 6 Q2). Uncertainty: 5 % (the paper) and 0.03e-50 (the reading).
fink_1990/fig5_linear#
{
"id": "fig5_linear",
"material": "Xe",
"file": "Xe/fink_1990__fig5_linear.csv",
"table": "fig_3ff16879fe95",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"scale": 1e-50,
"abscissa_unit": "hartree",
"use": "check",
"uncertainty": {
"relative": 0.065,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "relativistic time-dependent Dirac-Fock (TDDF), second order in the field (inhomogeneous RRPA, Eqs. 2.22, 2.24, 4.27), J = 0 and 2 final channels, Dirac-Fock thresholds (Table I), length form, lowest-order perturbation theory",
"definition": "J_tot = F^2 sigma^(2) (Eq. 4.1), J_tot the total photoelectron current and F = I/(hbar omega) the photon flux density in photons cm^-2 s^-1; plotted in 1e-50 cm4 s"
}
}
Fig. 5 (p. 3813), + markers, logarithmic axis: Xe total, linear polarisation, 18 markers from 0.2500 to 0.3416 a.u. (6.80-9.30 eV): row 01 the first computed frequency, on the frame line (3.83e-50), the smooth part to 0.2900 (2.18e-50), the rise from 0.3029 to 0.3080 (1.84e-47) into the 6s resonance, 0.3140 and 0.3149 on its far side, and 0.3370 to 0.3416 on the rise at the end. Not read: 0.262 and the cluster from 0.293 to 0.302 (some 30 markers of both curves merged), the dip from 0.315 to 0.336 (+ markers merged with the circular curve’s). Uncertainty: 6.5 % (the paper’s 5 % and 4 % reading).
fink_1990/fig5_circular#
{
"id": "fig5_circular",
"material": "Xe",
"file": "Xe/fink_1990__fig5_circular.csv",
"table": "fig_3ff16879fe95",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"scale": 1e-50,
"abscissa_unit": "hartree",
"use": "check",
"uncertainty": {
"relative": 0.065,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "circular",
"gauge": "length",
"method": "relativistic time-dependent Dirac-Fock (TDDF), second order in the field (inhomogeneous RRPA, Eqs. 2.22, 2.24, 4.27), J = 0 and 2 final channels, Dirac-Fock thresholds (Table I), length form, lowest-order perturbation theory",
"definition": "J_tot = F^2 sigma^(2) (Eq. 4.1), J_tot the total photoelectron current and F = I/(hbar omega) the photon flux density in photons cm^-2 s^-1; plotted in 1e-50 cm4 s"
}
}
Fig. 5 (p. 3813), diamond markers, logarithmic axis: Xe total, circular polarisation, 23 markers from 0.2500 to 0.3416 a.u. (6.80-9.30 eV): row 01 the first computed frequency, on the frame line (3.31e-50), the smooth part to 0.2899 (2.17e-50), 0.2950 and 0.2989 within the cluster, the rise from 0.3039 to 0.3079 (4.3e-48), the far side from 0.3139 to 0.3259 (11.3e-50), and 0.3380 and 0.3416 on the rise at the end. Not read: the rest of the cluster from 0.293 to 0.302 and of the dip. Uncertainty: 6.5 % (the paper’s 5 % and 4 % reading).
fink_1990/fig6_linear_p32#
{
"id": "fig6_linear_p32",
"material": "Xe",
"file": "Xe/fink_1990__fig6_linear_p32.csv",
"table": "fig_7bd44496e19f",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"scale": 1e-50,
"abscissa_unit": "hartree",
"use": "check",
"uncertainty": {
"relative": 0.065,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"channel": "Xe+ 5p5 2P3/2 core",
"gauge": "length",
"method": "relativistic time-dependent Dirac-Fock (TDDF), second order in the field (inhomogeneous RRPA, Eqs. 2.22, 2.24, 4.27), J = 0 and 2 final channels, Dirac-Fock thresholds (Table I), length form, lowest-order perturbation theory",
"definition": "J_tot = F^2 sigma^(2) (Eq. 4.1), J_tot the total photoelectron current and F = I/(hbar omega) the photon flux density in photons cm^-2 s^-1; plotted in 1e-50 cm4 s"
}
}
Fig. 6 (p. 3814), + markers, logarithmic axis: the Xe partial cross section leaving the Xe+ 2P3/2 core, linear polarisation, 14 markers from 0.2559 to 0.3417 a.u. (6.96-9.30 eV): the smooth part to 0.2940 (below 0.28 drawn over the circular 2P3/2 diamonds and read from the shared blots), 0.3140 (1.46e-48), the dip minimum 0.3261 to 0.3301 (7.75e-50) and 0.3417. Not read: the first marker on the frame line (merged with the diamond there), the steep and clustered stretches. Uncertainty: 6.5 % (the paper’s 5 % and 4 % reading).
fink_1990/fig6_linear_p12#
{
"id": "fig6_linear_p12",
"material": "Xe",
"file": "Xe/fink_1990__fig6_linear_p12.csv",
"table": "fig_7bd44496e19f",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"scale": 1e-50,
"abscissa_unit": "hartree",
"use": "check",
"uncertainty": {
"relative": 0.065,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"channel": "Xe+ 5p5 2P1/2 core",
"gauge": "length",
"method": "relativistic time-dependent Dirac-Fock (TDDF), second order in the field (inhomogeneous RRPA, Eqs. 2.22, 2.24, 4.27), J = 0 and 2 final channels, Dirac-Fock thresholds (Table I), length form, lowest-order perturbation theory",
"definition": "J_tot = F^2 sigma^(2) (Eq. 4.1), J_tot the total photoelectron current and F = I/(hbar omega) the photon flux density in photons cm^-2 s^-1; plotted in 1e-50 cm4 s"
}
}
Fig. 6 (p. 3814), x markers, logarithmic axis: the Xe partial cross section leaving the Xe+ 2P1/2 core, linear polarisation, 26 markers from 0.2560 to 0.3381 a.u. (6.97-9.20 eV): the smooth part to 0.2900 (1.09e-50 falling to 0.875e-50), and the whole far side of the 6s resonance from 0.3140 (18.6e-50) through the minimum at 0.3260 (0.945e-50) to 0.3381. Not read: the first marker on the frame line (the 10^0 tick’s stub beside it), the cluster from 0.294 to 0.307, 0.3416. Uncertainty: 6.5 % (the paper’s 5 % and 4 % reading).
fink_1990/fig6_circular_p32#
{
"id": "fig6_circular_p32",
"material": "Xe",
"file": "Xe/fink_1990__fig6_circular_p32.csv",
"table": "fig_7bd44496e19f",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"scale": 1e-50,
"abscissa_unit": "hartree",
"use": "check",
"uncertainty": {
"relative": 0.065,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "circular",
"channel": "Xe+ 5p5 2P3/2 core",
"gauge": "length",
"method": "relativistic time-dependent Dirac-Fock (TDDF), second order in the field (inhomogeneous RRPA, Eqs. 2.22, 2.24, 4.27), J = 0 and 2 final channels, Dirac-Fock thresholds (Table I), length form, lowest-order perturbation theory",
"definition": "J_tot = F^2 sigma^(2) (Eq. 4.1), J_tot the total photoelectron current and F = I/(hbar omega) the photon flux density in photons cm^-2 s^-1; plotted in 1e-50 cm4 s"
}
}
Fig. 6 (p. 3814), diamond markers, logarithmic axis: the Xe partial cross section leaving the Xe+ 2P3/2 core, circular polarisation, 11 markers from 0.2560 to 0.3417 a.u. (6.97-9.30 eV): the smooth part to 0.2941 (below 0.28 read from blots shared with the linear 2P3/2 + markers), 0.3140, 0.3260 and 0.3417. Not read: the first marker on the frame line, the rise into the 6s resonance and the dip (merged with the other curves’ markers). Uncertainty: 6.5 % (the paper’s 5 % and 4 % reading).
fink_1990/fig6_circular_p12#
{
"id": "fig6_circular_p12",
"material": "Xe",
"file": "Xe/fink_1990__fig6_circular_p12.csv",
"table": "fig_7bd44496e19f",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"scale": 1e-50,
"abscissa_unit": "hartree",
"use": "check",
"uncertainty": {
"relative": 0.065,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "circular",
"channel": "Xe+ 5p5 2P1/2 core",
"gauge": "length",
"method": "relativistic time-dependent Dirac-Fock (TDDF), second order in the field (inhomogeneous RRPA, Eqs. 2.22, 2.24, 4.27), J = 0 and 2 final channels, Dirac-Fock thresholds (Table I), length form, lowest-order perturbation theory",
"definition": "J_tot = F^2 sigma^(2) (Eq. 4.1), J_tot the total photoelectron current and F = I/(hbar omega) the photon flux density in photons cm^-2 s^-1; plotted in 1e-50 cm4 s"
}
}
Fig. 6 (p. 3814), square markers, logarithmic axis: the Xe partial cross section leaving the Xe+ 2P1/2 core, circular polarisation, 16 markers from 0.2500 to 0.3417 a.u. (6.80-9.30 eV): row 01 the first computed frequency, on the frame line (0.73e-50), the smooth part to 0.2901 (0.62e-50), the far side of the 6s resonance at 0.3149 to 0.3280 (minimum 0.24e-50 at 0.3218) and 0.3417 (4.4e-50). Not read: the cluster from 0.294 to 0.307 and the rising side from 0.329 to 0.340, where the squares overlap each other. Uncertainty: 6.5 % (the paper’s 5 % and 4 % reading).
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.