petrov_2016#
I. D. Petrov, B. M. Lagutin, V. L. Sukhorukov, A. Knie and A. Ehresmann, “Correlation and polarization effects in two-photon photoionization of Ar”, Phys. Rev. A 93, 033408 (2016)
Source record · Catalogue · Review register
DOI: 10.1103/PhysRevA.93.033408
Source kind: theory
Recorded technique: Lowest-order perturbation theory (LOPT) for the two-photon ionisation of the Ar 3p shell, 3p6 (1S) + 2 gamma -> Ar+ 3p5 (2P) el (1L), L = 0, 2 (Eq. 1), in LS coupling, three final channels: ep(1S), ep(1D) and ef(1D). Nonrelativistic Hartree-Fock orbitals, the core frozen at the ground configuration; continuum orbitals term-dependent (3p5 ep 1S, 1D; 3p5 ef 1D); the intermediate states in the potential of 3p5 es, ed (1P). The sum over intermediate states (Eq. 2) is done with the correlation-function (CF) technique: an inhomogeneous integro-differential equation (Eqs. 10-11), reduced to local differential equations and solved non-iteratively at any energy, to within E_R +- 2.5 meV of a resonance (p. 5). LOPT processes (Ia) 3p6 -> 3p5 e’l’ -> 3p5 el and (Ib) through 3s 3p6 el; many-electron correlations as the amplitudes of the next order (processes II-VI: intermediate-state interchannel, ground-state, intermediate-state shake-up, intermediate- and final-state electron scattering), the experimental double-ionisation energy E(3p^-2) = 3.189 Ry (NIST, Ref. 30) in processes III to VI (p. 6). Core polarisation (CP): an ab initio polarisation potential (Petrov, Sukhorukov and Hotop, J. Phys. B 32, 973 (1999), Ref. 25) added to the Hartree-Fock operator of the intermediate-state CFs, and the Coulomb matrix elements of processes II-VI reduced by a factor 1.25 for higher-order correlations (Eqs. 30-31, p. 6). Length and velocity forms of the dipole operator. The radiative widths of the intermediate resonances are not included (they depend on the laser intensity): the cross section is infinite at each resonance; ‘If the duration of the laser impulse is more than 1.5 fs and the intensity is less than 10^12 W/cm2 our approximation ... is accurate within less than 5% outside the photon-energy range omega_4s +- 0.25 eV’ (p. 8).
Materials in structured entries: Ar
Dataset quantities: multiphoton_ionization_cross_section
Contents: 12 datasets; 0 formulas.
Curation notes#
Journal pp. 033408-1 to 033408-15 = PDF pages 1 to 15. Identity checked on the first page (PDF p. 1: ‘PHYSICAL REVIEW A 93, 033408 (2016)’, I. D. Petrov and B. M. Lagutin (Rostov State University of Transport Communications), V. L. Sukhorukov (Southern Federal University), A. Knie and A. Ehresmann (Kassel); received 8 August 2015, published 9 March 2016) on 2026-10-08. The library copy is the version of record.
THE CROSS SECTION (p. 4, Eqs. 19-20): the generalised two-photon ionisation cross section (G2PICS), cm4 s, ‘which ... does not contain the photon flux’, used ‘as in’ Starace and Jiang (1987) and Pan, Gao and Starace (1990), Refs. 13-14; the sum over the channels of the partial cross sections sigma_q(L, l, omega) = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega(L, l)|^2, q = 0 linear polarisation, omega the photon energy in au, ‘+’ length and ‘-’ velocity form, alpha = 1/137.036, a0 = 5.29177e-9 cm and c = 2.99792e10 cm/s as printed. The paper does not write the rate; Starace and Jiang (Ref. 13, in the library, Eqs. 22-23) define sigma_2 by W = sigma_2 I^2 with I the photon flux in photons cm^-2 s^-1 and give sigma_2 = (8 pi^3 omega^2 / c^2) |T|^2 in au, the same as Eq. 20 with alpha = 1/c: Gamma = sigma Phi^2 (as uiterwaal_1998 and mckenna_2004). Circular polarisation was computed but ‘We do not present those results’ (p. 9).
THE ENERGY AXIS. Every figure’s abscissa is the photon energy (one photon, eV), 8 to 15 eV. The energy denominators use the experimental 3p ionisation energy E(3p) = 1.158 Ry (15.755 eV; Figs. 4 and 5 captions: the vertical lines there are ‘the energies of the intermediate 3p5 nl(1P) resonances calculated using the experimental value of 3p ionization potential’), the Hartree-Fock 3s energy 2.555 Ry (p. 4, ‘a very small change’, below 0.01 %), and the experimental double-ionisation energy (above). So the two-photon threshold lies at 7.88 eV, below the plots’ left edge. The resonances fall where the calculation puts its LS-coupled 3p5 ns, nd (1P) levels; core polarisation lowers them. The vertical lines of Figs. 9 and 10 mark ‘the experimental energies of the 3p5_3/2 nl’[3/2]_1 resonances’ (NIST ASD 5.2, Ref. 30), J-resolved levels, which the paper prints nowhere (only 4s, 11.62 eV, p. 5): as drawn (Fig. 10, calibrated) at 11.6229, 14.0893, 14.1526, 14.8483 and 14.8590 eV, each within 0.0009 eV of a NIST ASD level of Ar I (nist_asd_2026’s levels file, 3p5(2P3/2) nl [3/2] J = 1: 4s 11.6236, 5s 14.0900, 3d 14.1525, 6s 14.8484, 4d 14.8592 eV; checked by the script), labelled by arrows 4s, 5s, 3d, 6s and 4d (the 6s and 4d arrows both end at or just short of the 14.848 eV line). Fig. 2(a) alone (not taken) shifts E(3p) by -0.045 Ry to put the 4s resonance at 11.62 eV for comparison with Ref. 13. No shift or scaling of the taken curves’ axes. The drawn 4s peaks leave the frame at (highest drawn point) 11.639 eV (corr + CP, L) and 11.630 eV (V), against the 4s line at 11.623, and at 11.910 and 11.899 eV without core polarisation (the corr omega_4s ‘= 11.90 eV’, p. 6): the core polarisation brings the computed resonance to the experimental energy (the abstract).
EXTRACTED (tools/extract/petrov_2016.py). The paper prints no table of cross sections and no supplement exists: the values are only in figures, vector drawings, read from the PDF by data rule 8 (TC-699). Taken: Fig. 10 (the totals, log scale: corr L, corr V, corr + CP L, corr + CP V) and the partial cross sections drawn on the same footing (the same calculations, corr and corr + CP): Fig. 6, ep(1S), L and V; Fig. 7, ep(1D), L; Fig. 8, ef(1D), L. Every vertex inside the frame of each drawn curve: the solid lines’ polyline vertices, the dashed lines’ dash ends (the dashes are two-vertex segments cut from the plotted line, split at its vertices), put in order along the curve (by photon energy; in one 0.05 pt column of a resonance’s flank, in the direction the dashes run). Between dashes the line is not drawn (1.9 to 2.0 pt gaps in the dash-dot lines, 3.5 to 4.7 pt in the dashed ones) and not sampled. Vertices beyond the frame (the resonances run far above it, the dips of Figs. 6-8 to zero) are in the PDF but clipped from the figure and are not taken: the drawn resonance heights are bounded by the frame, and the calculation is infinite there. Curves of one colour and width are drawn one after the other, each starting at the left edge, in the legend’s order, and are told apart by their dash pattern (dash-dot: about one dot per 3.7 pt dash; dash-dot-dot: two per 3.0 pt dash; dashed: none), checked by the script. Axes calibrated from the drawings’ own tick marks (all four edges; the top and right repeat the bottom and left within 0.03 pt), linear in photon energy, linear in sigma (Figs. 6-9) or logarithmic in decades (Fig. 10, 31 pt per decade, from 2 at the bottom edge to 10^5): every tick within 0.03 pt of its fitted scale. Fig. 9 (the same four totals on a linear scale, 0 to 20) is read by the script for the checks only.
THE CHECKS (the script fails if one is missed): core polarisation increases the total ‘by 18% and 15%’ (L, V) at 9.5 eV (p. 8): read 1.184 and 1.151 (Fig. 9), 1.186 and 1.146 (Fig. 10); Fig. 10’s five vertical lines at the NIST levels (above); with the correlations the L and V totals differ by ‘8% at the 8-11-eV photon energy region’ (p. 6): V/L read 1.092, 1.060, 1.058, 1.039 at 8, 9, 10, 11 eV; ep(1S) ‘by 17% for the length form ... and by 11% for the velocity form’ (p. 7): 1.167 and 1.110 at 8 eV (1.223 and 1.119 at 9 eV, 1.365 and 1.163 at 10 eV; the text gives no energy); ef(1D) ‘by 16% in the 8-11 eV photon energy range’ (p. 8): 1.140, 1.154, 1.165 at 8, 9, 10 eV; ep(1D) ‘an additional shift of the theoretical minimum by 0.2 eV ..., but the threshold G2PICSs remained almost unchanged’ (p. 7): the minimum read at 10.226 eV (corr) and 10.100 eV (corr + CP), 0.126 eV (the minimum is flat, below 0.06e-51 over half an eV, and its position poorly defined; the script allows 0.1 eV), the threshold ratio 0.970. Eq. 19, the total as the sum of the three partials, in the length form (the 1D partials are drawn only in it), corr and corr + CP, at 8.0 to 10.5 eV: Figs. 6 + 7 + 8 over Fig. 9 within 0.05 % (0.9996 to 1.0004). The same calculation drawn twice: Fig. 10 over Fig. 9, all four curves at 8.0 to 10.5 and 13 eV, within 0.5 % (0.9957 to 1.0030). The extracted values, mapped back through the calibrations and overlaid on the rendered pages, follow every drawn curve, its resonances and its dips (inspected 2026-10-08).
NOT REPRODUCED by the drawing: the conclusions’ ‘increase of the computed two-photon photoionization total cross section by approximately 17% at the threshold’ (p. 10): the drawn totals’ corr + CP / corr at 8 eV, the lowest energy drawn, are 1.128 (L) and 1.130 (V), 1.16 and 1.14 at 9 eV; 17 % is the ep(1S) partial’s (1.167). The abstract’s ‘approximately 15%’ from 8 to 10 eV: L 1.13 to 1.22, V 1.13 to 1.17.
DIGITISING UNCERTAINTY: the drawing’s coordinates come in steps of about 0.05 pt and the tick residuals are at most 0.03 pt: 0.4 % of a value on Fig. 10’s log axis; 0.003 to 0.006 (x 10^-51 cm4 s) on the linear axes of Figs. 6-8 (12.5, 18.7 and 12.4 pt per unit 10^-51). Taken: 2 % for Fig. 10 (as mckenna_2004 and lagutin_2017), and 2e-53 cm4 s absolute for the linear partials (whose dips reach zero). In photon energy 0.05 pt is 0.0017 eV (29.6 to 30.6 pt/eV): on a resonance’s flank the value at a given energy is uncertain by the slope times that. The paper states no uncertainty; the L/V difference of the corr + CP totals is 9 % at 8 eV, 4 % at 9 eV, 1.4 % at 10 eV (Fig. 9).
VALUES (Fig. 9, x 10^-51 cm4 s, at 8, 9, 10, 11 eV): corr + CP L 11.53, 11.42, 10.73, 11.76 (the 4s wing); V 12.62, 11.88, 10.88, 10.60; corr L 10.22, 9.83, 8.83, 8.00; V 11.16, 10.41, 9.34, 8.32. Partials (corr + CP L at 8, 9, 10 eV): ep(1S) 6.15, 4.46, 3.41; ep(1D) 1.54, 0.44, 0.007; ef(1D) 3.85, 6.51, 7.30.
COMPARISON with mckenna_2004 (R-matrix Floquet at 1e12 W/cm2, its Fig. 5, log-interpolated in its committed file): corr + CP L / mckenna = 0.909, 0.918, 0.915, 1.044 at 8, 9, 10, 11 eV; V / mckenna = 0.995, 0.956, 0.928, 0.941 (at 11 eV this curve is on the wing of its 4s resonance at 11.63 eV, McKenna’s LS-coupled 4s at 11.97 eV). Without core polarisation (corr L) 0.81, 0.79, 0.75, 0.71.
NOT TAKEN. The LOPT curves (Figs. 1-4, 7, 8), approximations the paper improves on, and Figs. 3 and 4’s corr curves of the ep(1S) channel and the total (drawn again in Figs. 6 and 9 by their captions; the two drawings not compared). Other papers’ curves overlaid: Pindzola and Kelly, Phys. Rev. A 11, 1543 (1975) (Fig. 1; not in the library), Starace and Jiang, Phys. Rev. A 36, 1705 (1987) (Fig. 2(a); in the library) and Pan, Gao and Starace, Phys. Rev. A 41, 6271 (1990) (Figs. 2(b), 5; not in the library; ‘approximately 12% smaller than our G2PICS’ in the length form, 8-11.5 eV, p. 6). Figs. 11-12: the photoelectron angular-distribution parameters beta_2, beta_4, which no quantity of the vocabulary holds. Tables I-VII: the geometrical factors and angular coefficients of the amplitudes (Eqs. 7, A1-A20), properties of the method, not of argon. Table VIII: the summed amplitude of one pair of correlation processes (VIa + VIb) to the ep(1D) channel at 8 eV in five approximations (10^-25 cm2 s^1/2; Eq. A20 by direct integration -0.1440 L, -0.4826 V), a test of the approximations A21 and A23 against A20, not a cross section: its square, 2.1e-52 (L) and 2.3e-51 (V) cm4 s, is one term’s contribution before interference with the LOPT and other amplitudes (Eq. 21), so it cannot check Fig. 10 (ep(1D) corr L at 8 eV is 1.58e-51 in Fig. 7). Fig. 2(b)’s caption says the experimental E(3p) = 1.158 Ry ‘was used’, the text (p. 5) that ‘In both calculations the HF value of E(3p) was used’: a contradiction about a figure not taken.
COVERAGE for the rate: argon two-photon ionisation from 8 to 15 eV (155 to 83 nm), off resonance between 8 and 11 eV (1.0 to 1.2e-50 cm4 s).
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
petrov_2016/fig10_corrcp_L#
{
"id": "fig10_corrcp_L",
"material": "Ar",
"file": "Ar/petrov_2016__fig10_corrcp_L_sigma2_Ar.csv",
"table": "fig_8cec5ab9f473",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.02,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "nonrelativistic LOPT with the correlation-function technique, LS coupling, Hartree-Fock orbitals; with the next-order many-electron correlation amplitudes (processes II-VI, scaled by 1/1.25) and the core-polarisation potential (Fig. 10's 'corr+CP'); experimental E(3p) = 1.158 Ry; no widths of the intermediate states",
"definition": "sigma_q = sum over the channels ep(1S), ep(1D), ef(1D) of (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega(L, l)|^2 (Eqs. 19-20; omega the photon energy in au, + length and - velocity form): the generalised cross section of Starace and Jiang (1987), Gamma = sigma Phi^2 with Phi the photon flux in cm^-2 s^-1; perturbative, independent of intensity, infinite at the resonances"
}
}
Fig. 10 (p. 8): the total 3p two-photon cross section with correlations and core polarisation (corr + CP), length form, linear polarisation, 8.0 to 14.97 eV, log scale: every vertex of the solid line inside the frame (258). The paper’s final calculation. 1.15e-50 at 8 eV; the 4s resonance leaves the frame at 11.64 eV (the experimental 4s line 11.623); 5s/3d near 14.1 eV and 6s/4d near 14.85 eV; dips to 3.5e-51 (13.76 eV) and 2.4e-51 (14.72 eV). Agrees with Fig. 9 within 0.3 % off resonance, and with the sum of Figs. 6-8 within 0.05 %. 2 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
petrov_2016/fig10_corrcp_V#
{
"id": "fig10_corrcp_V",
"material": "Ar",
"file": "Ar/petrov_2016__fig10_corrcp_V_sigma2_Ar.csv",
"table": "fig_8cec5ab9f473",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.02,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "velocity",
"method": "nonrelativistic LOPT with the correlation-function technique, LS coupling, Hartree-Fock orbitals; with the next-order many-electron correlation amplitudes (processes II-VI, scaled by 1/1.25) and the core-polarisation potential (Fig. 10's 'corr+CP'); experimental E(3p) = 1.158 Ry; no widths of the intermediate states",
"definition": "sigma_q = sum over the channels ep(1S), ep(1D), ef(1D) of (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega(L, l)|^2 (Eqs. 19-20; omega the photon energy in au, + length and - velocity form): the generalised cross section of Starace and Jiang (1987), Gamma = sigma Phi^2 with Phi the photon flux in cm^-2 s^-1; perturbative, independent of intensity, infinite at the resonances"
}
}
Fig. 10 (p. 8): as fig10_corrcp_L in the velocity form (blue dashed), 8.0 to 14.97 eV: every dash end inside the frame (646). 1.26e-50 at 8 eV (9 % above the length form there, 1.4 % at 10 eV); the 4s resonance leaves the frame at 11.63 eV. Agrees with Fig. 9 within 0.2 % off resonance. 2 % (the record’s notes).
petrov_2016/fig10_corr_L#
{
"id": "fig10_corr_L",
"material": "Ar",
"file": "Ar/petrov_2016__fig10_corr_L_sigma2_Ar.csv",
"table": "fig_8cec5ab9f473",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.02,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "nonrelativistic LOPT with the correlation-function technique, LS coupling, Hartree-Fock orbitals; with the next-order many-electron correlation amplitudes (processes II-VI), without core polarisation (Fig. 10's 'corr'); experimental E(3p) = 1.158 Ry; no widths of the intermediate states",
"definition": "sigma_q = sum over the channels ep(1S), ep(1D), ef(1D) of (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega(L, l)|^2 (Eqs. 19-20; omega the photon energy in au, + length and - velocity form): the generalised cross section of Starace and Jiang (1987), Gamma = sigma Phi^2 with Phi the photon flux in cm^-2 s^-1; perturbative, independent of intensity, infinite at the resonances"
}
}
Fig. 10 (p. 8): the total with the correlations but without core polarisation (corr), length form (red dash-dot), 8.0 to 14.97 eV: every dash end inside the frame (847). 1.02e-50 at 8 eV; the 4s resonance leaves the frame at 11.91 eV (the paper’s corr omega_4s 11.90 eV). Agrees with Fig. 9 within 0.5 % off resonance, and with the sum of Figs. 6-8 within 0.04 %. 2 % (the record’s notes).
petrov_2016/fig10_corr_V#
{
"id": "fig10_corr_V",
"material": "Ar",
"file": "Ar/petrov_2016__fig10_corr_V_sigma2_Ar.csv",
"table": "fig_8cec5ab9f473",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.02,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "velocity",
"method": "nonrelativistic LOPT with the correlation-function technique, LS coupling, Hartree-Fock orbitals; with the next-order many-electron correlation amplitudes (processes II-VI), without core polarisation (Fig. 10's 'corr'); experimental E(3p) = 1.158 Ry; no widths of the intermediate states",
"definition": "sigma_q = sum over the channels ep(1S), ep(1D), ef(1D) of (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega(L, l)|^2 (Eqs. 19-20; omega the photon energy in au, + length and - velocity form): the generalised cross section of Starace and Jiang (1987), Gamma = sigma Phi^2 with Phi the photon flux in cm^-2 s^-1; perturbative, independent of intensity, infinite at the resonances"
}
}
Fig. 10 (p. 8): as fig10_corr_L in the velocity form (red dash-dot-dot), 8.0 to 14.97 eV: every dash end inside the frame (926). 1.12e-50 at 8 eV. Agrees with Fig. 9 within 0.3 % off resonance. 2 % (the record’s notes).
petrov_2016/fig6_corrcp_L_ep1S#
{
"id": "fig6_corrcp_L_ep1S",
"material": "Ar",
"file": "Ar/petrov_2016__fig6_corrcp_L_sigma2_ep1S_Ar.csv",
"table": "fig_ef2a6676c813",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 2e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"channel": "3p5 ep (1S)",
"method": "nonrelativistic LOPT with the correlation-function technique, LS coupling, Hartree-Fock orbitals; with the next-order many-electron correlation amplitudes (processes II-VI, scaled by 1/1.25) and the core-polarisation potential (Fig. 6's 'corr+CP'); experimental E(3p) = 1.158 Ry; no widths of the intermediate states",
"definition": "the partial cross section of one final channel, sigma_q(L, l, omega) = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega(L, l)|^2 (Eq. 20; omega the photon energy in au, + length and - velocity form), whose sum over the channels is the generalised cross section of Starace and Jiang (1987), Gamma = sigma Phi^2 with Phi the photon flux in cm^-2 s^-1"
}
}
Fig. 6 (p. 7): the partial cross section to the 3p5 ep(1S) channel, corr + CP, length form (blue solid), linear scale 0 to 12e-51, 8.0 to 14.97 eV: every vertex inside the frame (290). 6.15e-51 at 8 eV, falling to a minimum of 3.2e-51 at 10.49 eV; nearly zero (below 0.17e-51) from 12.3 to 13.9 eV. Not the total: fig10_corrcp_L is the sum of this, fig7_corrcp_L_ep1D and fig8_corrcp_L_ef1D. 2e-53 cm4 s: the digitising uncertainty (the record’s notes).
petrov_2016/fig6_corrcp_V_ep1S#
{
"id": "fig6_corrcp_V_ep1S",
"material": "Ar",
"file": "Ar/petrov_2016__fig6_corrcp_V_sigma2_ep1S_Ar.csv",
"table": "fig_ef2a6676c813",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 2e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "velocity",
"channel": "3p5 ep (1S)",
"method": "nonrelativistic LOPT with the correlation-function technique, LS coupling, Hartree-Fock orbitals; with the next-order many-electron correlation amplitudes (processes II-VI, scaled by 1/1.25) and the core-polarisation potential (Fig. 6's 'corr+CP'); experimental E(3p) = 1.158 Ry; no widths of the intermediate states",
"definition": "the partial cross section of one final channel, sigma_q(L, l, omega) = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega(L, l)|^2 (Eq. 20; omega the photon energy in au, + length and - velocity form), whose sum over the channels is the generalised cross section of Starace and Jiang (1987), Gamma = sigma Phi^2 with Phi the photon flux in cm^-2 s^-1"
}
}
Fig. 6 (p. 7): as fig6_corrcp_L_ep1S in the velocity form (blue dashed), 8.0 to 14.96 eV: every dash end inside the frame (527). 7.00e-51 at 8 eV. The 1D partials are drawn only in the length form, so the velocity total has no partial check. 2e-53 cm4 s (the record’s notes).
petrov_2016/fig6_corr_L_ep1S#
{
"id": "fig6_corr_L_ep1S",
"material": "Ar",
"file": "Ar/petrov_2016__fig6_corr_L_sigma2_ep1S_Ar.csv",
"table": "fig_ef2a6676c813",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 2e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"channel": "3p5 ep (1S)",
"method": "nonrelativistic LOPT with the correlation-function technique, LS coupling, Hartree-Fock orbitals; with the next-order many-electron correlation amplitudes (processes II-VI), without core polarisation (Fig. 6's 'corr'); experimental E(3p) = 1.158 Ry; no widths of the intermediate states",
"definition": "the partial cross section of one final channel, sigma_q(L, l, omega) = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega(L, l)|^2 (Eq. 20; omega the photon energy in au, + length and - velocity form), whose sum over the channels is the generalised cross section of Starace and Jiang (1987), Gamma = sigma Phi^2 with Phi the photon flux in cm^-2 s^-1"
}
}
Fig. 6 (p. 7): the ep(1S) partial with the correlations, without core polarisation (corr), length form (red dash-dot), 8.0 to 14.96 eV: every dash end inside the frame (946). 5.27e-51 at 8 eV. 2e-53 cm4 s (the record’s notes).
petrov_2016/fig6_corr_V_ep1S#
{
"id": "fig6_corr_V_ep1S",
"material": "Ar",
"file": "Ar/petrov_2016__fig6_corr_V_sigma2_ep1S_Ar.csv",
"table": "fig_ef2a6676c813",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 2e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "velocity",
"channel": "3p5 ep (1S)",
"method": "nonrelativistic LOPT with the correlation-function technique, LS coupling, Hartree-Fock orbitals; with the next-order many-electron correlation amplitudes (processes II-VI), without core polarisation (Fig. 6's 'corr'); experimental E(3p) = 1.158 Ry; no widths of the intermediate states",
"definition": "the partial cross section of one final channel, sigma_q(L, l, omega) = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega(L, l)|^2 (Eq. 20; omega the photon energy in au, + length and - velocity form), whose sum over the channels is the generalised cross section of Starace and Jiang (1987), Gamma = sigma Phi^2 with Phi the photon flux in cm^-2 s^-1"
}
}
Fig. 6 (p. 7): as fig6_corr_L_ep1S in the velocity form (red dash-dot-dot), 8.0 to 14.97 eV: every dash end inside the frame (769). 6.31e-51 at 8 eV. 2e-53 cm4 s (the record’s notes).
petrov_2016/fig7_corrcp_L_ep1D#
{
"id": "fig7_corrcp_L_ep1D",
"material": "Ar",
"file": "Ar/petrov_2016__fig7_corrcp_L_sigma2_ep1D_Ar.csv",
"table": "fig_6bb337bc395a",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 2e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"channel": "3p5 ep (1D)",
"method": "nonrelativistic LOPT with the correlation-function technique, LS coupling, Hartree-Fock orbitals; with the next-order many-electron correlation amplitudes (processes II-VI, scaled by 1/1.25) and the core-polarisation potential (Fig. 7's 'corr+CP'); experimental E(3p) = 1.158 Ry; no widths of the intermediate states",
"definition": "the partial cross section of one final channel, sigma_q(L, l, omega) = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega(L, l)|^2 (Eq. 20; omega the photon energy in au, + length and - velocity form), whose sum over the channels is the generalised cross section of Starace and Jiang (1987), Gamma = sigma Phi^2 with Phi the photon flux in cm^-2 s^-1"
}
}
Fig. 7 (p. 7): the partial cross section to the 3p5 ep(1D) channel, corr + CP, length form (blue solid), linear scale 0 to 8e-51, 8.0 to 14.97 eV: every vertex inside the frame (269). 1.54e-51 at 8 eV, a minimum near zero at 10.1 eV (the text: core polarisation shifts it by 0.2 eV; read 0.13). 2e-53 cm4 s (the record’s notes).
petrov_2016/fig7_corr_L_ep1D#
{
"id": "fig7_corr_L_ep1D",
"material": "Ar",
"file": "Ar/petrov_2016__fig7_corr_L_sigma2_ep1D_Ar.csv",
"table": "fig_6bb337bc395a",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 2e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"channel": "3p5 ep (1D)",
"method": "nonrelativistic LOPT with the correlation-function technique, LS coupling, Hartree-Fock orbitals; with the next-order many-electron correlation amplitudes (processes II-VI), without core polarisation (Fig. 7's 'corr'); experimental E(3p) = 1.158 Ry; no widths of the intermediate states",
"definition": "the partial cross section of one final channel, sigma_q(L, l, omega) = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega(L, l)|^2 (Eq. 20; omega the photon energy in au, + length and - velocity form), whose sum over the channels is the generalised cross section of Starace and Jiang (1987), Gamma = sigma Phi^2 with Phi the photon flux in cm^-2 s^-1"
}
}
Fig. 7 (p. 7): the ep(1D) partial with the correlations, without core polarisation (corr), length form (red dash-dot), 8.0 to 14.97 eV: every dash end inside the frame (810). 1.58e-51 at 8 eV, the minimum at 10.23 eV. 2e-53 cm4 s (the record’s notes).
petrov_2016/fig8_corrcp_L_ef1D#
{
"id": "fig8_corrcp_L_ef1D",
"material": "Ar",
"file": "Ar/petrov_2016__fig8_corrcp_L_sigma2_ef1D_Ar.csv",
"table": "fig_b0d6534b02ab",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 2e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"channel": "3p5 ef (1D)",
"method": "nonrelativistic LOPT with the correlation-function technique, LS coupling, Hartree-Fock orbitals; with the next-order many-electron correlation amplitudes (processes II-VI, scaled by 1/1.25) and the core-polarisation potential (Fig. 8's 'corr+CP'); experimental E(3p) = 1.158 Ry; no widths of the intermediate states",
"definition": "the partial cross section of one final channel, sigma_q(L, l, omega) = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega(L, l)|^2 (Eq. 20; omega the photon energy in au, + length and - velocity form), whose sum over the channels is the generalised cross section of Starace and Jiang (1987), Gamma = sigma Phi^2 with Phi the photon flux in cm^-2 s^-1"
}
}
Fig. 8 (p. 8): the partial cross section to the 3p5 ef(1D) channel, corr + CP, length form (blue solid), linear scale 0 to 12e-51, 8.0 to 14.84 eV: every vertex inside the frame (302). 3.85e-51 at 8 eV, a maximum of 7.3e-51 at 10.05 eV; the 4s resonance profile at 11.6 eV runs from zero to above the frame (interchannel correlation, p. 7). 2e-53 cm4 s (the record’s notes).
petrov_2016/fig8_corr_L_ef1D#
{
"id": "fig8_corr_L_ef1D",
"material": "Ar",
"file": "Ar/petrov_2016__fig8_corr_L_sigma2_ef1D_Ar.csv",
"table": "fig_b0d6534b02ab",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 2e-53,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"channel": "3p5 ef (1D)",
"method": "nonrelativistic LOPT with the correlation-function technique, LS coupling, Hartree-Fock orbitals; with the next-order many-electron correlation amplitudes (processes II-VI), without core polarisation (Fig. 8's 'corr'); experimental E(3p) = 1.158 Ry; no widths of the intermediate states",
"definition": "the partial cross section of one final channel, sigma_q(L, l, omega) = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega(L, l)|^2 (Eq. 20; omega the photon energy in au, + length and - velocity form), whose sum over the channels is the generalised cross section of Starace and Jiang (1987), Gamma = sigma Phi^2 with Phi the photon flux in cm^-2 s^-1"
}
}
Fig. 8 (p. 8): the ef(1D) partial with the correlations, without core polarisation (corr), length form (red dash-dot), 8.0 to 14.86 eV: every dash end inside the frame (817). 3.38e-51 at 8 eV. 2e-53 cm4 s (the record’s notes).
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.