lagutin_2017#
B. M. Lagutin, I. D. Petrov, V. L. Sukhorukov, Ph. V. Demekhin, A. Knie and A. Ehresmann, “Relativistic, correlation, and polarization effects in two-photon photoionization of Xe”, Phys. Rev. A 95, 063414 (2017)
Source record · Catalogue · Review register
DOI: 10.1103/PhysRevA.95.063414
Source kind: theory
Recorded technique: Lowest-order perturbation theory (LOPT) for the two-photon ionisation of the Xe 5p shell, 5p6 (J0 = 0) + 2 gamma -> Xe+ 5p_jc^5 el j (J = 0, 2) (Eq. 1), in jj coupling, eight channels (5p3/2^5 ep3/2 (J = 0, 2), ep1/2 (J = 2), ef5/2, ef7/2 (J = 2); 5p1/2^5 ep1/2 (J = 0), ep3/2 (J = 2), ef5/2 (J = 2)), extending the authors’ nonrelativistic method for Ar (Petrov et al., Phys. Rev. A 93, 033408 (2016), Ref. 8). The sum over intermediate states (Eqs. 4, 5, 9) is done with the correlation-function technique: an inhomogeneous equation (Eq. 11) solved non-iteratively at any energy (exchange terms and the Darwin derivative turned into systems of local first-order equations, Eqs. 19-21; Milne predictor-corrector). Orbitals: relativistic Pauli-Fock (Breit approximation: mass-velocity, Darwin and spin-orbit terms, Eqs. 15-18), the core frozen at the ground configuration, the intermediate-state functions in the potential of 5p5 el (1P1), optionally with a core-polarisation potential (Petrov, Sukhorukov and Hotop, J. Phys. B 32, 973 (1999), Ref. 28). Many-electron correlations as amplitudes of the next order (processes II-VI: interchannel, ground-state, intermediate-state shake-up, intermediate- and final-state electron scattering), scaled by 1/1.26 for some higher orders (p. 6). Length and velocity forms of the dipole operator. ‘In order to have the G2PICS as a property of a target only we did not consider the width of the intermediate state’ (p. 5): the cross section is infinite at every resonance. Approximations named in the figures: HF (nonrelativistic LOPT), PF (relativistic LOPT), PFCP (PF with core polarisation), CIPF and CIPFCP (with the correlation amplitudes, without and with core polarisation). Not included: the 5p5 5d - 5p5 ed interaction and s-d mixing, ‘particularly strong in Xe’ (p. 6).
Materials in structured entries: Xe
Dataset quantities: multiphoton_ionization_cross_section
Contents: 18 datasets; 0 formulas.
Curation notes#
Journal pp. 063414-1 to 063414-10 = PDF pages 1 to 10. Identity checked on the first page (PDF p. 1: ‘PHYSICAL REVIEW A 95, 063414 (2017)’, Lagutin, Petrov (Rostov-on-Don), Sukhorukov (Southern Federal University), Demekhin, Knie, Ehresmann (Kassel); received 7 April 2017, published 19 June 2017; DOI 10.1103/PhysRevA.95.063414) on 2026-10-08. The library copy is the version of record.
THE CROSS SECTION (p. 2, Eqs. 2-3): the generalised two-photon ionisation cross section (G2PICS, after Lambropoulos 1976, Ref. 9), cm4 s, ‘the property of an atom (i.e., it is independent of the strength of the exciting radiation)’, sigma_q(omega) = sum over channels of (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega|^2, q = 0 linear and q = +-1 circular polarisation, omega the energy of one of the two equal photons in atomic units, ‘+’ the length and ‘-’ the velocity form. The paper does not write the rate; the prefactor makes sigma the coefficient of the photon flux squared in the usual LOPT sense, which the paper does not state.
THE ENERGY AXIS. Every figure’s abscissa is ‘the single-photon energy, thus, the energy implemented to an atom is twice larger’ (Fig. 1 caption). The energy denominators use the experimental (NIST, Ref. 18) ionisation energies, E(5p3/2) = 0.8915 Ry and E(5p1/2) = 0.9875 Ry (12.129 and 13.436 eV), and the double-ionisation energy 2.4330 Ry (p. 3); the intermediate resonances fall where the computed (Pauli-Fock, with or without core polarisation) Rydberg energies put them, not at the experimental ones, which Figs. 3 and 4 (the ‘Exper.’ bars above the plots) and Fig. 8 (dotted vertical lines in the bottom panel) draw for comparison. Core polarisation shifts the 5p5 6s resonance by -0.36 eV and relativistic effects by -0.11 eV; the 5p5 5d by -0.08 and -0.02 eV (pp. 5-6). The resonances are J-resolved (jj coupling; labels in jK notation, 6s[3/2]1, 6s’[1/2]1, ...). No shift or scaling of the axis by the authors. Thresholds: the two-photon 5p3/2 threshold is at 12.129/2 = 6.065 eV per photon, the 5p1/2 at 6.718 eV; every curve of the paper starts at 6.72 eV (the CIPFCP curves’ first drawn vertex at 6.7215 eV; checked against 0.9875 Ry / 2 within 0.01 eV): the abstract’s ‘exciting-photon energies from 6.7 to 11.5 eV, which results in the ionization of Xe between 5p1/2 (13.43 eV) and 5s (23.40 eV) thresholds’. Nothing is computed between the 5p3/2 and 5p1/2 thresholds (6.065 to 6.718 eV), where the 5p1/2^5 ns, nd autoionising series lie; ‘A linear extrapolation of the CIPFCP cross section to the region below 6.72 eV shows good agreement between computed and measured [30] G2PICSs’ (p. 7), the extrapolation not drawn or given.
ACCURACY. ‘Taking into account the above correlations reduces the relative difference |sigma_L - sigma_V| / [(sigma_L + sigma_V)/2] at the threshold from 80% (PF approach) to 7.7% (CIPFCP). The latter number can be considered as a measure of accuracy of the present calculation’ (p. 6); with core polarisation the cross sections are ‘22% higher’ (p. 9; Fig. 3’s PFCP over PF at 7.1 eV: 1.17). The CIPFCP datasets carry 8 % (that measure with the digitising 2 %), the others 2 % (digitising only), the paper giving no accuracy for the approximations it improves on.
EXTRACTED (tools/extract/lagutin_2017.py). The paper prints no table of cross sections and no supplement exists: the values are only in figures, vector drawings (Origin), read from the PDF by data rule 8 (TC-699). Figs. 3 (both panels), 4, 6 (the present curves), 7 and 8 (the CIPFCP curves): every vertex inside the frame of each drawn curve, solid lines’ polyline vertices and dashed lines’ dash ends (each dash a two-vertex segment on the plotted line), sorted by photon energy. Vertices beyond the frame (the resonances run far above it) are in the PDF but clipped from the figure and are not taken; the drawn resonance heights are therefore bounded by the frame, and the calculation is infinite there. Where two curves share a colour and width, each is drawn in one block and told apart by its dash pattern (the script; Fig. 4’s PF L has 8 dashes, shortened at bends, that match PF V’s dash length; none elsewhere). Axes calibrated from the drawings’ own tick marks, linear in energy, logarithmic in decades in sigma (Fig. 7 linear): every tick within 0.03 pt of its fitted scale in every plot. The tick labels are text objects, checked against the values written in the script; the top panel of Fig. 8 shares the bottom panel’s x ticks (checked).
THE CHECKS (the script fails if one is missed): the L/V difference at the threshold (6.722 eV, Fig. 4): CIPFCP 7.4 % (printed 7.7 %), PF 80.1 % (printed 80 %); the first CIPFCP vertex at 6.7215 eV against the 5p1/2 threshold 0.9875 Ry / 2 = 6.7178 eV; Fig. 3’s resonance shifts (pp. 5-6): 6s relativistic (HF to PF) -0.112 eV (printed -0.11), 6s core polarisation (PF to PFCP) -0.375 (-0.36), 5d core polarisation -0.073 (-0.08), 5d relativistic -0.001 (-0.02; the drawn HF and PF 5d resonances coincide, 10.595 and 10.596 eV; within the 0.02 eV margin but at its edge); Fig. 6’s WO / W at 8 eV 1.93 (‘the respective factor equals only to 2’, p. 7); McCown et al.’s point (mccown_1982), drawn as a star in Figs. 4 and 8: at 6.4238 and 6.4229 eV, 4.1175e-50 and 4.1171e-50 cm4 s, against 193 nm (6.4241 eV) and mccown_1982’s 4 x 10^-32 cm4 W-1 times the photon energy, 4.117e-50 cm4 s (to 0.01 %: the y calibration of both log axes is right); the ‘Exper.’ bars of Figs. 3 (6) and 4 (10) and the dotted lines of Fig. 8 (5) each at a NIST odd J = 1 level of Xe I (nist_asd_2026’s levels file) within 0.0018 eV: 6s[3/2]1 8.4365, 6s’[1/2]1 9.5697, 5d[1/2]1 9.9171, 5d[3/2]1 10.4010, 7s[3/2]1 10.5932, and in Fig. 4 6d, 8s, 7d up to 11.4951 eV (the x calibration of each plot is right). The same calculation drawn twice agrees off resonance: Fig. 4’s CIPFCP L and Fig. 8’s linear curve within 0.8 % (587 vertices, 6.75 to 8.2 and 8.8 to 9.4 eV); Fig. 3’s PF and Fig. 4’s PF L within 1.4 %; Fig. 3’s top panel and its enlargement within 2.5 %. The extracted values, mapped back through the calibrations and overlaid on the rendered pages, follow every drawn curve (inspected 2026-10-08).
DIGITISING UNCERTAINTY: the tick residuals (up to 0.03 pt) are 0.1 to 0.4 % of a value on the log axes (17.5 pt per decade in Fig. 3, 27 in Fig. 4, 30 in Figs. 6 and 8) and 0.01 % of Fig. 7’s full scale; a dash’s straight chord lies within a few hundredths of a point of the plotted line. 2 % is taken for a drawn vertex. In photon energy 0.03 pt is 0.0006 eV (Fig. 4, 36 pt/eV) or less: on a resonance’s flank the value at a given energy is uncertain by the slope times that. The curves’ energy grid is not given; the top panel of Fig. 3 draws its PFCP curve with 116 vertices 0.03 to 0.14 eV apart, the bottom panel the same curve with 909.
RESONANCES (drawn, CIPFCP length form): 6s[3/2]1 at 8.40 eV (experiment 8.4365), 6s’[1/2]1 at 9.70 (9.5697), 5d at 10.52 and 7s at 10.58 (Fig. 3: 10.52, 10.575; experiment 10.401 and 10.593 for 5d[3/2]1 and 7s[3/2]1): the computed positions differ from the experimental marks by up to 0.13 eV (‘the overall agreement between experiment and theory is not as good as in Ar’, p. 6). Deep minima (interference between resonances) near 10.13 eV (4.5e-51) and 10.95 eV (1.0e-51, at the bottom of Fig. 4’s frame). Values (CIPFCP L, Fig. 4): 4.49e-50 at 6.722 eV, 3.44e-50 at 8.0, 2.09e-50 at 9.0, 7.7e-51 at 10.0 eV. The circular-to-linear ratio (Fig. 8, bottom over top), not recorded as data: 1.01 at 6.8 eV, 1.05 at 7.0, 1.08 at 7.5, 0.92 at 8.0 (the 6s resonance’s wing), 1.15 at 9.0, 0.69 at 10.0 eV.
NOT TAKEN. Table I: geometric factors f_q of Eq. 8 (for circular polarisation f_1(J = 2) = sqrt(3/2) f_0(J = 2), f_1(J = 0) = 0), not a quantity of the vocabulary. Fig. 1 (p. 5, the PDF’s one image, raster): LS-coupled LOPT partial cross sections of Ar 3p and Xe 5p into ep(1S) and ep(1D), velocity form, near the first (n+1)s resonance, and the radial integrals <ep|d_V|(n+1)s>; an illustration of a simplified model (Xe orbitals without spin-orbit), its resonance ‘widths’ read at 6e-51 cm4 s; not taken. Fig. 2 (p. 6): single-photon partial cross sections np -> ed, es of Ar and Xe in a frozen-core single-electron model against the electron energy, an illustration, not two-photon. Fig. 5: partial amplitudes of the excited 5p3/2^5 6s (J0 = 2) state (Mb^1/2); Fig. 9: the photoelectron angular-distribution parameters beta_2, beta_4: no quantity of the vocabulary. Values of other papers drawn for comparison, not taken: Fig. 6, L’Huillier and Wendin, Phys. Rev. A 36, 4747 (1987) (Ref. 14; library LHuillier_1987_LinearNonlinearScreening), with and without nonlinear screening; Fig. 8, Fink and Johnson, Phys. Rev. A 42, 3801 (1990) (Ref. 16, TDDF, length form, linear and circular, blue dashed), Gangopadhyay, Tang, Lambropoulos and Shakeshaft, Phys. Rev. A 34, 2998 (1986) (Ref. 13, MQDT, linear, squares), McGuire, Phys. Rev. A 24, 835 (1981) (Ref. 11, circular, dash-dot; library McGuire_1981_TwoThreePhoton), and McCown, Ediger and Eden, Phys. Rev. A 26, 3318 (1982) (Ref. 30, mccown_1982; the star in Figs. 4 and 8, used above as a check). The text: McGuire ‘overestimated the G2PICS at the off-resonance region by a factor of about 4’, Gangopadhyay et al.’s is ‘about a factor of 3 smaller than ours’ (p. 8), Fink and Johnson in ‘close agreement’ between the 5p1/2 threshold and the 6s resonance. The figures’ other calculations (Fink and Johnson, Gangopadhyay et al.) and Pan, Gao and Starace, Phys. Rev. A 41, 6271 (1990) (Ref. 15, Ar) are not in the library.
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
lagutin_2017/fig3a_hf#
{
"id": "fig3a_hf",
"material": "Xe",
"file": "Xe/lagutin_2017__fig3a_hf.csv",
"table": "fig_2941080626c2",
"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",
"method": "nonrelativistic LOPT, processes (Ia) and (Ib) only: Hartree-Fock orbitals, jj-coupled channels (Fig. 3's 'HF')",
"gauge": "length",
"definition": "sigma_q = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega|^2 (Eq. 3; omega the energy of one of the two equal photons in au, + length and - velocity form; alpha = 1/137.036, a0 = 5.29177e-9 cm, c = 2.99792e10 cm/s as printed), T the two-photon amplitude of Eqs. 4-6, summed over the final channels (Eq. 2): the generalised two-photon ionisation cross section (G2PICS) of Lambropoulos (1976, Ref. 9), 'a property of an atom', cm4 s; LOPT with no width of the intermediate states, so infinite at each resonance (p. 5)"
}
}
Fig. 3, top panel (p. 6): the total 5p cross section in nonrelativistic LOPT (HF; red dash-dot), length form, linear polarisation, 7.04 to 10.96 eV: every vertex of the dashes inside the frame (277). Resonances (drawn) 6s at 8.87 eV (‘the 6s and 6s’ resonances have equal energy’ in a nonrelativistic calculation, p. 7), another at 10.18 eV, and 5d and 7s at 10.595 and 10.69 eV (Fig. 3, bottom). 2 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none for this approximation.
lagutin_2017/fig3a_pf#
{
"id": "fig3a_pf",
"material": "Xe",
"file": "Xe/lagutin_2017__fig3a_pf.csv",
"table": "fig_2941080626c2",
"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",
"method": "relativistic LOPT, processes (Ia) and (Ib) only: Pauli-Fock orbitals (mass-velocity, Darwin and spin-orbit terms, Eqs. 15-18), eight jj-coupled channels 5p_jc^5 ep/ef (J = 0, 2) (Fig. 3's and Fig. 4's 'PF')",
"gauge": "length",
"definition": "sigma_q = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega|^2 (Eq. 3; omega the energy of one of the two equal photons in au, + length and - velocity form; alpha = 1/137.036, a0 = 5.29177e-9 cm, c = 2.99792e10 cm/s as printed), T the two-photon amplitude of Eqs. 4-6, summed over the final channels (Eq. 2): the generalised two-photon ionisation cross section (G2PICS) of Lambropoulos (1976, Ref. 9), 'a property of an atom', cm4 s; LOPT with no width of the intermediate states, so infinite at each resonance (p. 5)"
}
}
Fig. 3, top panel (p. 6): relativistic LOPT (PF; blue dashed), length form, linear polarisation, 7.02 to 10.94 eV: every vertex of the dashes inside the frame (174). The same calculation as Fig. 4’s PF L (agreeing within 1.4 % off resonance). Resonances (drawn) 6s 8.76 eV, 6s’ 10.08 eV, 5d and 7s 10.596 and 10.66 eV (Fig. 3, bottom). 2 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none for this approximation.
lagutin_2017/fig3a_pfcp#
{
"id": "fig3a_pfcp",
"material": "Xe",
"file": "Xe/lagutin_2017__fig3a_pfcp.csv",
"table": "fig_2941080626c2",
"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",
"method": "relativistic LOPT, processes (Ia) and (Ib) only with the core-polarisation potential V^CP (Petrov et al. 1999, Ref. 28) in the orbitals (Fig. 3's 'PFCP')",
"gauge": "length",
"definition": "sigma_q = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega|^2 (Eq. 3; omega the energy of one of the two equal photons in au, + length and - velocity form; alpha = 1/137.036, a0 = 5.29177e-9 cm, c = 2.99792e10 cm/s as printed), T the two-photon amplitude of Eqs. 4-6, summed over the final channels (Eq. 2): the generalised two-photon ionisation cross section (G2PICS) of Lambropoulos (1976, Ref. 9), 'a property of an atom', cm4 s; LOPT with no width of the intermediate states, so infinite at each resonance (p. 5)"
}
}
Fig. 3, top panel (p. 6): relativistic LOPT with core polarisation (PFCP; black solid), length form, linear polarisation, 7.07 to 10.97 eV: the 116 vertices of the drawn polyline inside the frame, 0.03 to 0.14 eV apart (the bottom panel draws the same curve with 909 vertices from 10.3 eV). Resonances 6s 8.39 eV, 6s’ 9.70 eV. 2 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none for this approximation.
lagutin_2017/fig3b_hf#
{
"id": "fig3b_hf",
"material": "Xe",
"file": "Xe/lagutin_2017__fig3b_hf.csv",
"table": "fig_2941080626c2",
"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",
"method": "nonrelativistic LOPT, processes (Ia) and (Ib) only: Hartree-Fock orbitals, jj-coupled channels (Fig. 3's 'HF')",
"gauge": "length",
"definition": "sigma_q = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega|^2 (Eq. 3; omega the energy of one of the two equal photons in au, + length and - velocity form; alpha = 1/137.036, a0 = 5.29177e-9 cm, c = 2.99792e10 cm/s as printed), T the two-photon amplitude of Eqs. 4-6, summed over the final channels (Eq. 2): the generalised two-photon ionisation cross section (G2PICS) of Lambropoulos (1976, Ref. 9), 'a property of an atom', cm4 s; LOPT with no width of the intermediate states, so infinite at each resonance (p. 5)"
}
}
Fig. 3, bottom panel (p. 6): the top panel enlarged, 10.30 to 10.79 eV, HF (red dash-dot): every vertex of the dashes inside the frame (186). 5d and 7s resonances at 10.595 and 10.69 eV (drawn). 2 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none for this approximation.
lagutin_2017/fig3b_pf#
{
"id": "fig3b_pf",
"material": "Xe",
"file": "Xe/lagutin_2017__fig3b_pf.csv",
"table": "fig_2941080626c2",
"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",
"method": "relativistic LOPT, processes (Ia) and (Ib) only: Pauli-Fock orbitals (mass-velocity, Darwin and spin-orbit terms, Eqs. 15-18), eight jj-coupled channels 5p_jc^5 ep/ef (J = 0, 2) (Fig. 3's and Fig. 4's 'PF')",
"gauge": "length",
"definition": "sigma_q = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega|^2 (Eq. 3; omega the energy of one of the two equal photons in au, + length and - velocity form; alpha = 1/137.036, a0 = 5.29177e-9 cm, c = 2.99792e10 cm/s as printed), T the two-photon amplitude of Eqs. 4-6, summed over the final channels (Eq. 2): the generalised two-photon ionisation cross section (G2PICS) of Lambropoulos (1976, Ref. 9), 'a property of an atom', cm4 s; LOPT with no width of the intermediate states, so infinite at each resonance (p. 5)"
}
}
Fig. 3, bottom panel (p. 6): PF (blue dashed), 10.31 to 10.80 eV, every vertex of the dashes inside the frame (119). 5d and 7s resonances at 10.596 and 10.66 eV (drawn). 2 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none for this approximation.
lagutin_2017/fig3b_pfcp#
{
"id": "fig3b_pfcp",
"material": "Xe",
"file": "Xe/lagutin_2017__fig3b_pfcp.csv",
"table": "fig_2941080626c2",
"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",
"method": "relativistic LOPT, processes (Ia) and (Ib) only with the core-polarisation potential V^CP (Petrov et al. 1999, Ref. 28) in the orbitals (Fig. 3's 'PFCP')",
"gauge": "length",
"definition": "sigma_q = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega|^2 (Eq. 3; omega the energy of one of the two equal photons in au, + length and - velocity form; alpha = 1/137.036, a0 = 5.29177e-9 cm, c = 2.99792e10 cm/s as printed), T the two-photon amplitude of Eqs. 4-6, summed over the final channels (Eq. 2): the generalised two-photon ionisation cross section (G2PICS) of Lambropoulos (1976, Ref. 9), 'a property of an atom', cm4 s; LOPT with no width of the intermediate states, so infinite at each resonance (p. 5)"
}
}
Fig. 3, bottom panel (p. 6): PFCP (black solid), 10.31 to 10.80 eV, the 909 vertices of the drawn polyline inside the frame. 5d and 7s resonances at 10.52 and 10.575 eV (drawn). 2 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none for this approximation.
lagutin_2017/fig4_pf_length#
{
"id": "fig4_pf_length",
"material": "Xe",
"file": "Xe/lagutin_2017__fig4_pf_length.csv",
"table": "fig_8ed2e2069b66",
"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",
"method": "relativistic LOPT, processes (Ia) and (Ib) only: Pauli-Fock orbitals (mass-velocity, Darwin and spin-orbit terms, Eqs. 15-18), eight jj-coupled channels 5p_jc^5 ep/ef (J = 0, 2) (Fig. 3's and Fig. 4's 'PF')",
"gauge": "length",
"definition": "sigma_q = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega|^2 (Eq. 3; omega the energy of one of the two equal photons in au, + length and - velocity form; alpha = 1/137.036, a0 = 5.29177e-9 cm, c = 2.99792e10 cm/s as printed), T the two-photon amplitude of Eqs. 4-6, summed over the final channels (Eq. 2): the generalised two-photon ionisation cross section (G2PICS) of Lambropoulos (1976, Ref. 9), 'a property of an atom', cm4 s; LOPT with no width of the intermediate states, so infinite at each resonance (p. 5)"
}
}
Fig. 4 (p. 7): relativistic LOPT (PF L; red dash-dot), length form, linear polarisation, 6.72 to 11.45 eV: every vertex of the dashes and dots inside the frame (445). Differs from the velocity form by 80 % at the threshold (the text; read 80.1 %). 2 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none for this approximation.
lagutin_2017/fig4_pf_velocity#
{
"id": "fig4_pf_velocity",
"material": "Xe",
"file": "Xe/lagutin_2017__fig4_pf_velocity.csv",
"table": "fig_8ed2e2069b66",
"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",
"method": "relativistic LOPT, processes (Ia) and (Ib) only: Pauli-Fock orbitals (mass-velocity, Darwin and spin-orbit terms, Eqs. 15-18), eight jj-coupled channels 5p_jc^5 ep/ef (J = 0, 2) (Fig. 3's and Fig. 4's 'PF')",
"gauge": "velocity",
"definition": "sigma_q = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega|^2 (Eq. 3; omega the energy of one of the two equal photons in au, + length and - velocity form; alpha = 1/137.036, a0 = 5.29177e-9 cm, c = 2.99792e10 cm/s as printed), T the two-photon amplitude of Eqs. 4-6, summed over the final channels (Eq. 2): the generalised two-photon ionisation cross section (G2PICS) of Lambropoulos (1976, Ref. 9), 'a property of an atom', cm4 s; LOPT with no width of the intermediate states, so infinite at each resonance (p. 5)"
}
}
Fig. 4 (p. 7): PF V (red dash-dot-dot), velocity form, linear polarisation, 6.72 to 11.49 eV: every vertex of the dashes and dots inside the frame (630). 2 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none for this approximation.
lagutin_2017/fig4_cipfcp_length#
{
"id": "fig4_cipfcp_length",
"material": "Xe",
"file": "Xe/lagutin_2017__fig4_cipfcp_length.csv",
"table": "fig_8ed2e2069b66",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.08,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"method": "relativistic Pauli-Fock with core polarisation and the correlation amplitudes (II)-(VI) of the next order (interchannel, ground-state, intermediate-state shake-up, intermediate- and final-state scattering), scaled by 1/1.26 (CIPFCP; Eqs. 6, 13, 14)",
"gauge": "length",
"definition": "sigma_q = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega|^2 (Eq. 3; omega the energy of one of the two equal photons in au, + length and - velocity form; alpha = 1/137.036, a0 = 5.29177e-9 cm, c = 2.99792e10 cm/s as printed), T the two-photon amplitude of Eqs. 4-6, summed over the final channels (Eq. 2): the generalised two-photon ionisation cross section (G2PICS) of Lambropoulos (1976, Ref. 9), 'a property of an atom', cm4 s; LOPT with no width of the intermediate states, so infinite at each resonance (p. 5)"
}
}
Fig. 4 (p. 7): CIPFCP L (black solid), length form, linear polarisation, 6.72 to 11.50 eV: the 3211 vertices of the drawn polyline inside the frame. The paper’s final result for linear polarisation (also Fig. 8, top, which agrees within 0.8 %). Resonances (drawn) 6s 8.40, 6s’ 9.70 eV; deep interference minima near 10.15 and 11.0 eV, below the frame (0.01e-49) near 11.0 eV. 8 %: the digitising uncertainty (2 %) with the paper’s ‘measure of accuracy’, the 7.7 % L/V difference of CIPFCP at the threshold (p. 6); the record’s notes.
lagutin_2017/fig4_cipfcp_velocity#
{
"id": "fig4_cipfcp_velocity",
"material": "Xe",
"file": "Xe/lagutin_2017__fig4_cipfcp_velocity.csv",
"table": "fig_8ed2e2069b66",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.08,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"method": "relativistic Pauli-Fock with core polarisation and the correlation amplitudes (II)-(VI) of the next order (interchannel, ground-state, intermediate-state shake-up, intermediate- and final-state scattering), scaled by 1/1.26 (CIPFCP; Eqs. 6, 13, 14)",
"gauge": "velocity",
"definition": "sigma_q = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega|^2 (Eq. 3; omega the energy of one of the two equal photons in au, + length and - velocity form; alpha = 1/137.036, a0 = 5.29177e-9 cm, c = 2.99792e10 cm/s as printed), T the two-photon amplitude of Eqs. 4-6, summed over the final channels (Eq. 2): the generalised two-photon ionisation cross section (G2PICS) of Lambropoulos (1976, Ref. 9), 'a property of an atom', cm4 s; LOPT with no width of the intermediate states, so infinite at each resonance (p. 5)"
}
}
Fig. 4 (p. 7): CIPFCP V (black dashed), velocity form, linear polarisation, 6.72 to 11.49 eV: every vertex of the dashes inside the frame (247). At the threshold (6.722 eV) 4.84e-50 against the length form’s 4.49e-50: |L - V| / mean = 7.4 % read, 7.7 % printed (p. 6). 8 %: the digitising uncertainty (2 %) with the paper’s ‘measure of accuracy’, the 7.7 % L/V difference of CIPFCP at the threshold (p. 6); the record’s notes.
lagutin_2017/fig6_present_w#
{
"id": "fig6_present_w",
"material": "Xe",
"file": "Xe/lagutin_2017__fig6_present_w.csv",
"table": "fig_b52931f6435b",
"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",
"method": "as CIPFCP but without the intermediate-state shake-up correlation (IV), with the 'nonlinear screening' (final-state scattering) correlations (V) and (VI) (Fig. 6's 'present (W)')",
"gauge": "length",
"definition": "sigma_q = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega|^2 (Eq. 3; omega the energy of one of the two equal photons in au, + length and - velocity form; alpha = 1/137.036, a0 = 5.29177e-9 cm, c = 2.99792e10 cm/s as printed), T the two-photon amplitude of Eqs. 4-6, summed over the final channels (Eq. 2): the generalised two-photon ionisation cross section (G2PICS) of Lambropoulos (1976, Ref. 9), 'a property of an atom', cm4 s; LOPT with no width of the intermediate states, so infinite at each resonance (p. 5)"
}
}
Fig. 6 (p. 7): the present total 5p cross section with ‘nonlinear screening’ (W; black solid), correlation (IV) excluded for comparison with L’Huillier and Wendin, length form, linear polarisation, 6.72 to 10.80 eV: the 2779 vertices of the drawn polyline inside the frame. 2 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none for this approximation.
lagutin_2017/fig6_present_wo#
{
"id": "fig6_present_wo",
"material": "Xe",
"file": "Xe/lagutin_2017__fig6_present_wo.csv",
"table": "fig_b52931f6435b",
"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",
"method": "as CIPFCP but without the intermediate-state shake-up correlation (IV) and without the 'nonlinear screening' correlations (V) and (VI) (Fig. 6's 'present (WO)')",
"gauge": "length",
"definition": "sigma_q = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega|^2 (Eq. 3; omega the energy of one of the two equal photons in au, + length and - velocity form; alpha = 1/137.036, a0 = 5.29177e-9 cm, c = 2.99792e10 cm/s as printed), T the two-photon amplitude of Eqs. 4-6, summed over the final channels (Eq. 2): the generalised two-photon ionisation cross section (G2PICS) of Lambropoulos (1976, Ref. 9), 'a property of an atom', cm4 s; LOPT with no width of the intermediate states, so infinite at each resonance (p. 5)"
}
}
Fig. 6 (p. 7): the same without ‘nonlinear screening’ (WO; black dashed), 6.72 to 10.76 eV: every vertex of the dashes inside the frame (203). WO / W at 8 eV: 1.93 read, ‘only ... 2’ printed (p. 7). 2 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none for this approximation.
lagutin_2017/fig7_cipf_length#
{
"id": "fig7_cipf_length",
"material": "Xe",
"file": "Xe/lagutin_2017__fig7_cipf_length.csv",
"table": "fig_2ce602ac73f9",
"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",
"method": "relativistic Pauli-Fock with the correlation amplitudes (II)-(VI) (CIPF; Fig. 7)",
"gauge": "length",
"channel": "5p3/2^5 ep3/2 (J = 0)",
"definition": "sigma_q = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega|^2 (Eq. 3; omega the energy of one of the two equal photons in au, + length and - velocity form; alpha = 1/137.036, a0 = 5.29177e-9 cm, c = 2.99792e10 cm/s as printed), T the two-photon amplitude of Eqs. 4-6, one final channel (Eq. 3, the partial G2PICS): the generalised two-photon ionisation cross section (G2PICS) of Lambropoulos (1976, Ref. 9), 'a property of an atom', cm4 s; LOPT with no width of the intermediate states, so infinite at each resonance (p. 5)"
}
}
Fig. 7 (p. 8): the partial cross section of the 5p3/2^5 ep3/2 (J = 0) channel, CIPF L (black solid), length form, linear polarisation, linear axis, 6.80 to 9.12 eV: the 40 vertices of the drawn polyline inside the frame (it leaves the frame at the 6s resonance, about 8.8 eV). 2 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none for this approximation.
lagutin_2017/fig7_cipf_velocity#
{
"id": "fig7_cipf_velocity",
"material": "Xe",
"file": "Xe/lagutin_2017__fig7_cipf_velocity.csv",
"table": "fig_2ce602ac73f9",
"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",
"method": "relativistic Pauli-Fock with the correlation amplitudes (II)-(VI) (CIPF; Fig. 7)",
"gauge": "velocity",
"channel": "5p3/2^5 ep3/2 (J = 0)",
"definition": "sigma_q = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega|^2 (Eq. 3; omega the energy of one of the two equal photons in au, + length and - velocity form; alpha = 1/137.036, a0 = 5.29177e-9 cm, c = 2.99792e10 cm/s as printed), T the two-photon amplitude of Eqs. 4-6, one final channel (Eq. 3, the partial G2PICS): the generalised two-photon ionisation cross section (G2PICS) of Lambropoulos (1976, Ref. 9), 'a property of an atom', cm4 s; LOPT with no width of the intermediate states, so infinite at each resonance (p. 5)"
}
}
Fig. 7 (p. 8): the same channel, CIPF V (black dashed), velocity form, 6.82 to 9.18 eV: every vertex of the dashes inside the frame (92). 2 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none for this approximation.
lagutin_2017/fig7_noshakeup_length#
{
"id": "fig7_noshakeup_length",
"material": "Xe",
"file": "Xe/lagutin_2017__fig7_noshakeup_length.csv",
"table": "fig_2ce602ac73f9",
"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",
"method": "relativistic Pauli-Fock with the correlation amplitudes (II)-(VI) less the intermediate-state shake-up (IV) (Fig. 7's 'CIPF shake-up excluded')",
"gauge": "length",
"channel": "5p3/2^5 ep3/2 (J = 0)",
"definition": "sigma_q = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega|^2 (Eq. 3; omega the energy of one of the two equal photons in au, + length and - velocity form; alpha = 1/137.036, a0 = 5.29177e-9 cm, c = 2.99792e10 cm/s as printed), T the two-photon amplitude of Eqs. 4-6, one final channel (Eq. 3, the partial G2PICS): the generalised two-photon ionisation cross section (G2PICS) of Lambropoulos (1976, Ref. 9), 'a property of an atom', cm4 s; LOPT with no width of the intermediate states, so infinite at each resonance (p. 5)"
}
}
Fig. 7 (p. 8): the same channel without the shake-up correlation (IV), length form (red dash-dot), 6.81 to 9.19 eV: every vertex of the dashes and dots inside the frame (173). 2 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none for this approximation.
lagutin_2017/fig7_noshakeup_velocity#
{
"id": "fig7_noshakeup_velocity",
"material": "Xe",
"file": "Xe/lagutin_2017__fig7_noshakeup_velocity.csv",
"table": "fig_2ce602ac73f9",
"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",
"method": "relativistic Pauli-Fock with the correlation amplitudes (II)-(VI) less the intermediate-state shake-up (IV) (Fig. 7's 'CIPF shake-up excluded')",
"gauge": "velocity",
"channel": "5p3/2^5 ep3/2 (J = 0)",
"definition": "sigma_q = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega|^2 (Eq. 3; omega the energy of one of the two equal photons in au, + length and - velocity form; alpha = 1/137.036, a0 = 5.29177e-9 cm, c = 2.99792e10 cm/s as printed), T the two-photon amplitude of Eqs. 4-6, one final channel (Eq. 3, the partial G2PICS): the generalised two-photon ionisation cross section (G2PICS) of Lambropoulos (1976, Ref. 9), 'a property of an atom', cm4 s; LOPT with no width of the intermediate states, so infinite at each resonance (p. 5)"
}
}
Fig. 7 (p. 8): the same, velocity form (red dash-dot-dot), 6.80 to 9.18 eV: every vertex of the dashes and dots inside the frame (272). 2 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none for this approximation.
lagutin_2017/fig8_cipfcp_linear#
{
"id": "fig8_cipfcp_linear",
"material": "Xe",
"file": "Xe/lagutin_2017__fig8_cipfcp_linear.csv",
"table": "fig_edb8d8774747",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.08,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"method": "relativistic Pauli-Fock with core polarisation and the correlation amplitudes (II)-(VI) of the next order (interchannel, ground-state, intermediate-state shake-up, intermediate- and final-state scattering), scaled by 1/1.26 (CIPFCP; Eqs. 6, 13, 14)",
"gauge": "length",
"definition": "sigma_q = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega|^2 (Eq. 3; omega the energy of one of the two equal photons in au, + length and - velocity form; alpha = 1/137.036, a0 = 5.29177e-9 cm, c = 2.99792e10 cm/s as printed), T the two-photon amplitude of Eqs. 4-6, summed over the final channels (Eq. 2): the generalised two-photon ionisation cross section (G2PICS) of Lambropoulos (1976, Ref. 9), 'a property of an atom', cm4 s; LOPT with no width of the intermediate states, so infinite at each resonance (p. 5)"
}
}
Fig. 8, top panel (p. 8): CIPFCP, length form, linear polarisation (black solid), 6.72 to 10.80 eV: the 2746 vertices of the drawn polyline inside the frame. The same calculation as Fig. 4’s CIPFCP L (within 0.8 % off resonance). 8 %: the digitising uncertainty (2 %) with the paper’s ‘measure of accuracy’, the 7.7 % L/V difference of CIPFCP at the threshold (p. 6); the record’s notes.
lagutin_2017/fig8_cipfcp_circular#
{
"id": "fig8_cipfcp_circular",
"material": "Xe",
"file": "Xe/lagutin_2017__fig8_cipfcp_circular.csv",
"table": "fig_edb8d8774747",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.08,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "circular",
"method": "relativistic Pauli-Fock with core polarisation and the correlation amplitudes (II)-(VI) of the next order (interchannel, ground-state, intermediate-state shake-up, intermediate- and final-state scattering), scaled by 1/1.26 (CIPFCP; Eqs. 6, 13, 14)",
"gauge": "length",
"definition": "sigma_q = (8 pi^3 alpha a0^5 / c) omega^(+-2) |T_q,omega|^2 (Eq. 3; omega the energy of one of the two equal photons in au, + length and - velocity form; alpha = 1/137.036, a0 = 5.29177e-9 cm, c = 2.99792e10 cm/s as printed), T the two-photon amplitude of Eqs. 4-6, summed over the final channels (Eq. 2): the generalised two-photon ionisation cross section (G2PICS) of Lambropoulos (1976, Ref. 9), 'a property of an atom', cm4 s; LOPT with no width of the intermediate states, so infinite at each resonance (p. 5)"
}
}
Fig. 8, bottom panel (p. 8): CIPFCP, length form, circular polarisation (black solid), 6.72 to 10.80 eV: the 2697 vertices of the drawn polyline inside the frame (it runs below 0.01e-49 between about 10.1 and 10.3 eV, clipped). Circular over linear (Fig. 8, top): 1.01 at 6.8 eV, 1.05 at 7.0, 1.08 at 7.5, 0.92 at 8.0, 1.15 at 9.0, 0.69 at 10.0 eV. 8 %: the digitising uncertainty (2 %) with the paper’s ‘measure of accuracy’, the 7.7 % L/V difference of CIPFCP at the threshold (p. 6); 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.