mihelic_2021#
A. Mihelič and M. Horvat, “Calculation of multiphoton ionization amplitudes and cross sections of few-electron atoms”, Phys. Rev. A 103, 043108 (2021)
Source record · Catalogue · Review register
DOI: 10.1103/PhysRevA.103.043108
Source kind: theory
Recorded technique: Time-independent lowest-order perturbation theory: K driven Schrodinger equations (E_j - H) Psi_j = D Psi_(j-1), E_j = E_0 + j omega (Eqs. 28-30), solved with exterior complex scaling (ECS); the partial amplitude of each channel is extracted from the radial function at large r by a least-squares fit to a few outgoing Coulomb waves with the wave numbers of the open intermediate and final channels (Eqs. 23-26), which handles above-threshold ionisation and resonance-enhanced ionisation (pp. 043108-2 to -5). Dipole operator in the velocity form (‘Henceforth, we limit our attention to the dipole operator in the velocity form’, p. 043108-3). He: two-electron basis of modified B-splines, single-particle angular momenta up to l_max = 6; below the one-photon threshold (BTI) 150 B-splines of order seven per l, R_max = 170, R0 = 120; above it (ATI) 85 B-splines per l, R_max = 85, R0 = 50; theta = 0.70 in both; ‘Partial ionization cross sections of channels with n_a <= 5 were included in the sum [Eq. (32)] to obtain the cross sections in Fig. 3’ (p. 043108-6). Fig. 4’s second calculation: channels n_a <= 10, R0 = 120, R_max = 160, 120 B-splines per l for each electron (p. 043108-7). Linear polarisation along z: final states M_L = S = M_S = 0 (p. 043108-5). Checked by increasing R_max (R0) and the basis: ‘Except for the differences close to the ionization thresholds arising due to additional bound and resonance states with high principal quantum numbers, the cross sections remained unchanged’ (p. 043108-6). The method fails exactly on a core resonance (40.8 eV) and near bound intermediate states, where no decay or field dressing is included (pp. 043108-5, -7).
Materials in structured entries: He
Dataset quantities: multiphoton_ionization_cross_section
Contents: 25 datasets; 0 formulas.
Curation notes#
PDF pages 1-11 = pp. 043108-1 to -11. Identity checked on the first page: Phys. Rev. A 103, 043108 (2021), Andrej Mihelič (Jožef Stefan Institute and Faculty of Mathematics and Physics, Ljubljana) and Martin Horvat (Faculty of Mathematics and Physics, Ljubljana); received 11 December 2020, accepted 29 March 2021, published 13 April 2021 (checked 2026-10-08).
THE CROSS SECTION (p. 043108-5, Eq. 31): sigma_gamma^(K)(omega) = 2 pi (2 pi / (c omega))^K |B_gamma|^2 in atomic units, ‘converted to SI units by multiplying the right-hand side of Eq. (31) with a0^2K t0^(K-1)’; the partial cross section sigma_L^(K) is the sum over n_a, l_a, l of the channels of total angular momentum L (Eq. 32). The paper does not write the rate; it relates its two-photon cross section to Karule’s intensity-normalised Q^(2)/I = (hbar omega)^-1 sigma^(2), I in W/cm2 and sigma in cm4 s (p. 043108-5): the generalised cross section of uiterwaal_1998 and saenz_1999, the rate sigma F^K with F the photon flux. Its He cross sections agree with Saenz and Lambropoulos’s (the comparison below).
THE ENERGY AXES are the photon energy, as drawn; no shift is stated. Each order’s figure is split at the one-photon threshold, 24.6 eV: the frames run from 12.30 to 24.60 eV and 24.60 to 43.54 eV (two photons), 8.20 to 12.30 and 12.30 to 43.54 eV (three), 6.15 to 8.20 and 8.20 to 43.54 eV (four), the (N+W)-photon ATI thresholds ‘12.3 eV [Fig. 3(c)] and 24.6 eV [Fig. 3(d)]’ and the 2 l_a eps l channels at ‘32.7, 21.8, and 16.35 eV in Figs. 3(b), 3(d), and 3(f)’ (pp. 043108-6, -7); the second ionisation threshold is 65.4 eV (p. 043108-8). The paper does not give its ground-state energy.
EXTRACTED (tools/extract/mihelic_2021.py). The paper prints no table and no supplement; the cross sections are only in figures, drawn by matplotlib as vectors, read from the PDF by data rule 8 (TC-699): Fig. 3 (p. 043108-6), the He partial cross sections sigma_L for two (L = 0, 2), three (L = 1, 3) and four photons (L = 0, 2, 4), each below (BTI) and above (ATI) the one-photon threshold, 14 curves; Fig. 4 (p. 043108-7), the total three-photon cross section from 25.25 to 27.35 eV in two calculations (n_a <= 10 and n_a <= 5); Fig. 5 (p. 043108-7), the two-photon partial cross sections of single channels n_a l_a eps l L near the lowest 1Po autoionising states, 59.05 to 64.30 eV, L = 0 (the total and 1s eps s, 2s eps s, 2p eps p) and L = 2 (the total and 1s eps d, 2s eps d, 2p eps p, 2p eps f). Each curve is a stroked polyline (Fig. 3(a) and (e)’s L = 0 in several pieces, joined in drawing order) clipped to its plot’s frame; every vertex inside the frame is taken (vertices beyond the clip, which the figure does not show, are not). The drawing program simplified the paths: there are fewer vertices than the calculation has energies (75 to 656 per curve; the copy of Saenz and Lambropoulos’s 1D curve in Fig. 3(a) has 118 against the 1729 of saenz_1999’s own drawing), and between vertices the drawn line is straight. Axes calibrated from the drawing’s own ticks (matplotlib’s major and minor ticks; the labels, glyphs drawn as paths, read on the rendered page, and the ticks of the unlabelled decades placed by their spacing): every tick within 0.001 pt of its fitted scale. The right-hand axes of Fig. 3(b), (d), (f) carry no unit label; they are taken in the unit of the row’s left-hand label (10^-52 cm^4 s, 10^-84 cm^6 s^2, 10^-118 cm^8 s^3), as the caption’s rows (‘two- (top), three- (middle), and four-photon (bottom)’) and the continuity of the curves across the split at 24.6 eV imply. The extracted values, mapped back through the calibrations and overlaid on the rendered pages, follow every drawn line (inspected 2026-10-08).
THE CHECKS (the script fails if one is missed), against every number the text prints for these curves: the core-excited peak ‘At hbar omega ~ 40.8 eV’ in Figs. 3(b), (d), (f): read 40.803, 40.808 and 40.824 eV; the jumps at the 2 l_a eps l thresholds: 32.708 eV in Fig. 3(b) (printed 32.7; 1.0 and 0.9 decades for L = 0 and 2), 21.801 eV in Fig. 3(d) L = 1 (printed 21.8); in Fig. 3(f) (printed 16.35) the step is clear only for L = 2 (16.347 eV, 0.9 decade; reported); the dotted line of Fig. 4 at ‘the limit of 1 a.u. (27.2 eV)’ reads 27.2114 eV (1 a.u. = 27.2114 eV). Fig. 4’s n_a <= 5 curve is Fig. 3(d)’s L = 1 and 3 summed within 1.4 % (25.3 to 27.3 eV), one calculation in two figures. The paper prints no value of a cross section of He.
COMPARISON WITH saenz_1999 (not part of the extraction; read with both scripts, 2026-10-08). The dotted copies of Saenz and Lambropoulos’s curves in Fig. 3(a) agree with saenz_1999’s own Fig. 1 (velocity gauge) within 1 % from 13 to 20 eV (2 % at 20.4 eV), and differ from its length gauge by up to 22 %: the copies are the velocity gauge, on Saenz and Lambropoulos’s shifted axis as published. Mihelič and Horvat’s own cross sections are 0.75 to 1.06 times saenz_1999’s (1S, L = 0) and 0.89 to 1.19 times (1D, L = 2) from 13 to 20.5 eV; at 13.5 eV they read 0.151e-51 (L = 0) and 1.16e-51 cm4 s (L = 2), against saenz_1999’s velocity 0.2 and 1.3e-51, length 0.15 and 1.35e-51, and complex-scaling 0.1 and 1.15e-51. Four photons at 7.5 eV: the sum of L = 0, 2, 4 is 2.40e-118 cm8 s3, against saenz_1999’s 2.65e-118; ‘slightly larger differences are present in the case of the four-photon partial cross sections’ (p. 043108-6); L = 0 is 0.27 to 0.78 times saenz_1999’s 1S from 6.5 to 7.5 eV. The caption calls the copies ‘dotted lines’, the text ‘(dashed black line)’ (p. 043108-6): they are dotted.
DIGITISING UNCERTAINTY: the drawing’s coordinates are given to 0.001 pt and every tick lies within 0.001 pt of its scale, against 6 to 33 pt per decade (Fig. 5(b) 6.0, Fig. 3(d), (f) 7.8, Fig. 3(a), (c), (e) 10.8, Fig. 4 33): 0.04 % of a value at a vertex. 0.5 % is taken for the value at a drawn vertex, to cover the line’s simplification by the drawing program (the vertices are the drawn line’s; whether each is a point of the calculation is not known). Between vertices the straight drawn line may depart from the calculation by more, on a resonance by much more. In photon energy 0.0005 eV or less. The paper states no uncertainty of the calculation.
NOT TAKEN: the dotted copies of saenz_1999’s curves in Fig. 3(a), (c), (e) (the original is taken there; the comparison above); Fig. 2, the hydrogen cross sections (two photons l = 0, 2 and their total; three photons l = 1, 3; four photons l = 0, 2, 4; up to 20 eV): in this PDF its lines are not stroked paths but filled outlines of the strokes (the line’s two edges, dashes as separate outlines, joins as Bezier arcs), so the drawn line’s centre is not in the file and would have to be reconstructed from its edges; the paper says they ‘agree perfectly with the results of the analytic treatment by Karule’ (p. 043108-5), whose tables, E. Karule, J. Phys. B 11, 441 (1978) and J. Phys. B 21, 1997 (1988), not in the library, are the primary numbers for hydrogen; its markers are Karule’s. Fig. 1 (a radial function) and Fig. 6 (the asymmetry parameters beta_2 ... beta_8 of the photoelectron angular distribution, compared with Boll et al., Phys. Rev. A 99, 023416 (2019)) hold no quantity of the vocabulary. The text cites, without printing values: Proulx et al., Phys. Rev. A 49, 1208 (1994) (three-photon rates of He, in ‘excellent agreement’, not shown); none of the cited multiphoton papers is in the library besides saenz_1999.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
mihelic_2021/fig3a_sigma2_L0#
{
"id": "fig3a_sigma2_L0",
"material": "He",
"file": "He/mihelic_2021__fig3a_sigma2_L0_He.csv",
"table": "fig_5f3321672a12",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"final_symmetry": "L = 0 (1S)",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-splines, l_max = 6, 150 B-splines of order 7 per l, R_max = 170, R0 = 120, theta = 0.70; channels n_a <= 5",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 3(a) (p. 043108-6), solid blue: the generalised two-photon partial ionisation cross section of He to L = 0, below the one-photon threshold (BTI), 12.30 to 24.58 eV, 135 vertices. Through zero near 18.5 eV and 22.6 eV (clipped by the frame at 1e-55); the 1s2p resonance at 21.2 eV runs off the frame. 0.151e-51 at 13.5 eV (saenz_1999: 0.2e-51 velocity, 0.15e-51 length, 0.1e-51 complex scaling). cm4 s (the axis prints 10^-52 cm^4 s), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
mihelic_2021/fig3a_sigma2_L2#
{
"id": "fig3a_sigma2_L2",
"material": "He",
"file": "He/mihelic_2021__fig3a_sigma2_L2_He.csv",
"table": "fig_5f3321672a12",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"final_symmetry": "L = 2 (1D)",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-splines, l_max = 6, 150 B-splines of order 7 per l, R_max = 170, R0 = 120, theta = 0.70; channels n_a <= 5",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 3(a), dashed orange: the generalised two-photon partial ionisation cross section of He to L = 2, BTI, 12.30 to 24.58 eV, 117 vertices. 1.16e-51 at 13.5 eV (saenz_1999: 1.3e-51 velocity, 1.35e-51 length, 1.15e-51 complex scaling). cm4 s (the axis prints 10^-52 cm^4 s), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
mihelic_2021/fig3b_sigma2_L0#
{
"id": "fig3b_sigma2_L0",
"material": "He",
"file": "He/mihelic_2021__fig3b_sigma2_L0_He.csv",
"table": "fig_5f3321672a12",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"final_symmetry": "L = 0 (1S)",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-splines, 85 B-splines per l, R_max = 85, R0 = 50, theta = 0.70; channels n_a <= 5",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 3(b) (p. 043108-6), solid blue: the generalised two-photon partial ionisation cross section of He to L = 0 above the one-photon threshold (ATI), 24.61 to 43.36 eV, 229 vertices: one-photon ionisation is open, the second photon is absorbed in the continuum. 1Se autoionising resonances below the He+(n = 2) channels, which open with a jump at 32.7 eV (read 32.708 eV); the core-excited (1s eps p -> 2p eps p) peak at 40.8 eV (read 40.803 eV, 2.6e-47). The right-hand axis carries no unit label; the row’s, 10^-52 cm^4 s, is taken (the record’s notes). cm4 s (the axis prints 10^-52 cm^4 s), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
mihelic_2021/fig3b_sigma2_L2#
{
"id": "fig3b_sigma2_L2",
"material": "He",
"file": "He/mihelic_2021__fig3b_sigma2_L2_He.csv",
"table": "fig_5f3321672a12",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"final_symmetry": "L = 2 (1D)",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-splines, 85 B-splines per l, R_max = 85, R0 = 50, theta = 0.70; channels n_a <= 5",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 3(b), dashed orange: the generalised two-photon partial ionisation cross section of He to L = 2, ATI, 24.61 to 43.28 eV, 228 vertices. 1De resonances, the jump at 32.7 eV (read 32.708 eV), the core-excited peak at 40.8 eV (read 40.803 eV, 5.3e-47). Unit as Fig. 3(a) (the record’s notes). cm4 s (the axis prints 10^-52 cm^4 s), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
mihelic_2021/fig3c_sigma3_L1#
{
"id": "fig3c_sigma3_L1",
"material": "He",
"file": "He/mihelic_2021__fig3c_sigma3_L1_He.csv",
"table": "fig_5f3321672a12",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm6 s2",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 3,
"polarization": "linear",
"final_symmetry": "L = 1 (1P)",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-splines, l_max = 6, 150 B-splines of order 7 per l, R_max = 170, R0 = 120, theta = 0.70; channels n_a <= 5",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 3(c) (p. 043108-6), solid green: the generalised three-photon partial ionisation cross section of He to L = 1, BTI, 8.20 to 12.29 eV, 168 vertices. Two-photon resonances (drawn peak 10.3 eV, off the frame), a zero near 11.0 eV; the (2+1)-photon ATI threshold at 12.3 eV (the frame’s edge). cm6 s2 (the axis prints 10^-84 cm^6 s^2), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
mihelic_2021/fig3c_sigma3_L3#
{
"id": "fig3c_sigma3_L3",
"material": "He",
"file": "He/mihelic_2021__fig3c_sigma3_L3_He.csv",
"table": "fig_5f3321672a12",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm6 s2",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 3,
"polarization": "linear",
"final_symmetry": "L = 3 (1F)",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-splines, l_max = 6, 150 B-splines of order 7 per l, R_max = 170, R0 = 120, theta = 0.70; channels n_a <= 5",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 3(c), dashed purple: the generalised three-photon partial ionisation cross section of He to L = 3, BTI, 8.20 to 12.29 eV, 92 vertices; 1.0e-85 to 2e-85 below 11.4 eV. cm6 s2 (the axis prints 10^-84 cm^6 s^2), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
mihelic_2021/fig3d_sigma3_L1#
{
"id": "fig3d_sigma3_L1",
"material": "He",
"file": "He/mihelic_2021__fig3d_sigma3_L1_He.csv",
"table": "fig_5f3321672a12",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm6 s2",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 3,
"polarization": "linear",
"final_symmetry": "L = 1 (1P)",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-splines, 85 B-splines per l, R_max = 85, R0 = 50, theta = 0.70; channels n_a <= 5",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 3(d) (p. 043108-6), solid green: the generalised three-photon partial ionisation cross section of He to L = 1 from the (2+1)-photon threshold, 12.32 to 43.53 eV, 481 vertices: a minimum near 17.9 eV, the (1+2)-photon threshold at 24.6 eV, the jump at 21.8 eV (read 21.801 eV), the core-excited peak at 40.8 eV (read 40.808 eV). The right-hand axis has major ticks every second decade; unit as Fig. 3(c) (the record’s notes). cm6 s2 (the axis prints 10^-84 cm^6 s^2), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
mihelic_2021/fig3d_sigma3_L3#
{
"id": "fig3d_sigma3_L3",
"material": "He",
"file": "He/mihelic_2021__fig3d_sigma3_L3_He.csv",
"table": "fig_5f3321672a12",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm6 s2",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 3,
"polarization": "linear",
"final_symmetry": "L = 3 (1F)",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-splines, 85 B-splines per l, R_max = 85, R0 = 50, theta = 0.70; channels n_a <= 5",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 3(d), dashed purple: the generalised three-photon partial ionisation cross section of He to L = 3, 12.32 to 43.50 eV, 384 vertices; the core-excited peak at 40.808 eV. cm6 s2 (the axis prints 10^-84 cm^6 s^2), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
mihelic_2021/fig3e_sigma4_L0#
{
"id": "fig3e_sigma4_L0",
"material": "He",
"file": "He/mihelic_2021__fig3e_sigma4_L0_He.csv",
"table": "fig_5f3321672a12",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm8 s3",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 4,
"polarization": "linear",
"final_symmetry": "L = 0 (1S)",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-splines, l_max = 6, 150 B-splines of order 7 per l, R_max = 170, R0 = 120, theta = 0.70; channels n_a <= 5",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 3(e) (p. 043108-6), solid blue: the generalised four-photon partial ionisation cross section of He to L = 0, BTI, 6.15 to 8.20 eV, 143 vertices: three-photon resonance at 7.08 eV (off the frame), a zero near 7.63 eV. cm8 s3 (the axis prints 10^-118 cm^8 s^3), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
mihelic_2021/fig3e_sigma4_L2#
{
"id": "fig3e_sigma4_L2",
"material": "He",
"file": "He/mihelic_2021__fig3e_sigma4_L2_He.csv",
"table": "fig_5f3321672a12",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm8 s3",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 4,
"polarization": "linear",
"final_symmetry": "L = 2 (1D)",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-splines, l_max = 6, 150 B-splines of order 7 per l, R_max = 170, R0 = 120, theta = 0.70; channels n_a <= 5",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 3(e), dashed orange: the generalised four-photon partial ionisation cross section of He to L = 2, BTI, 6.15 to 8.20 eV, 140 vertices. cm8 s3 (the axis prints 10^-118 cm^8 s^3), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
mihelic_2021/fig3e_sigma4_L4#
{
"id": "fig3e_sigma4_L4",
"material": "He",
"file": "He/mihelic_2021__fig3e_sigma4_L4_He.csv",
"table": "fig_5f3321672a12",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm8 s3",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 4,
"polarization": "linear",
"final_symmetry": "L = 4 (1G)",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-splines, l_max = 6, 150 B-splines of order 7 per l, R_max = 170, R0 = 120, theta = 0.70; channels n_a <= 5",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 3(e), dashed red: the generalised four-photon partial ionisation cross section of He to L = 4, BTI, 6.15 to 8.20 eV, 75 vertices; 4.7e-120 to 1.3e-117. cm8 s3 (the axis prints 10^-118 cm^8 s^3), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
mihelic_2021/fig3f_sigma4_L0#
{
"id": "fig3f_sigma4_L0",
"material": "He",
"file": "He/mihelic_2021__fig3f_sigma4_L0_He.csv",
"table": "fig_5f3321672a12",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm8 s3",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 4,
"polarization": "linear",
"final_symmetry": "L = 0 (1S)",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-splines, 85 B-splines per l, R_max = 85, R0 = 50, theta = 0.70; channels n_a <= 5",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 3(f) (p. 043108-6), solid blue: the generalised four-photon partial ionisation cross section of He to L = 0 from the (3+1)-photon threshold, 8.20 to 43.49 eV, 656 vertices; the core-excited peak at 40.8 eV (read 40.824 eV). At the printed threshold of the 2 l_a eps l channels, 16.35 eV, the drawn step (16.334 to 16.361 eV) is smaller than the resonances beside it. Unit as Fig. 3(e) (the record’s notes). cm8 s3 (the axis prints 10^-118 cm^8 s^3), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
mihelic_2021/fig3f_sigma4_L2#
{
"id": "fig3f_sigma4_L2",
"material": "He",
"file": "He/mihelic_2021__fig3f_sigma4_L2_He.csv",
"table": "fig_5f3321672a12",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm8 s3",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 4,
"polarization": "linear",
"final_symmetry": "L = 2 (1D)",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-splines, 85 B-splines per l, R_max = 85, R0 = 50, theta = 0.70; channels n_a <= 5",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 3(f), dashed orange: the generalised four-photon partial ionisation cross section of He to L = 2, 8.20 to 43.49 eV, 631 vertices; a step of 0.9 decade at 16.347 eV (the printed 16.35 eV threshold); the core-excited peak at 40.824 eV. cm8 s3 (the axis prints 10^-118 cm^8 s^3), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
mihelic_2021/fig3f_sigma4_L4#
{
"id": "fig3f_sigma4_L4",
"material": "He",
"file": "He/mihelic_2021__fig3f_sigma4_L4_He.csv",
"table": "fig_5f3321672a12",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm8 s3",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 4,
"polarization": "linear",
"final_symmetry": "L = 4 (1G)",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-splines, 85 B-splines per l, R_max = 85, R0 = 50, theta = 0.70; channels n_a <= 5",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 3(f), dashed red: the generalised four-photon partial ionisation cross section of He to L = 4, 8.20 to 43.49 eV, 475 vertices; the core-excited peak at 40.824 eV. cm8 s3 (the axis prints 10^-118 cm^8 s^3), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
mihelic_2021/fig4_sigma3_na10#
{
"id": "fig4_sigma3_na10",
"material": "He",
"file": "He/mihelic_2021__fig4_sigma3_na10_He.csv",
"table": "fig_9c2c2686d9cd",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm6 s2",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 3,
"polarization": "linear",
"final_symmetry": "total (L = 1 and 3)",
"channels": "n_a <= 10",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-splines, 120 B-splines per l for each electron, R_max = 160, R0 = 120; channels n_a <= 10",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 4 (p. 043108-7), solid black: the total generalised three-photon ionisation cross section of He (L = 1 and 3) in the region of (1+2)-photon ATI, 25.26 to 27.33 eV, 187 vertices, with the channels n_a <= 10: two resonances near 25.5 and 26.1 eV and a series of peaks converging to 1 a.u. (27.2 eV; pathways g.s. -> 1s eps1 p -> 1s eps2 l -> n_a p eps3 l, n_a >= 4, p. 043108-7). 0.5 to 170e-84. cm6 s2 (the axis prints 10^-84 cm^6 s^2), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
mihelic_2021/fig4_sigma3_na5#
{
"id": "fig4_sigma3_na5",
"material": "He",
"file": "He/mihelic_2021__fig4_sigma3_na5_He.csv",
"table": "fig_9c2c2686d9cd",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm6 s2",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 3,
"polarization": "linear",
"final_symmetry": "total (L = 1 and 3)",
"channels": "n_a <= 5",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-splines, channels n_a <= 5, as in Fig. 3 (the basis not restated)",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 4, dashed blue: the same with the channels n_a <= 5, 25.26 to 27.33 eV, 119 vertices: the two resonances near 25.5 and 26.1 eV only. Fig. 3(d)’s L = 1 and 3 summed, within 1.4 % (checked by the script). cm6 s2 (the axis prints 10^-84 cm^6 s^2), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
mihelic_2021/fig5_sigma2_L0#
{
"id": "fig5_sigma2_L0",
"material": "He",
"file": "He/mihelic_2021__fig5_sigma2_L0_He.csv",
"table": "fig_1b0120cd87bd",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"final_symmetry": "L = 0 (1S)",
"channel": "total",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-spline basis not stated for this figure",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 5 (p. 043108-7), upper panel: the generalised two-photon partial ionisation cross section of He, the total of L = 0 (black), in the region of the lowest 1Po autoionising intermediate states sp2+, sp3-, sp3+ and 2p3d (REMPI; drawn peaks 60.15, 62.76, 63.66, 64.12 eV), 59.21 to 64.29 eV, 127 vertices, 3.6e-54 to 9.2e-51 cm4 s (the axis prints 10^-52 cm^4 s), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
mihelic_2021/fig5_sigma2_L0_1ses#
{
"id": "fig5_sigma2_L0_1ses",
"material": "He",
"file": "He/mihelic_2021__fig5_sigma2_L0_1ses_He.csv",
"table": "fig_1b0120cd87bd",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"final_symmetry": "L = 0 (1S)",
"channel": "1s eps s",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-spline basis not stated for this figure",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 5 (p. 043108-7), upper panel: the generalised two-photon partial ionisation cross section of He, the 1s eps s channel of L = 0 (blue), in the region of the lowest 1Po autoionising intermediate states sp2+, sp3-, sp3+ and 2p3d (REMPI; drawn peaks 60.15, 62.76, 63.66, 64.12 eV), 60.03 to 64.18 eV, 42 vertices, 1.6e-54 to 9.0e-54 cm4 s (the axis prints 10^-52 cm^4 s), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
mihelic_2021/fig5_sigma2_L0_2ses#
{
"id": "fig5_sigma2_L0_2ses",
"material": "He",
"file": "He/mihelic_2021__fig5_sigma2_L0_2ses_He.csv",
"table": "fig_1b0120cd87bd",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"final_symmetry": "L = 0 (1S)",
"channel": "2s eps s",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-spline basis not stated for this figure",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 5 (p. 043108-7), upper panel: the generalised two-photon partial ionisation cross section of He, the 2s eps s channel of L = 0 (dashed orange), in the region of the lowest 1Po autoionising intermediate states sp2+, sp3-, sp3+ and 2p3d (REMPI; drawn peaks 60.15, 62.76, 63.66, 64.12 eV), 59.13 to 64.30 eV, 125 vertices, 4.0e-56 to 1.3e-51 cm4 s (the axis prints 10^-52 cm^4 s), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
mihelic_2021/fig5_sigma2_L0_2pep#
{
"id": "fig5_sigma2_L0_2pep",
"material": "He",
"file": "He/mihelic_2021__fig5_sigma2_L0_2pep_He.csv",
"table": "fig_1b0120cd87bd",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"final_symmetry": "L = 0 (1S)",
"channel": "2p eps p",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-spline basis not stated for this figure",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 5 (p. 043108-7), upper panel: the generalised two-photon partial ionisation cross section of He, the 2p eps p channel of L = 0 (dotted red), in the region of the lowest 1Po autoionising intermediate states sp2+, sp3-, sp3+ and 2p3d (REMPI; drawn peaks 60.15, 62.76, 63.66, 64.12 eV), 59.13 to 64.30 eV, 132 vertices, 6.5e-56 to 1.9e-51 cm4 s (the axis prints 10^-52 cm^4 s), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
mihelic_2021/fig5_sigma2_L2#
{
"id": "fig5_sigma2_L2",
"material": "He",
"file": "He/mihelic_2021__fig5_sigma2_L2_He.csv",
"table": "fig_1b0120cd87bd",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"final_symmetry": "L = 2 (1D)",
"channel": "total",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-spline basis not stated for this figure",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 5 (p. 043108-7), lower panel: the generalised two-photon partial ionisation cross section of He, the total of L = 2 (black), in the region of the lowest 1Po autoionising intermediate states sp2+, sp3-, sp3+ and 2p3d (REMPI; drawn peaks 60.15, 62.76, 63.66, 64.12 eV), 59.25 to 64.29 eV, 108 vertices, 1.0e-53 to 2.3e-50 cm4 s (the axis prints 10^-52 cm^4 s), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
mihelic_2021/fig5_sigma2_L2_1sed#
{
"id": "fig5_sigma2_L2_1sed",
"material": "He",
"file": "He/mihelic_2021__fig5_sigma2_L2_1sed_He.csv",
"table": "fig_1b0120cd87bd",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"final_symmetry": "L = 2 (1D)",
"channel": "1s eps d",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-spline basis not stated for this figure",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 5 (p. 043108-7), lower panel: the generalised two-photon partial ionisation cross section of He, the 1s eps d channel of L = 2 (blue), in the region of the lowest 1Po autoionising intermediate states sp2+, sp3-, sp3+ and 2p3d (REMPI; drawn peaks 60.15, 62.76, 63.66, 64.12 eV), 59.50 to 64.21 eV, 47 vertices, 4.1e-54 to 1.0e-52 cm4 s (the axis prints 10^-52 cm^4 s), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
mihelic_2021/fig5_sigma2_L2_2sed#
{
"id": "fig5_sigma2_L2_2sed",
"material": "He",
"file": "He/mihelic_2021__fig5_sigma2_L2_2sed_He.csv",
"table": "fig_1b0120cd87bd",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"final_symmetry": "L = 2 (1D)",
"channel": "2s eps d",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-spline basis not stated for this figure",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 5 (p. 043108-7), lower panel: the generalised two-photon partial ionisation cross section of He, the 2s eps d channel of L = 2 (dashed orange), in the region of the lowest 1Po autoionising intermediate states sp2+, sp3-, sp3+ and 2p3d (REMPI; drawn peaks 60.15, 62.76, 63.66, 64.12 eV), 59.24 to 64.27 eV, 115 vertices, 4.7e-56 to 1.8e-51 cm4 s (the axis prints 10^-52 cm^4 s), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
mihelic_2021/fig5_sigma2_L2_2pep#
{
"id": "fig5_sigma2_L2_2pep",
"material": "He",
"file": "He/mihelic_2021__fig5_sigma2_L2_2pep_He.csv",
"table": "fig_1b0120cd87bd",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"final_symmetry": "L = 2 (1D)",
"channel": "2p eps p",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-spline basis not stated for this figure",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 5 (p. 043108-7), lower panel: the generalised two-photon partial ionisation cross section of He, the 2p eps p channel of L = 2 (dotted red), in the region of the lowest 1Po autoionising intermediate states sp2+, sp3-, sp3+ and 2p3d (REMPI; drawn peaks 60.15, 62.76, 63.66, 64.12 eV), 59.18 to 64.29 eV, 115 vertices, 2.3e-55 to 7.6e-51 cm4 s (the axis prints 10^-52 cm^4 s), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
mihelic_2021/fig5_sigma2_L2_2pef#
{
"id": "fig5_sigma2_L2_2pef",
"material": "He",
"file": "He/mihelic_2021__fig5_sigma2_L2_2pef_He.csv",
"table": "fig_1b0120cd87bd",
"digitised": "vector",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"relative": 0.005,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"final_symmetry": "L = 2 (1D)",
"channel": "2p eps f",
"gauge": "velocity",
"method": "ECS driven Schrodinger equations, amplitudes from Coulomb-wave fits (Eq. 23); two-electron B-spline basis not stated for this figure",
"definition": "sigma^(K) = 2 pi (2 pi / (c omega))^K |B|^2 (Eq. 31, atomic units; times a0^2K t0^(K-1) in SI), the partial sigma_L summed over n_a, l_a, l (Eq. 32)",
"energy_axis": "photon energy as drawn; no shift stated"
}
}
Fig. 5 (p. 043108-7), lower panel: the generalised two-photon partial ionisation cross section of He, the 2p eps f channel of L = 2 (dash-dotted green), in the region of the lowest 1Po autoionising intermediate states sp2+, sp3-, sp3+ and 2p3d (REMPI; drawn peaks 60.15, 62.76, 63.66, 64.12 eV), 59.18 to 64.26 eV, 120 vertices, 5.0e-60 to 4.5e-53 cm4 s (the axis prints 10^-52 cm^4 s), against the photon energy; every vertex inside the frame. 0.5 %: the digitising uncertainty of a drawn vertex (the record’s notes); the paper states none.
Formulas#
No formulas are recorded.
Corrections#
No dataset errata are recorded in this source record.
Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.