proulx_1993#
D. Proulx and R. Shakeshaft, “Two- and excess-photon ionization of helium”, J. Phys. B: At. Mol. Opt. Phys. 26, L7-L14 (1993)
Source record · Catalogue · Review register
DOI: 10.1088/0953-4075/26/1/002
Source kind: theory
Recorded technique: Lowest-order (second-order) perturbation theory, the amplitude from the Dalgarno-Lewis harmonic components (Eqs. 1-3) recast so that the final state is the symmetrised product of a Coulomb wave in (Z - 1) e^2 / r and the bound He+ orbital, final-state correlation included exactly (Eq. 8, p. L8). Two-electron basis of complex Sturmian functions, l, l’ <= 3, n_r, n_r’ <= 20, the wavenumber kappa in the upper right quadrant (|kappa| = 1.0, arg kappa = 80 degrees for the tables); ground-state binding energy 2.90283 to 2.90316 au depending on kappa (Pekeris 2.903724374), (1s2s) 1S 2.145892 to 2.145926 au (p. L9). Velocity gauge (‘convergence ... is more rapid in the velocity gauge’, p. L9); Pade summation for the divergent discrete-basis series. Linearly polarised light (abstract, p. L9); the He+ ion left in its ground state; rates integrated over angles. Non-relativistic, spin-orbit coupling neglected.
Materials in structured entries: He
Dataset quantities: multiphoton_ionization_cross_section
Contents: 2 datasets; 0 formulas.
Curation notes#
J. Phys. B 26, L7-L14 (1993), a Letter: PDF page 1 is the IOPscience download banner, journal pp. L7-L14 are PDF pages 2-9 (journal page L(PDF page + 5)), scanned with a text layer. Identity checked on the first page (PDF p. 2: ‘J. Phys. B: At. Mol. Opt. Phys. 26 (1993) L7-L14’, Daniel Proulx and Robin Shakeshaft, University of Southern California; received 24 August 1992) on 2026-10-09. The library’s identity is VALIDATED_WITH_WARNINGS; the copy is the version of record.
THE TWO-PHOTON DATA in numbers are two tables (p. L11), both for the ground state of He; every cell checked against the table images (all agree). Table 1: ‘Gamma_a and Gamma_b are, respectively, the rates for two-photon ionization (below the threshold for one-photon ionization) of ground-state He calculated from equation (8) and from the induced width of the ground-state level for various values of the photoelectron energy epsilon ... All quantities are in au’: Gamma / I^2 at epsilon = 0.15, 0.30, 0.45, 0.60, 0.75 au. Table 2: the two-photon cross sections, 10^-53 cm4 s, at omega = 1.0, 1.1, 1.2, 1.3 au, above the one-photon threshold, ‘Present’ beside ‘Bachau et al’ (Bachau, Lambropoulos and Tang 1990). The agreement ‘is at best fair; at one frequency, 1.1 au, the disagreement is rather striking, apparently due to the presence of a 1De resonance ... not accounted for in the calculations of Bachau et al’ (p. L10): 750 against 17.89.
THE ENERGY AXES. Table 2 is against the photon energy omega in au, as printed. Table 1 is against the photoelectron energy epsilon (au), which the vocabulary has no abscissa for: the script converts it to the photon energy, hbar omega = (epsilon + I_p) / 2, with I_p = 0.902995 au the calculation’s own ionisation energy (the ground-state binding energy the text prints, 2.90283 to 2.90316 au, less He+’s 2 au; the range is +-0.00008 au in hbar omega). epsilon is kept as printed in each row’s id and printed cell. The calculation’s ground state is 0.0006 to 0.0009 au above Pekeris’s; no energy was shifted by the authors.
THE UNIT OF Gamma / I^2. ‘All quantities are in au’ (Table 1), the atomic unit of intensity not named. The text fixes it (p. L14): an ‘average’ resonant two-photon rate of ‘1 x I^2 au’ is ‘about 10^11 s^-1’ at 10^13 W/cm2, which holds with I in units of E_h / (hbar a_0^2) = 6.436 x 10^15 W/cm2 (1.0e11 s^-1; the intensity of a field of 1 au amplitude, 3.51 x 10^16 W/cm2, would give 3.4e9). In that unit sigma_2 = (Gamma / I^2) omega^2 a_0^4 t_au (Gamma = sigma_2 Phi^2, Phi = I / hbar omega).
THE CHECKS (tools/extract/proulx_1993.py; the script fails if one is missed): Gamma_b within 0.04 to 0.13 % of Gamma_a (the table); Table 2’s Bachau column equal to bachau_1990’s Table I L^2 column, cell for cell; the text’s 10^11 s^-1 (above); Table 1 as sigma_2 against saenz_1999’s 1S + 1D partial curves summed (TC-873), at omega x 27.2114 eV on that record’s (shifted) axis: 0.884, 0.952, 1.019, 1.122, 1.104 at epsilon = 0.15 to 0.75 (omega 0.5265 to 0.8265 au; sigma_2 1.22e-51, 9.85e-52, 8.03e-52, 1.05e-51, 3.48e-52 cm4 s), within a factor 1.2 (the other intensity unit would put them 30 times apart). vanderhart_2005’s dashed line (Saenz’s numbers again) gives the same ratios within 0.2 %. The 1.12 at 0.7515 au is on the wing of the 1s2p resonance, where the two calculations’ resonance positions matter.
NIKOLOPOULOS AND LAMBROPOULOS (2001) draw Table 2’s ‘Present’ column as the circles of their Fig. 4 (‘He+, Proulx and Shakesaft,1993’; nikolopoulos_2001, TC-875, not taken there): read with that record’s calibrated vector axes, 0.997 to 1.005 times Table 2 at 27.208, 29.925, 32.642 and 35.375 eV (omega x 27.2114 eV within 0.01 eV). They agree.
NOT TAKEN. Figs. 1-6 (rates Gamma / I^2 in au against the photoelectron energy, 0 to 2 au, from the ground state (Figs. 1, 3, 4) and from the (1s2s) 1S state (Figs. 2, 5, 6), with and without final-state correlation): raster figures of the scan, not read in this round (the tables give the numbers at their check points; the smooth part of Fig. 1 below the one-photon threshold, epsilon 0 to 0.55 au, could be read from the image). Fig. 5’s peak heights ‘in au’ (two-photon ionisation of the metastable state through the autoionising resonances). Tables 3 and 4: positions (as photoelectron energies) and widths of the 1Se and 1De resonances below the n = 2 threshold, au, with Ho’s (1986) and Oza’s (1986): no quantity holds a resonance position on the photoelectron energy or an autoionisation width. The text’s ‘average’ resonant rates 1 x I^2 au (ground state, near 30 eV) and 0.1 x I^2 au (metastable, near 20 eV), and the one-photon rates of 10^13 and 10^12 s^-1 at 10^13 W/cm2 (p. L14): order-of-magnitude estimates.
FURTHER TWO-PHOTON DATA CITED: B. Ritchie, Phys. Rev. A 16, 2080 (1977) (since curated, ritchie_1977); A. L’Huillier, L. Jonsson and G. Wendin, Phys. Rev. A 33, 3938 (1986) (lhuillier_1986); K. C. Kulander, Phys. Rev. A 36, 2726 (1987) (kulander_1987) (He two-photon ionisation below the one-photon threshold). Not in the library: G. A. Victor, Proc. Phys. Soc. 91, 825 (1967); L. A. Lompre et al., J. Phys. B 13, 1799 (1980) (multiphoton ionisation of metastable He); D. Proulx and R. Shakeshaft, Phys. Rev. A 46, R2221 (1992) (H- multiphoton detachment).
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
proulx_1993/tbl1_rate2#
{
"id": "tbl1_rate2",
"material": "He",
"file": "He/proulx_1993__tbl1_rate2_He.csv",
"table": "tbl_677dfb58bbf0",
"quantity": "multiphoton_ionization_cross_section",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "velocity",
"final_state": "He+ (1s) + e-",
"method": "lowest-order perturbation theory, final-state correlation included (Eq. 8); complex Sturmian two-electron basis l, l' <= 3, n_r, n_r' <= 20, |kappa| = 1.0, arg kappa = 80 degrees; Pade summation",
"definition": "Gamma / I^2, Gamma the total (angle-integrated) rate and I the intensity, both in atomic units, I in units of E_h / (hbar a_0^2) = 6.436e15 W/cm2 (fixed by the text, the record's notes); sigma_2 = (Gamma / I^2) omega^2 a_0^4 t_au for Gamma = sigma_2 Phi^2"
}
}
Table 1 (p. L11), Gamma_a / I^2: the two-photon ionisation rate of ground-state He over the squared intensity, atomic units, below the one-photon threshold: 0.23170, 0.14357, 0.09246, 0.09828, 0.02685 at the photoelectron energies epsilon = 0.15, 0.30, 0.45, 0.60, 0.75 au, converted to the photon energy (epsilon + 0.902995) / 2 = 0.5265 to 0.8265 au (the record’s notes; epsilon is the row id). Gamma_b (the induced width) agrees within 0.13 %. As sigma_2: 1.22e-51 to 3.48e-52 cm4 s. No uncertainty stated.
proulx_1993/tbl2_sigma2#
{
"id": "tbl2_sigma2",
"material": "He",
"file": "He/proulx_1993__tbl2_sigma2_He.csv",
"table": "tbl_8d4370f4f253",
"scale": 1e-53,
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "velocity",
"final_state": "He+ (1s) + e-",
"method": "lowest-order perturbation theory, final-state correlation included (Eq. 8); complex Sturmian two-electron basis l, l' <= 3, n_r, n_r' <= 20, |kappa| = 1.0, arg kappa = 80 degrees; Pade summation",
"definition": "sigma_2 in cm4 s, Gamma = sigma_2 Phi^2 with Phi the photon flux in cm^-2 s^-1 (the definition not printed; Table 1's Gamma / I^2 so converted agrees with saenz_1999, the record's notes)"
}
}
Table 2 (p. L11), ‘Present’: the two-photon ionisation cross section of ground-state He above the one-photon threshold (excess-photon ionisation), x 10^-53 cm4 s, at omega = 1.0, 1.1, 1.2, 1.3 au: 26.7, 750, 16.2, 10.5. 1.1 au is on a 1De doubly excited resonance below the n = 2 threshold (photoelectron energy 1.297 au; Table 4 places the 2(1,0)2+ 1De peak at 1.2983). The ‘Bachau et al’ column beside it is bachau_1990’s Table I, not taken. No uncertainty stated.
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.