santra_2004#
R. Santra and C. H. Greene, “Multiphoton ionization of xenon in the vuv regime”, arXiv:physics/0407010v2 [physics.atom-ph] (2004); published as Phys. Rev. A 70, 053401 (2004)
Source record · Catalogue · Review register
DOI: 10.48550/arxiv.physics/0407010
Source kind: theory
Recorded technique: Independent-particle Floquet calculation with a complex absorbing potential (pp. 3-6 of the preprint). The one-electron potential is Herman and Skillman’s Hartree-Fock-Slater (X-alpha) potential, its X-alpha parameter adjusted per charge state so that the calculated 5p binding energy equals the experimental ionisation potential (Table I: Xe 12.1 eV, Xe+ 21.0 eV, ...; Xe4+ and Xe5+ from a CASSCF calculation); central, no multiplet structure, no spin-orbit splitting (pp. 3-4). Radial finite-element basis (4801 functions, r up to 80 bohr; for each l the first 50 eigenfunctions above the 5s level). The CAP -i eta W(r), W = (r - 4)^2 outside 4 bohr (Eq. 4), the Siegert energy from the stabilised eta trajectory (Eq. 5 and p. 5). Electric-dipole coupling ‘in length gauge’ (p. 5) to a quantised single mode, ‘assuming linear polarization’ (p. 5), Floquet blocks mu = 0 to mu_max, the minimum number of photons to ionise, the CAP only in the last block (p. 6). The rate of the 5p, m level, averaged over m (Eq. 15) and multiplied by the number of 5p electrons, 6 - q (Eq. 16); the N-photon cross section sigma_N from the rate in the lowest-order law of the rate equations, Eq. (24): dn/dt = -sigma_N (I / omega)^N n (atomic units, so I / omega is the photon flux). A crude estimate of a 5s-mediated (Auger-like) contribution, an autoionisation width of 65 meV on the final block’s states that the 5p -> 5s energy can ionise (Eq. 26, p. 10), added to the 5p cross sections without interference (Eqs. 27-31).
Materials in structured entries: Xe, Xe+
Dataset quantities: multiphoton_ionization_cross_section, photoionization_cross_section
Contents: 4 datasets; 0 formulas.
Curation notes#
The library copy is the arXiv preprint physics/0407010v2 (13 August 2004 in the margin; the ‘Dated’ line shows the date the PDF was generated), 21 pages; identity checked against its first page on 2026-10-08. The journal version, Phys. Rev. A 70, 053401 (2004), doi:10.1103/PhysRevA.70.053401, is linked from the arXiv abstract page (the library’s provenance file) but is not in the library and was not checked: the citation and the page numbers are the preprint’s (PDF pages).
THE CROSS SECTIONS. The rate of the m-averaged 5p level times the number of 5p electrons (Eqs. 15-16), and sigma_N the coefficient of the lowest-order rate, dn/dt = sigma_N (I/omega)^N n (Eq. 24, atomic units: the photon flux Phi = I / hbar omega; the convention of uiterwaal_1998 and mckenna_2004). The intensity at which the multiphoton rates were computed is not stated; the one-photon rate was computed at 1 x 10^11 W/cm2 and checked to be linear in I there (p. 7).
CHECKED (p. 7). The one-photon rate gamma_5p averaged over m, 2.35 x 10^-5 a.u. at 1 x 10^11 W/cm2 (Eq. 15; gamma_5p,0 = 3.05 x 10^-5, gamma_5p,+-1 = 2.01 x 10^-5), times 6 electrons, is 5.83 x 10^12 s^-1; over the photon flux at 12.7 eV (4.91 x 10^28 cm^-2 s^-1) it is 118.6 Mb, the printed 119 Mb.
THE ENERGY AXIS. Photon energies as printed: 12.7 eV (the DESY VUV-FEL experiment’s) and 6.42 eV (ArF, 193 nm). The model’s thresholds are single (no spin-orbit, no multiplets) and fixed to the experimental ionisation potentials by the X-alpha parameter (Table I). In particular, neutral Xe’s two-photon threshold is one limit at 12.1 eV: the model has no 2P3/2-2P1/2 splitting and none of the autoionising resonances between them, where the 193 nm two-photon energy (12.83 eV) lies and where mccown_1982’s measurement averages over a resonance.
WHAT IS TAKEN, as inline points (table = ‘text’): sigma_2 of Xe+ at 12.7 eV, without (Eq. 17) and with (Eq. 27) the 5s-mediated estimate; sigma_2 of neutral Xe at 6.42 eV (p. 7), the authors’ test against experiment (‘Experimentally, this is known to be about 4 x 10^-50 cm^4 s [89]’, Ref. 89 being mccown_1982; ‘Other calculations of this quantity, which are similarly accurate, are reported in Refs. [90, 91, 92]’); the one-photon cross section of neutral Xe at 12.7 eV (p. 7), which ‘differs from the experimental cross section [87] by a little more than a factor of 2’ (Samson 1966) and was confirmed with an R-matrix code in the same potential. All theory, use = check.
NOT TAKEN. sigma_3 to sigma_6 of Xe2+ to Xe5+ (Eqs. 18-21, 28-31): no such materials in the registry (only Xe+), and the vocabulary does not need them. Table I’s ionisation potentials (taken from Refs. 41-47 or computed, and used to tune the model) and X-alpha parameters: model inputs. The quoted experimental 4 x 10^-50 cm4 s: McCown et al.’s alpha converted by hbar omega (mccown_1982 holds the original). The charge-state yields of Figs. 4 and 6 (a model of one experiment’s pulses, figures only). No figure is digitised.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
santra_2004/sigma2_Xe+#
{
"id": "sigma2_Xe+",
"material": "Xe+",
"table": "text",
"scale": 1e-49,
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "independent-particle (Hartree-Fock-Slater, X-alpha tuned to the 5p binding energy) Floquet with a complex absorbing potential, 5p ionisation, m-averaged rate times 6 - q electrons (Eqs. 15-16)",
"definition": "dn/dt = -sigma_N (I / omega)^N n (Eq. 24, atomic units): Gamma = sigma_2 Phi^2, Phi the photon flux in cm^-2 s^-1",
"contribution": "5p only (Eq. 17)"
}
}
1 inline points in the source record.
Eq. (17), preprint p. 7: sigma_2(Xe+) = 4.5 x 10^-49 cm4 s at a photon energy of 12.7 eV, the 5p electrons only (Hartree-Fock-Slater CAP-Floquet; the record’s technique). No uncertainty stated; the same model’s one-photon cross section of Xe is about a factor of 2 from experiment (p. 7).
santra_2004/sigma2_5s_Xe+#
{
"id": "sigma2_5s_Xe+",
"material": "Xe+",
"table": "text",
"scale": 1e-49,
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "as Eq. (17), plus a 5s-excitation path with an assigned autoionisation width of 65 meV (Eq. 26)",
"definition": "dn/dt = -sigma_N (I / omega)^N n (Eq. 24, atomic units): Gamma = sigma_2 Phi^2, Phi the photon flux in cm^-2 s^-1",
"contribution": "5p plus the 5s-mediated estimate (Eq. 27)"
}
}
1 inline points in the source record.
Eq. (27), preprint p. 10: sigma_2(Xe+) = 4.6 x 10^-49 cm4 s at 12.7 eV, Eq. (17) plus the crude estimate of the 5s-mediated (Auger-like) path (autoionisation width 65 meV, Eq. 26), added without interference. The authors’ estimate, ‘crudely’ made (p. 10).
santra_2004/sigma2_Xe#
{
"id": "sigma2_Xe",
"material": "Xe",
"table": "text",
"scale": 1e-50,
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"parameters": {
"photons": 2,
"polarization": "linear",
"gauge": "length",
"method": "independent-particle (Hartree-Fock-Slater, X-alpha tuned to the 5p binding energy) Floquet with a complex absorbing potential, s to f waves, mu_max = 2",
"definition": "dn/dt = -sigma_N (I / omega)^N n (Eq. 24, atomic units): Gamma = sigma_2 Phi^2, Phi the photon flux in cm^-2 s^-1",
"wavelength_nm": 193
}
}
1 inline points in the source record.
Preprint p. 7: ‘we investigated the two-photon ionization cross section of neutral Xe at 6.42 eV ... With atomic s through f waves and mu_max = 2, we calculated a cross section of 6.2 x 10^-50 cm4 s’, against the experimental ‘about 4 x 10^-50’ (mccown_1982 converted). The model’s single threshold at 12.1 eV has no autoionising structure between the Xe+ 2P3/2 and 2P1/2 limits, where 2 x 6.42 eV lies (the record’s notes).
santra_2004/sigma1_Xe#
{
"id": "sigma1_Xe",
"material": "Xe",
"table": "text",
"quantity": "photoionization_cross_section",
"unit": "Mb",
"abscissa_unit": "eV",
"use": "check",
"parameters": {
"method": "independent-particle (Hartree-Fock-Slater) Floquet with a complex absorbing potential, length gauge, linear polarisation, s to d waves, mu_max = 1",
"intensity_w_cm2": 100000000000.0
}
}
1 inline points in the source record.
Preprint p. 7: ‘within the Herman-Skillman-based independent-particle model, the one-photon ionization cross section of neutral Xe, at a photon energy of 12.7 eV, is 119 Mb’, from the m-averaged 5p rate at 1 x 10^11 W/cm2 (reproduced, the record’s notes); ‘differs from the experimental cross section [87] by a little more than a factor of 2’ (Samson 1966), confirmed with an R-matrix code in the same potential. s, p and d waves, mu_max = 1. A model test, not a recommended value.
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.