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 `__ · :doc:`Catalogue ` · :doc:`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\+ ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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\+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 :doc:`review register ` for the checks and decisions.