lhuillier_1986 ============== A\. L'Huillier, L\. Jonsson and G\. Wendin, "Many\-electron effects in multiphoton ionization\: Screening effects in single\-electron ionization", Phys\. Rev\. A 33, 3938\-3955 \(1986\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1103/PhysRevA\.33\.3938 `__ **Source kind:** theory **Recorded technique:** Lowest\-order \(weak\-field\) perturbation theory for two\-photon ionisation of He 1s2 1S with linearly polarised light \(Sec\. IV, pp\. 3946\-3949\)\: the rate p = 2 pi \(alpha c / a\_0\)\(I / I\_0\)^2 \[\|d^2\_\(epsilon d,1s\)\|^2 \+ \|d^2\_\(epsilon s,1s\)\|^2\] \(Eq\. 4\.6, I in W/cm2, I\_0 = 14\.038e16 W/cm2\), the two\-photon matrix element in the length form \(the dipole operator e\.r, Eqs\. 3\.4, 4\.7, A3b\), the intermediate sum explicit over a discretised continuum \(about 250 states over 0\.02\-20 Ry, Appendix A\) of a local\-density \(LDA, V\_xc ~ \-rho^\(1/3\)\) one\-electron basis, which supports no bound p states \(so no intermediate resonances\)\. 'One\-electron approximation'\: unscreened matrix elements; 'random\-phase approximation' \(LDRPA\)\: each dipole matrix element screened at the frequency omega by the linear response epsilon^\-1\(r, omega\) \(Eqs\. 3\.26\-3\.28, A4\-A7, Fredholm approximation\), the screening at 2 omega neglected \(Appendix B\)\. The LDA ionisation threshold is 1\.13 Ry, against the real 1\.81 Ry\. Non\-relativistic; the authors\: 'The purpose of the calculation is not to obtain any accurate results' \(p\. 3946\) but to show the effect of the screening\. **Materials in structured entries:** He **Dataset quantities:** multiphoton\_ionization\_cross\_section **Contents:** 2 datasets; 0 formulas. Curation notes -------------- Phys\. Rev\. A 33, 3938\-3955 \(1986\), NUMBER 6, June 1986\: PDF pages 1\-18 = journal pp\. 3938\-3955\. Identity checked on the first page \(PDF p\. 1\: 'PHYSICAL REVIEW A VOLUME 33, NUMBER 6 JUNE 1986', 'Many\-electron effects in multiphoton ionization\: Screening effects in single\-electron ionization', Anne L'Huillier \(Saclay\), Lars Jonsson and Goran Wendin \(Chalmers\); received 19 August 1985, revised 21 January 1986\) on 2026\-10\-09\. The library's identity is VALIDATED\_WITH\_WARNINGS; the copy is the version of record\. The PDF is a scan \(pdfimages\: one 5060 x 6898 bilevel JBIG2 image per page, 612 x 627 dpi; pdffonts\: only a non\-embedded Times\-Roman text layer\)\: every figure is raster\. HELIUM ONLY\. The only calculation is the one\- and two\-photon ionisation of He\. NO KRYPTON values of any kind\: krypton appears once, 'In Xe, two\-photon ionization is possible \(omega ~ 6\.4 eV\), while in Kr, Ar, and Ne, three\-photon absorption is necessary for ionization' \(p\. 3950, of the ArF laser\), with no number\. No xenon two\-photon cross section either\: for Xe the paper gives only the LDRPA screening factors \ in the 4d and 5p regions \(below, NOT TAKEN\), and the multiphoton orders discussed for Xe \(ion yields of other papers\) carry no cross sections\. THE QUANTITY\. Figs\. 11\-13 plot 'the ionization rate divided by the square of the laser intensity, p/I^2, in 10^\-16 s^\-1 W^\-2 cm^4 units' \(p\. 3948\) against the photon energy in Ry\. With W = sigma\_2 Phi^2 \(Phi = I / hbar omega\) sigma\_2 = \(p / I^2\) \(hbar omega\)^2; kept as printed \(unit s\-1 cm4/W2, scale 1e\-16, as bachau\_1990's Fig\. 1\(a\)\)\. 'Two\-photon ionization cross section' and 'rate' are used for the same curve \(pp\. 3948, 3952\)\. THE ENERGY AXIS is the photon energy in Ry \(R\_inf hc; 1 Ry = 0\.5 hartree\), as printed; nothing converted and nothing shifted\. The curves are the LDA's, unshifted\: the calculation's two\-photon threshold is half the LDA ionisation energy, 0\.57 Ry, and its one\-photon threshold 1\.13 Ry \('For computational reasons, we have avoided the close vicinity of the LDA threshold, which explains the gaps in the curves', p\. 3948\)\. The figure marks the experimental thresholds \(2ph\. 0\.90 Ry, 1s^\-1 1\.81 Ry, 1s^\-1 2p\) with dotted lines\. The authors divide the axis into four regions \(p\. 3948\)\: \(i\) 0\.57\-0\.90 Ry, below the real two\-photon threshold, 'an average representation of the two\-photon absorption spectrum \(transitions to discrete levels\)', not ionisation; \(ii\) 0\.90\-1\.13 Ry, real two\-photon ionisation with the intermediate state discrete in both spectra; \(iii\) 1\.13\-1\.81 Ry, 'an average representation' of the real spectrum's 1s \-\> np resonances \(the LDA has none\); \(iv\) above 1\.81 Ry, 'expected to give a good description' \(not read here\: the lines run into the axis\)\. 'A realistic approximation \.\.\. starts at omega = 0\.90 Ry, follows first the solid curve in Fig\. 11, then the dash\-dotted interpolation \.\.\., and finally again the solid curve' \(p\. 3948\)\. THE DRAWING\. The ticks put the frame's left edge, labelled '0\.57' \(and '0\.6' in Fig\. 13\), at 0\.62 Ry; the text says Fig\. 11 runs 'from 0\.6 to 2\.5 Ry' \(p\. 3948\)\. The values are read on the tick scale and the edge's label is not used\. On that scale the dotted lines labelled 0\.90, 1\.13 and 1\.81 lie at 0\.90, 1\.12 and 1\.80 Ry \(the drawing's precision\)\. Fig\. 12's ordinate is labelled 'p/I^2 \(arb\. u\.\)'\. EXTRACTED \(tools/extract/lhuillier\_1986\.py\)\: Fig\. 11's two lines, read from the page image at its native pixels \(data rule 8, TC\-699; no vector drawing\)\: the axes from the frame's inward ticks \(x every 0\.1 Ry, 0\.7\-2\.4, less those under the dotted lines and the curves; y every 0\.5 from 0 to 6\.5 on both edges, the scale interpolated between the edges by column\: the page is slightly rotated, the bottom line 6 pixels higher at the right, and the drawing's spacing differs by up to 7 pixels between the edges\); the lines tracked column by column \(every fourth\) from seeds, each sample the centre of the line's run in that column\. The pieces\: 0\.67\-1\.02 Ry \(both lines; the left edge's ticks hide 0\.62\-0\.67\), 1\.20\-1\.28 Ry \(solid, clear of the thin interpolation\), 1\.20\-1\.39 Ry \(dashed\), and 1\.55\-1\.78 Ry, where the two lines lie 12\-15 pixels apart and the upper, continuous one is the solid \(checked\: every column with a single run has it on the upper track\); 1\.28\-1\.55 Ry, where the lines touch, and beyond the 1\.81 Ry dotted line, where they run into the axis, are not read\. Fig\. 11's x ticks fit a line within 3\.7 pixels \(0\.004 Ry\), the y ticks within 4\.8 \(left\) and 5\.1 \(right\) pixels \(0\.03\)\. The overlay of the samples on the page image was inspected \(2026\-10\-09\)\: every sample on its line\. THE CHECKS \(the script fails if one is missed\)\: 'at 1 Ry, the two\-photon ionization rate is lowered by a factor of 1\.4' \(p\. 3949\)\: the dashed over the solid line at 1\.0 Ry, 3\.541 / 2\.513 = 1\.409; 'This effect is reversed around 1\.5 Ry' \(p\. 3949\), 'above 1\.45 Ry' \(p\. 3952\)\: the dashed line lies 0\.92 or more above the solid one at 1\.20\-1\.24 Ry and below it \(by 0\.03 or more\) beyond 1\.54 Ry\: the lines cross between 1\.28 and 1\.55 Ry, where they touch\. Fig\. 13's dashed line \(Ritchie's, read at 0\.91\-1\.33 Ry with Fig\. 13's own calibrated axes, ticks within 3\.5 and 4\.3 pixels\) against ritchie\_1977's Table I, column E, converted to W / I^2 by that record's definition \(2 v a\_0^2 / I\_0 hbar omega\)\: drawn / converted = 0\.926 \(1\.012 Ry\), 0\.949 \(1\.140\) and 1\.010 \(1\.302\), within 10 % \(the reading and the drawing\)\: Fig\. 13 draws Ritchie's numbers, and ritchie\_1977's reading of its own quantity \(the factor 2I / I\_0\) is the one L'Huillier et al\. used\. Its first point, 2\.54 at 0\.912 Ry, lies at the dashed line's start \(overlay\)\. Fig\. 13's 2p peak \(about 3\.7\) stands above Ritchie's largest value near it converted \(2\.82 at 1\.572 Ry\)\: drawn through the resonance, not from the table's points\. COMPARISON \(reported by the script, not checked\)\: Fig\. 11's RPA line as sigma\_2 = \(p / I^2\)\(hbar omega\)^2 at 0\.92, 0\.95 and 1\.00 Ry \(12\.52\-13\.61 eV, region ii\)\: 1\.18, 1\.16 and 1\.19 x 10^\-51 cm^4 s; over mihelic\_2021 \(L = 0 \+ 2\), 0\.90, 0\.88, 0\.92 \(OEP 6's He model, TC\-943, the same\); over saenz\_1999 0\.80 and 0\.81 \(0\.95, 1\.00 Ry\); over nikolopoulos\_2001 0\.74, 0\.78, 0\.85; over bachau\_1990's Table I at 0\.5 au \(1 Ry, 1\.307 x 10^\-51\), 0\.91\. The one\-electron \(unscreened\) line is 1\.41 times the RPA at 1 Ry and therefore 1\.1 to 1\.3 times the correlated calculations\. DIGITISING UNCERTAINTY\: the y scales' residuals \(up to 5\.1 pixels, 0\.034\), the x scale's \(3\.7 pixels, 0\.004 Ry\) on the lines' slope \(up to 7 per Ry at 0\.67 Ry\: 0\.03\), the run centre \(1 pixel, 0\.007\)\: 0\.05 in the printed unit \(10^\-16 s^\-1 W^\-2 cm^4\), absolute\: 1\-2 % at the left, 20 % at the right end \(0\.27 at 1\.78 Ry\)\. The paper states no uncertainty, and disclaims accuracy \(above\); the LDA's threshold and the missing resonances are the calculation's main errors, not numerical ones\. NOT TAKEN\. Fig\. 9 \(p\. 3947\)\: He one\-photon photoionisation cross section \(Mb\) against the photon energy, the LDA one\-electron and LDRPA results with an HF\-RPA calculation and Marr and West's data reproduced \(a one\-photon LDA calculation; the library holds better one\-photon He data; its caption gives the references 59 and 60 the other way round from the text\)\. Fig\. 12 \(p\. 3948\)\: the 1s \-\> epsilon s and 1s \-\> epsilon d contributions, 0\.62\-1\.02 Ry, in arbitrary units \('p/I^2 \(arb\. u\.\)'\), so not a cross section as printed \(by eye their sums match Fig\. 11's lines at 1 Ry, but no scale is stated\)\. Fig\. 13's solid line \('our result extrapolated around the LDA threshold', Fig\. 11's RPA line joined by the interpolation\), Victor's solid circles and Ritchie's dashed line \(reproduced from other papers\: Ritchie's is ritchie\_1977's Table I, read here only for the check above; Victor's is not in the library\)\. Fig\. 13's caption cites Victor as 'Ref\. 35' \(Pindzola and Kelly\); the text's Ref\. 33 is Victor\: a misprint in the caption, no number affected\. The Xe screening factors \(pp\. 3949\-3950\)\: \\_4d ~ 0\.2 to \\_4d ~ \-0\.2, \\_5p ~ 0\.7 to \\_5p ~ 0\.5 \(omega in eV\), the effective intensity in the 5p region reduced 'by a factor of 2\-4'\: no quantity holds a screening factor\. The angular coefficients C = 0\.1778 and 0\.2222 \(p\. 3953\), the Appendix B ratios 1 \: 0\.6 \: 0\.06 of the Coulomb interactions\: no quantity\. FURTHER TWO\-PHOTON DATA CITED, not in the library\: G\. A\. Victor, Proc\. Phys\. Soc\. 91, 825 \(1967\) \(He, coupled Hartree\-Fock\)\. B\. Ritchie, Phys\. Rev\. A 16, 2080 \(1977\) is ritchie\_1977\. M\. S\. Pindzola and H\. P\. Kelly, Phys\. Rev\. A 11, 1543 \(1975\) \(Ar\) is pindzola\_1975; R\. Moccia, N\. K\. Rahman and A\. Rizzo, J\. Phys\. B 16, 2737 \(1983\) \(Ne, Ar\) is moccia\_1983\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- lhuillier\_1986/fig11\_rpa ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "fig11_rpa", "material": "He", "file": "He/lhuillier_1986__fig11_rpa_He.csv", "table": "fig_6afcab30a614", "digitised": "raster", "scale": 1e-16, "quantity": "multiphoton_ionization_cross_section", "unit": "s-1 cm4/W2", "abscissa_unit": "rydberg", "use": "check", "uncertainty": { "absolute": 0.05, "level": "not stated" }, "parameters": { "photons": 2, "polarization": "linear", "gauge": "length", "method": "lowest-order perturbation theory, local-density (LDA) one-electron basis, dipole matrix elements screened at omega in the random-phase approximation (LDRPA; screening at 2 omega neglected)", "definition": "p / I^2, p the two-photon ionisation rate (s^-1, Eq. 4.6) and I the intensity (W/cm2), as the axis prints it; equal to sigma_2 / (hbar omega)^2 for p = sigma_2 Phi^2" } } Fig\. 11 \(p\. 3948\), solid line \('random\-phase approximation', LDRPA\)\: p / I^2 of two\-photon ionisation of He, 10^\-16 s^\-1 W^\-2 cm^4, against the photon energy in Ry \(unshifted LDA thresholds\: 0\.57 Ry two\-photon, 1\.13 Ry one\-photon\), read from the page image \(the record's notes\)\: 0\.67\-1\.02 Ry \(4\.98 falling to 2\.51 at 1 Ry, an upturn to 2\.53 at the end\), 1\.20\-1\.28 Ry \(1\.12\-1\.08\), 1\.55\-1\.78 Ry \(0\.54\-0\.27\)\. Below 0\.90 Ry the curve is not ionisation in reality \(the authors' region \(i\)\); 1\.13\-1\.81 Ry averages over the real 1s \-\> np resonances \(region iii\)\. 0\.05 absolute \(in 10^\-16 units\)\: the digitising uncertainty \(the record's notes\); the paper states none\. lhuillier\_1986/fig11\_one\_electron ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "fig11_one_electron", "material": "He", "file": "He/lhuillier_1986__fig11_one_electron_He.csv", "table": "fig_6afcab30a614", "digitised": "raster", "scale": 1e-16, "quantity": "multiphoton_ionization_cross_section", "unit": "s-1 cm4/W2", "abscissa_unit": "rydberg", "use": "check", "uncertainty": { "absolute": 0.05, "level": "not stated" }, "parameters": { "photons": 2, "polarization": "linear", "gauge": "length", "method": "lowest-order perturbation theory, local-density (LDA) one-electron basis, unscreened dipole matrix elements (one-electron approximation)", "definition": "p / I^2, as fig11_rpa" } } Fig\. 11 \(p\. 3948\), dashed line \('one\-electron approximation'\)\: as fig11\_rpa without the screening, read from the page image \(the record's notes\)\: 0\.67\-1\.02 Ry \(5\.81 falling to 3\.54 at 1 Ry, 3\.58 at the end\), 1\.20\-1\.39 Ry \(2\.37\-1\.03\), 1\.55\-1\.78 Ry \(0\.50\-0\.19\)\. 1\.41 times the RPA line at 1 Ry \('a factor of 1\.4', p\. 3949\), below it beyond 1\.54 Ry\. Regions as fig11\_rpa\. 0\.05 absolute \(in 10^\-16 units\)\: the digitising uncertainty; 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 :doc:`review register ` for the checks and decisions.