lhuillier_1987b =============== A\. L'Huillier and G\. Wendin, "Two\-photon one\-electron ionisation cross section of the 5p shell of xenon including screening effects", J\. Phys\. B\: At\. Mol\. Phys\. 20, L37\-L44 \(1987\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1088/0022\-3700/20/2/002 `__ **Source kind:** theory **Recorded technique:** Diagrammatic many\-body perturbation theory of two\-photon one\-electron ionisation of the Xe 5p shell, lowest \(second\) order in the field, with every electron\-photon interaction replaced by the RPA\-screened dipole operator r\(omega\) = r epsilon^\-1\(r, omega\) \(Eqs\. 2\-3, Fig\. 1\(a\)\)\: 'non\-linear screening', which brings in double excitations of the 5p shell; for comparison only the first interaction screened \(Fig\. 1\(c\)\), and the unscreened independent\-electron amplitude \(Fig\. 1\(b\)\)\. Two bases\: local density \(LDA, LDRPA; 5p ionisation limit 0\.62 Ry, no discrete states\) and Hartree\-Fock average \(HF, RPAE; 5p^\-1 ns, n = 6\-8, and nd, n = 5\-6, resonances included; 'our HF zeroth\-order potential is more attractive than the configuration average HF potential; in particular, the discrete levels are more closely bound', p\. L41\)\. Free\-free matrix elements above the 5p limit \(ATI\)\. Nonrelativistic; linear polarisation\. **Materials in structured entries:** Xe **Dataset quantities:** multiphoton\_ionization\_cross\_section **Contents:** 6 datasets; 0 formulas. Curation notes -------------- Journal pp\. L37\-L44 = PDF pages 2\-9 \(PDF page 1 is the publisher's cover sheet\); a scan, each page one 1\-bit image of 2076 x 2945 pixels \(300 dpi\), with a text layer\. Identity checked on PDF page 2 \(J\. Phys\. B\: At\. Mol\. Phys\. 20 \(1987\) L37\-L44, Letter to the Editor; Anne L'Huillier and Goran Wendin, Chalmers and CEN\-Saclay; received 10 October 1986\) on 2026\-10\-09\. THE DEFINITION \(p\. L38, Eq\. 1\)\: 'The two\-photon one\-electron ionisation generalised cross section sigma\_2 \(cm4 s\) can be written as sigma\_2 = 2 pi \(alpha c / a0\) \(omega / F0\)^2 sum\_l \|t\_eps\_i\(omega\)\|^2 where alpha is the fine\-structure constant, c the speed of light, a0 the Bohr radius, omega the photon energy and F0 is equal to 3\.22 x 10^34 \(photons/cm2 s\)'; the rate is sigma\_2 F^2, F the photon flux\. Length form \(the dipole operator r\)\. Linear polarisation \(every figure caption\)\. wendin\_1987's Eq\. \(14\) writes the same cross section with \(1 / F F0\)^2 and the intensity carried in t \(its Eqs\. 9a, 13\)\. THE ENERGY AXES\: the PHOTON energy in Ry, as printed in every figure \('Photon energy \(Ryd\)'\)\. The thresholds and resonances are the calculation's own\: the LDA 5p limit 0\.62 Ry \('lower than the experimental threshold \(~0\.90 Ryd\)', p\. L40\), so the LDA two\-photon threshold is 0\.31 Ry; the HF two\-photon and one\-photon thresholds 0\.46 and 0\.92 Ry \(Fig\. 4's caption\); resonance positions nonrelativistic, without the spin\-orbit splitting of the core, and 'the RPAE screening leads to an important shift of the positions of the 5p^\-1 nd resonances towards higher energies' \(p\. L41\)\. No shift or scaling was applied by the authors, and none here\. EXTRACTED \(tools/extract/lhuillier\_1987b\.py\), by data rule 8 \(TC\-699\)\: the cross sections are in figures only, read from the page images at their native resolution, the method of lhuillier\_1987 \(TC\-883\) scaled to 300 dpi\. Every tick mark is found where the script writes it \(within 2 pixels\) and lies on the fitted scale within 1\.5 pixels; Fig\. 2 is calibrated from its top and right lines \(no curve meets them\), Figs\. 3 and 4 from the bottom and left\. Fig\. 3's frame lines lie at the text's 0\.46 and 0\.86 Ry \(p\. L41\) within 0\.002 Ry\. Lettering, the hatched threshold marks, McCown et al\.'s crosses and Fig\. 4's six squares are erased; pieces of ink are sorted by size into the solid line \(at least 75 pixels; 40 in Fig\. 4, where the squares cut it\), dots \(at most 7\) and dashes; a value is read only where its line is one run at most 7 pixels tall, not touching anything erased, and agrees with a neighbour\. Steep flanks and peaks are not read\. One pixel is 0\.00097 Ry and 0\.0054e\-49 cm4 s in Fig\. 2, 0\.00035 Ry and 1\.9 % in Fig\. 3, 0\.00093 Ry and 1\.8 % in Fig\. 4\. The overlays of every value on the page images were inspected \(2026\-10\-09\)\: all lie on their lines\. CHECKS \(the script raises if any fails\)\. \(1\) Fig\. 4's squares \('theoretical \(MQDT\) results by Gangopadhyay et al \(1986\)'\) are gangopadhyay\_1986's Table I, the sum of its two cores, at half the total energy\: 0\.978\-1\.069 of the sums, drawn 0\.001\-0\.0055 Ry to the right of Table I's energies \(hand\-placed; six squares, Table I's first six rows\)\. \(2\) Fig\. 4's cross lies at 0\.4719 Ry, 193 nm's 0\.4722 \(the text\: 'at 0\.47 Ryd \(193 nm\)', p\. L43\), 1\.00 times mccown\_1982's alpha hbar omega \(TC\-884\)\. \(3\) Fig\. 4's LDRPA \(log axis\) is Fig\. 2's LDRPA \(linear\) redrawn\: median ratio 1\.016 \(0\.992\-1\.053\) where Fig\. 2's value exceeds 0\.3\. \(4\) Fig\. 3's solid and dashed lines are lhuillier\_1987's Fig\. 6 HF and RPAE\: median ratios 0\.991 \(0\.964\-1\.012\) and 0\.993 \(0\.931\-1\.037\) at the shared grid points; the overlay of lhuillier\_1987's values on this Fig\. 3 was inspected\. Reported\: Fig\. 4's RPAE and LDRPA over lhuillier\_1987's Figs\. 6 and 7\: medians 1\.006 \(0\.980\-1\.037\) and 1\.001 \(0\.918\-1\.049\)\. COMPANION \(lhuillier\_1987, TC\-883, Phys\. Rev\. A 36, 4747, received 9 February 1987\: the full account, published after this letter\)\. The same calculations\: this letter's HF and RPAE \(Fig\. 3\) and RPAE and LDRPA \(Fig\. 4\) are that paper's Figs\. 6 and 7 within the reading \(checks 3 and 4\)\. NEW here\: \(a\) the LDA basis, Fig\. 2, from the LDA two\-photon threshold 0\.31 Ry to 1\.40 Ry on a linear axis\: the LDA independent\-electron cross section \(with the 5p \-\> eps d peak at 0\.68 Ry, p\. L40\) and the LDRPA with only the first interaction screened, neither in the PRA; \(b\) the HF\-basis RPAE with only the first interaction screened \(Fig\. 3, dotted\); \(c\) Fig\. 4's RPAE and LDRPA from 0\.31 to 1\.40 Ry, including the LDRPA below the HF two\-photon threshold \(0\.31\-0\.46 Ry\) and between the PRA's two figures \(0\.86\-0\.98 Ry\)\. The PRA's Fig\. 10 'RPAE linear screening' \(dash\-dot; not taken by lhuillier\_1987\) has, by eye, the shape of this letter's Fig\. 3 dotted line \(not compared numerically\); its Figs\. 9\-12 \(the 5s shell, TDAE, screening at 2 omega\) are not in the letter\. FINDINGS\. \(1\) Fig\. 3 draws McCown et al\.'s cross at 0\.4846 Ry, 0\.0124 Ry \(35 pixels\) above 193 nm, on the dotted line at 1\.07 times McCown's value; Fig\. 4 \(and lhuillier\_1987's Fig\. 6\) draw it at 193 nm\. \(2\) Fig\. 4's hatched marks stand at 0\.457 and 0\.907 Ry; the caption gives the HF thresholds as 0\.46 and 0\.92 Ry\: the one\-photon mark is drawn 0\.013 Ry low\. Fig\. 2's hatched mark stands at 0\.621 Ry, the text's LDA limit 0\.62\. \(3\) Gangopadhyay et al\.'s values, here and in every later drawing \(gangopadhyay\_1986's notes\), are the open\-continuum Table I above the 2P1/2 limit, not the region between the thresholds that 193 nm reaches\. THE TEXT \(pp\. L42\-L43\)\: Gangopadhyay et al\.'s MQDT 'leads to good agreement with the present non\-linear LDRPA and RPAE results in the 0\.5\-0\.6 Ryd range'; McCown et al\.'s point 'may be somewhat fortuitous because this point lies in the region of autoionising resonances'; McGuire's result 'is slightly below our independent\-electron result'\. NOT TAKEN\: Fig\. 3's solid \(HF\) and dashed \(RPAE\) lines, the calculations lhuillier\_1987 holds from its Fig\. 6 \(checked above\); the squares \(gangopadhyay\_1986 holds Table I\) and the crosses \(mccown\_1982\); Fig\. 1 \(diagrams\)\. Further two\-photon calculations the paper cites, not in the library\: M\. S\. Pindzola and H\. P\. Kelly, Phys\. Rev\. A 11, 1543 \(1975\); B\. Ritchie, Phys\. Rev\. A 16, 2080 \(1977\); R\. Moccia, N\. K\. Rahman and A\. Rizzo, J\. Phys\. B 16, 2737 \(1983\); A\. F\. Starace, Phys\. Scr\. \(1986, Proc\. 8th VUV conference\); G\. A\. Victor, Proc\. Phys\. Soc\. 91, 825 \(1967\)\. **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\_1987b/fig2\_lda ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "fig2_lda", "material": "Xe", "file": "Xe/lhuillier_1987b__fig2_lda_Xe.csv", "table": "fig_171e5219ba1c", "digitised": "raster", "quantity": "multiphoton_ionization_cross_section", "unit": "cm4 s", "scale": 1e-49, "abscissa_unit": "rydberg", "use": "check", "uncertainty": { "absolute": 0.015, "level": "not stated" }, "parameters": { "photons": 2, "polarization": "linear", "channel": "5p shell", "method": "independent-electron approximation on a local-density (LDA) basis, lowest-order perturbation theory, nonrelativistic; LDA 5p ionisation limit 0.62 Ry, no discrete states", "definition": "sigma_2 = 2 pi (alpha c / a0) (omega / F0)^2 sum_l |t_eps_i(omega)|^2 (Eq. 1), omega the photon energy, F0 = 3.22e34 photons/cm2 s; the rate is sigma_2 F^2, F the photon flux", "gauge": "length (dipole operator r, Eq. 2)" } } Fig\. 2 \(p\. L40\), solid line\: the independent\-electron \(zeroth\-order, Fig\. 1\(b\)\) two\-photon cross section of the Xe 5p shell on the LDA basis, 1e\-49 cm4 s on a linear axis, against the photon energy, read every 0\.002 Ry from 0\.352 to 1\.196 Ry where readable \(the steep rise and fall of the 0\.68 Ry peak and the tangle below 0\.35 Ry not read\)\. 0\.015 \(in 1e\-49 cm4 s\)\: one pixel is 0\.0054, the line 3\-4 pixels wide, the ticks within 1\.5 pixels\. lhuillier\_1987b/fig2\_ldrpa ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "fig2_ldrpa", "material": "Xe", "file": "Xe/lhuillier_1987b__fig2_ldrpa_Xe.csv", "table": "fig_171e5219ba1c", "digitised": "raster", "quantity": "multiphoton_ionization_cross_section", "unit": "cm4 s", "scale": 1e-49, "abscissa_unit": "rydberg", "use": "check", "uncertainty": { "absolute": 0.015, "level": "not stated" }, "parameters": { "photons": 2, "polarization": "linear", "channel": "5p shell", "method": "LDRPA (RPA on an LDA basis, continuum states only) with every electron-photon interaction screened (non-linear screening), nonrelativistic", "definition": "sigma_2 = 2 pi (alpha c / a0) (omega / F0)^2 sum_l |t_eps_i(omega)|^2 (Eq. 1), omega the photon energy, F0 = 3.22e34 photons/cm2 s; the rate is sigma_2 F^2, F the photon flux", "gauge": "length (screened dipole operator r(omega), Eqs. 2-3)" } } Fig\. 2 \(p\. L40\), dashed line\: the LDRPA two\-photon cross section of the Xe 5p shell with every electron\-photon interaction screened \(Fig\. 1\(a\)\), 1e\-49 cm4 s on a linear axis, against the photon energy, read every 0\.002 Ry from 0\.346 to 1\.380 Ry where readable \(dashes merged into long pieces near 1\.2\-1\.33 Ry and values within a few pixels of the bottom line not read\)\. The same calculation as Fig\. 4's dashed line \(check 3 of the record's notes\)\. 0\.015 \(in 1e\-49 cm4 s\), as for the solid line\. lhuillier\_1987b/fig2\_ldrpa\_first ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "fig2_ldrpa_first", "material": "Xe", "file": "Xe/lhuillier_1987b__fig2_ldrpa_first_Xe.csv", "table": "fig_171e5219ba1c", "digitised": "raster", "quantity": "multiphoton_ionization_cross_section", "unit": "cm4 s", "scale": 1e-49, "abscissa_unit": "rydberg", "use": "check", "uncertainty": { "absolute": 0.015, "level": "not stated" }, "parameters": { "photons": 2, "polarization": "linear", "channel": "5p shell", "method": "LDRPA with only the first electron-photon interaction screened (linear screening), nonrelativistic", "definition": "sigma_2 = 2 pi (alpha c / a0) (omega / F0)^2 sum_l |t_eps_i(omega)|^2 (Eq. 1), omega the photon energy, F0 = 3.22e34 photons/cm2 s; the rate is sigma_2 F^2, F the photon flux", "gauge": "length (first dipole operator screened, Fig. 1(c))" } } Fig\. 2 \(p\. L40\), dotted line\: the LDRPA two\-photon cross section of the Xe 5p shell with only the first electron\-photon interaction screened \(Fig\. 1\(c\)\), 'an approximation which \.\.\. has been used in all other calculations of multiphoton ionisation of the rare gases' \(p\. L40\), 1e\-49 cm4 s on a linear axis, against the photon energy, read every 0\.002 Ry from 0\.346 to 1\.392 Ry where readable\. Near 0\.6\-0\.75 Ry the line runs within a few pixels of zero\. 0\.015 \(in 1e\-49 cm4 s\), as for the solid line\. lhuillier\_1987b/fig3\_rpae\_first ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "fig3_rpae_first", "material": "Xe", "file": "Xe/lhuillier_1987b__fig3_rpae_first_Xe.csv", "table": "fig_fea006c5adce", "digitised": "raster", "quantity": "multiphoton_ionization_cross_section", "unit": "cm4 s", "scale": 1e-49, "abscissa_unit": "rydberg", "use": "check", "uncertainty": { "relative": 0.06, "level": "not stated" }, "parameters": { "photons": 2, "polarization": "linear", "channel": "5p shell", "method": "RPAE on a Hartree-Fock basis with only the first electron-photon interaction screened (linear screening), nonrelativistic; 5p^-1 ns (n = 6-8) and nd (n = 5-6) resonances", "definition": "sigma_2 = 2 pi (alpha c / a0) (omega / F0)^2 sum_l |t_eps_i(omega)|^2 (Eq. 1), omega the photon energy, F0 = 3.22e34 photons/cm2 s; the rate is sigma_2 F^2, F the photon flux", "gauge": "length (first dipole operator screened, Fig. 1(c))" } } Fig\. 3 \(p\. L41\), dotted line\: the RPAE two\-photon cross section of the Xe 5p shell \(HF basis\) with only the first electron\-photon interaction screened, 1e\-49 cm4 s on a logarithmic axis, against the photon energy, read every 0\.002 Ry from 0\.464 to 0\.782 Ry where readable \(the steep 6s rise near 0\.665\-0\.68 Ry not read; above 0\.79 Ry the resonances of the three lines overlap\)\. 0\.42 near threshold, 0\.09 at 0\.664 Ry before the 6s rise, 0\.08 at 0\.776 Ry\. 6 %\: 1\.9 % per pixel, the dots 5\-7 pixels across\. lhuillier\_1987b/fig4\_rpae ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "fig4_rpae", "material": "Xe", "file": "Xe/lhuillier_1987b__fig4_rpae_Xe.csv", "table": "fig_1a8946c9a5c6", "digitised": "raster", "quantity": "multiphoton_ionization_cross_section", "unit": "cm4 s", "scale": 1e-49, "abscissa_unit": "rydberg", "use": "check", "uncertainty": { "relative": 0.05, "level": "not stated" }, "parameters": { "photons": 2, "polarization": "linear", "channel": "5p shell", "method": "RPAE on a Hartree-Fock basis with every electron-photon interaction screened (non-linear screening), nonrelativistic; 5p^-1 ns (n = 6-8) and nd (n = 5-6) resonances", "definition": "sigma_2 = 2 pi (alpha c / a0) (omega / F0)^2 sum_l |t_eps_i(omega)|^2 (Eq. 1), omega the photon energy, F0 = 3.22e34 photons/cm2 s; the rate is sigma_2 F^2, F the photon flux", "gauge": "length (screened dipole operator r(omega), Eqs. 2-3)" } } Fig\. 4 \(p\. L42\), solid line\: the RPAE two\-photon cross section of the Xe 5p shell with every interaction screened, 1e\-49 cm4 s on a logarithmic axis, against the photon energy, read every 0\.002 Ry from 0\.462 to 0\.790 Ry and from 0\.976 to 1\.374 Ry where readable \(under Gangopadhyay et al\.'s squares, the resonance flanks and the overlapping 5d\-8s resonances not read\)\. The calculation of lhuillier\_1987's Figs\. 6 and 7 \(dashed lines there\), redrawn\: median ratio 1\.006 \(the record's notes\)\. 5 %\: 1\.8 % per pixel and the line's width\. lhuillier\_1987b/fig4\_ldrpa ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "fig4_ldrpa", "material": "Xe", "file": "Xe/lhuillier_1987b__fig4_ldrpa_Xe.csv", "table": "fig_1a8946c9a5c6", "digitised": "raster", "quantity": "multiphoton_ionization_cross_section", "unit": "cm4 s", "scale": 1e-49, "abscissa_unit": "rydberg", "use": "check", "uncertainty": { "relative": 0.06, "level": "not stated" }, "parameters": { "photons": 2, "polarization": "linear", "channel": "5p shell", "method": "LDRPA (RPA on an LDA basis, continuum states only) with every electron-photon interaction screened (non-linear screening), nonrelativistic", "definition": "sigma_2 = 2 pi (alpha c / a0) (omega / F0)^2 sum_l |t_eps_i(omega)|^2 (Eq. 1), omega the photon energy, F0 = 3.22e34 photons/cm2 s; the rate is sigma_2 F^2, F the photon flux", "gauge": "length (screened dipole operator r(omega), Eqs. 2-3)" } } Fig\. 4 \(p\. L42\), dashed line\: the LDRPA two\-photon cross section of the Xe 5p shell with every interaction screened, 1e\-49 cm4 s on a logarithmic axis, against the photon energy, read every 0\.002 Ry from 0\.344 to 1\.380 Ry where readable\: 0\.06\-0\.31 below 0\.62 Ry \(a minimum of 0\.062 at 0\.604 Ry\), 0\.81\-1\.0 from 0\.73 to 0\.95 Ry, 0\.32\-0\.69 above 1\.0 Ry\. Fig\. 2's dashed line on a log axis \(check 3\) and lhuillier\_1987's dotted line \(median ratio 1\.001\)\. 6 %\: 1\.8 % per pixel and the dashes' width\. 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.