drag_2021 ========= C\. Drag, F\. Marmuse and C\. Blondel, "Measurement of the two\-photon excitation cross\-section of the 6p'\[3/2\]2 and 6p'\[1/2\]0 levels of Xe I at the wavelengths 224\.3 and 222\.6 nm", Plasma Sources Sci\. Technol\. 30, 075026 \(2021\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1088/1361\-6595/abfbeb `__ **Source kind:** measurement **Recorded technique:** Two\-photon absorption, not fluorescence\: the energy of each pulse before and after a 0\.51 m cell of xenon \(100 to 10^4 Pa, mostly 1000\-10^4 Pa; 296\.15 K assumed, \+\-2 C\), with Brewster\-angle windows, shot by shot, while an injection\-seeded single\-mode Ti\:sapphire laser \(under 30 MHz at 890\.3 and 897\.2 nm, Lottigier et al\. 2019\), frequency\-quadrupled in two BBO crystals to 222\.6 and 224\.3 nm, is scanned across the line; pulses of about 0\.5 mJ \(up to 1 mJ\), an asymmetric Gaussian time profile \(rise and fall 4\.27 and 8\.59 ns, tau about 6\.4 ns, Fig\. 7\), waists about 300 to 440 um, the beam profile and its low\-intensity periphery \(up to 20 % of the energy, subtracted\) measured daily\. Each transmission K\(omega\) is inverted with the paper's closed form for a spatially and temporally Gaussian beam in the quasi\-static, low\-excitation regime, K = Li\_3/2\(\-a\) / \(\-a\), a = 2 n sigma^\(2\)\(omega\) Phi\_0 z \(Eqs\. 29, 30\), into sigma^\(2\)\(omega\), which is integrated over the two\-photon angular frequency 2 omega \(Eq\. 8\) to the integrated cross section sigma\-bar^\(2\)\. A single\-mode laser, G2\(0\) = 1, 'to measure the two\-photon cross\-section in an unambiguous way' \(p\. 21\)\. The analysis of Sec\. 2 \(optical Bloch equations, rate equation, quasi\-static and low\-excitation models, Figs\. 2, 3\) supports integrating over the line rather than using the resonant absorption\. **Materials in structured entries:** Kr, Xe **Dataset quantities:** two\_photon\_excitation\_cross\_section **Contents:** 5 datasets; 0 formulas. Curation notes -------------- The library holds the accepted manuscript \(HAL hal\-03449890, deposited 25 November 2021\)\: IOP's 'Accepted Manuscript' cover \(PDF p\. 2\) and the manuscript 'AUTHOR SUBMITTED MANUSCRIPT \- PSST\-104268\.R2', pages 1\-33 = PDF pages 3\-35 \(page = PDF page \- 2\), with the published citation Plasma Sources Sci\. Technol\. 30\(7\), 075026 \(2021\)\. Identity checked against the HAL cover and the manuscript's first page \(title, authors\)\. The version of record is not in the library; its numbers are not checked\. The extracted text carries the manuscript's line numbers and a garbled abstract\: every number taken was read on the rendered pages \(pp\. 1, 5, 25, 26\)\. WHAT IS TAKEN\. The integrated two\-photon excitation cross sections, 'the generalized cross\-section sigma\-bar^\(2\) appears to be 1\.36 \(\+0\.46 \-0\.34\) and 1\.88 \(\+0\.75 \-0\.54\) x 10^\-43 m4 for the 6p'\[3/2\]2 and 6p'\[1/2\]0 levels, respectively' \(p\. 25, and the abstract, p\. 1\)\: inline points, the asymmetric errors as the parameters error\_plus and error\_minus \(the schema holds no asymmetric uncertainty; as uiterwaal\_1998\)\. The wavelengths 224\.3 and 222\.6 nm are vacuum wavelengths\: half the levels' energies the text gives, 8 916 235\.6 and 8 986 001\.5 m\-1 \(Kramida et al\. 2020, pp\. 3 and 5\), are 224\.310 and 222\.568 nm \(the script\)\. Table 1's absolute values of other authors \(tools/extract/drag\_2021\.py\), as reproduced datasets\. DEFINITION \(frequency\_variable\)\. sigma\-bar^\(2\) = integral of sigma^\(2\)\(omega\) 2 d omega \(Eq\. 8\), with T = sigma^\(2\)\(omega\) Phi^2 \(Eq\. 6\) and sigma^\(2\)\(omega\) = sigma\-bar^\(2\) g\(omega\), g normalised on the 2 omega scale \(Eq\. 10\)\: the profile is normalised in the two\-photon angular frequency, 'the commonly \.\.\. admitted convention' \(footnote, p\. 8, citing Bamford et al\. 1986 and kroll\_1990\)\. Table 2's numbers follow it \(the script\)\: the Doppler peak D\(0\) = c / \(2 omega\_0\) sqrt\(M / \(2 pi k T\)\) of Eq\. \(32\) at 300 K is 5\.13e\-11 s \(printed 5\.1e\-11\), sigma\-bar D\(0\) = 9\.18e\-54 m4 s \(9\.2e\-54\), sigma\-bar / \(pi beta\) = 3\.82e\-51 m4 s \(3\.9e\-51\), sqrt\(2 sigma\-bar / pi\) Phi\_0 = 5\.75e7 rad/s \(5\.9e7\)\. Polarisation\: not stated; linear is implied \(BBO harmonics through Brewster\-angle windows; the comparison of the two levels 'makes sense for linear polarization only', p\. 27\)\. UNCERTAINTY\. Table 3 \(p\. 26\)\: statistical dispersion \+\-7 % \(6p'\[3/2\]2\) and \+\-12 % \(6p'\[1/2\]0\), pulse energy \+\-13 % \(the energy meter, with a 1\.15 correction between two meters that disagreed by 1\.27\), waists \+\-6 %, duration, cell length, temperature and pressure \+\-1 % each; 'calculated as the product of all uncertainty factors', '1\.00 \(\+34 \-26\) or 1\.00 \(\+40 \-29\)'\. Checked\: the products of \(1 \+ u\) are 1\.334 and 1\.396; \+0\.46 and \+0\.75 are 34 % and 40 % of the values, \-0\.34 and \-0\.54 are 25\.0 % and 28\.7 %, that is \(1 \- 1/product\) to 0\.4 % \(the printed relative \-26 % is 1 point more than the \-0\.34 it goes with\)\. The interval has no stated confidence level\. The ratio sigma\-bar\(6p'\[1/2\]0\) / sigma\-bar\(6p'\[3/2\]2\) = 1\.38 \(\+0\.21 \-0\.18\) \(p\. 26\), with a smaller uncertainty because the pulse\-energy error is common \(1\.88/1\.36 = 1\.382, checked\); no quantity holds a ratio of two levels' cross sections\: kept here\. TABLE 1 \(p\. 5\), 'Most recent data available for integrated 2\-photon excitation cross\-sections', reproduced\: Kr 6p\[3/2\]2 at 193\.5 nm, 5\.4 x 10^\-45 m4 \+\- 50 %, Khambatta et al\. \(N\. M\. Khambatta, J\. A\. Oertel, R\. Silk, L\. J\. Radziemski and J\. M\. Mack, J\. Appl\. Phys\. 64, 4809 \(1988\); not in the library\); Kr 5p\[3/2\]2 at 214\.8 nm, 5\.2 x 10^\-43 m4 \+\- 40 %, dakka\_2018 \(5\.2 \+\- 2\.1 x 10^\-35 cm4\: the conversion and the 40 % are right\); Xe 6p\[1/2\]0, 6p\[3/2\]2, 6p\[5/2\]2 at 249\.6, 252\.5, 256\.0 nm, 5\.0, 1\.7, 2\.9 x 10^\-43 m4 \+\- 30, 30, 50 %, kroll\_1990's sigma\_tot \(10^\-35 cm4 = 10^\-43 m4\: right; these are Kroll and Bischel's values corrected with an assumed G2\(0\) = 1\.4, which Table 1 does not say; their uncertainty is the measurement's\)\. Checked by the script against the curated records\. The table's wavelengths agree with the vacuum two\-photon wavelengths of the levels to the printed 0\.1 nm\. Not taken\: the ratios to H, N and O \(Kr/H = 0\.62 and Kr/N = 0\.67 \+\- 50 %, Niemi et al\. 2001; Xe/O = 0\.36 and 0\.51 \+\- 50 %, Goehlich et al\. 1998; Xe/O = 1\.9 \+\- 20 %, Niemi et al\. 2005; Xe/H = 0\.024 \+\- 54 %, Elliott et al\. 2016\)\: no quantity holds a ratio to another species' two\-photon cross section\. The value deduced from Niemi et al\. \(2005\) and Bamford et al\.'s oxygen cross section, 1\.9\(2\) x 1\.87\(60\) x 10^\-43 = 3\.6 \(\+1\.7 \-1\.4\) x 10^\-43 m4 for 6p'\[3/2\]2 \(p\. 26\)\: derived from other papers, not taken; the measured value is 'more than a factor of 2' smaller\. NOT TAKEN, OTHER\. Table 4's two\-photon amplitudes per intermediate state \(atomic units, from the dipole matrix elements of Aymar and Coulombe 1978 and Salah and Hassouneh 2019\)\: partial amplitudes without signs, not a transition strength\. The pressure shift of the 6p'\[1/2\]0 line, \-2\.8\(2\) x 10^\-4 m\-1/Pa or \-2\.2\(2\) x 10^\-15 m3 s\-1, and its broadening, 6\.7\(1\.3\) x 10^\-15 m3 s\-1 \(half width; p\. 29\)\: no quantity for an atomic two\-photon line's shift or width\. The quenching coefficients k\_Q \(Bruce et al\. 1990; Whitehead et al\. 1995\) and the photoionisation estimate 'about 1\.5 x 10^\-24 m2' from Chang and Kim \(1982\) \(p\. 20\)\: other papers' values\. Figs\. 5 and 8 \(profiles and the individual measurements; the latter's error bars are 'only the numerical uncertainty' of the integration\)\. Fig\. 5's caption prints the peak cross section in 'm4 s\-1' and the integrated one in 'm2' \(for m4 s and m4\)\: slips in a caption, no value taken\. TWO\-PHOTON DATA CITED, NOT IN THE LIBRARY\: Khambatta et al\. \(1988\), above; K\. Niemi, V\. Schulz\-von der Gathen and H\. F\. Dobele, J\. Phys\. D 34, 2330 \(2001\) and Plasma Sources Sci\. Technol\. 14, 375 \(2005\); A\. Goehlich, T\. Kawetzki and H\. F\. Dobele, J\. Chem\. Phys\. 108, 9362 \(1998\); D\. Elliott, E\. Scime and Z\. Short, Rev\. Sci\. Instrum\. 87, 11E504 \(2016\); V\. Alekseev and D\. W\. Setser, J\. Phys\. Chem\. 100, 5766 \(1996\) \(Xe cross\-section ratios\); D\. J\. Bamford, M\. J\. Dyer and W\. K\. Bischel, Phys\. Rev\. A 36, 3497 \(1987\) \(oxygen, 226 nm\); R\. P\. Saxon and J\. Eichler, Phys\. Rev\. A 34, 199 \(1986\) \(oxygen, theory\)\. **Recorded bibliographic identity status:** VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- drag\_2021/sigma\_6p1\_32\_2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "sigma_6p1_32_2", "material": "Xe", "table": "text", "scale": 1e-43, "quantity": "two_photon_excitation_cross_section", "unit": "m4", "abscissa_unit": "nm", "use": "primary", "parameters": { "frequency_variable": "angular", "polarization": "linear (not stated; implied by the Brewster-angle windows)", "photon_statistics": "corrected: a single-mode laser, G2(0) = 1 (p. 21)", "method": "two-photon absorption in a 0.51 m cell, transmission inverted with Eq. (30) and integrated over the line", "definition": "sigma-bar^(2) = integral of sigma^(2)(omega) 2 d omega (Eq. 8), T = sigma^(2)(omega) Phi^2 (Eq. 6), Phi the photon flux", "error_plus": 0.46, "error_minus": 0.34, "error_definition": "as printed, +0.46 -0.34 in the printed scale: the value times (product - 1) and (1 - 1/product), the product of Table 3's factors (1 + u); no stated confidence level" } } 1 inline points in the source record. p\. 25 \(Sec\. 4\.1\) and the abstract \(p\. 1\)\: sigma\-bar^\(2\) of the 5p6 1S0 \-\> 5p5 6p'\[3/2\]2 transition, 1\.36 \(\+0\.46 \-0\.34\) x 10^\-43 m4, two photons at the vacuum wavelength 224\.3 nm\. The errors are Table 3's budget multiplied as factors \(record notes\), no stated confidence level\. drag\_2021/sigma\_6p1\_12\_0 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "sigma_6p1_12_0", "material": "Xe", "table": "text", "scale": 1e-43, "quantity": "two_photon_excitation_cross_section", "unit": "m4", "abscissa_unit": "nm", "use": "primary", "parameters": { "frequency_variable": "angular", "polarization": "linear (not stated; implied by the Brewster-angle windows)", "photon_statistics": "corrected: a single-mode laser, G2(0) = 1 (p. 21)", "method": "two-photon absorption in a 0.51 m cell, transmission inverted with Eq. (30) and integrated over the line", "definition": "sigma-bar^(2) = integral of sigma^(2)(omega) 2 d omega (Eq. 8), T = sigma^(2)(omega) Phi^2 (Eq. 6), Phi the photon flux", "error_plus": 0.75, "error_minus": 0.54, "error_definition": "as printed, +0.75 -0.54 in the printed scale: the value times (product - 1) and (1 - 1/product), the product of Table 3's factors (1 + u); no stated confidence level" } } 1 inline points in the source record. p\. 25 \(Sec\. 4\.1\) and the abstract \(p\. 1\)\: sigma\-bar^\(2\) of the 5p6 1S0 \-\> 5p5 6p'\[1/2\]0 transition \(J = 0, no hyperfine structure\), 1\.88 \(\+0\.75 \-0\.54\) x 10^\-43 m4, two photons at the vacuum wavelength 222\.6 nm\. The errors are Table 3's budget multiplied as factors \(record notes\), no stated confidence level\. drag\_2021/khambatta\_1988\_Kr ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "khambatta_1988_Kr", "material": "Kr", "file": "Kr/drag_2021__khambatta_1988_Kr.csv", "table": "tbl_e87cefb4180f", "quantity": "two_photon_excitation_cross_section", "unit": "m4", "scale": 1e-45, "abscissa_unit": "nm", "use": "reproduced", "reproduced_from": [ "N. M. Khambatta, J. A. Oertel, R. Silk, L. J. Radziemski and J. M. Mack, J. Appl. Phys. 64, 4809 (1988)" ], "uncertainty": { "relative": 0.5, "level": "not stated" }, "parameters": { "frequency_variable": "angular", "polarization": "not stated", "photon_statistics": "not stated", "method": "calibrated fluorescence (Table 1: 'calibr.')" } } Table 1 \(p\. 5\)\: Kr 6p\[3/2\]2 at 193\.5 nm, 5\.4 x 10^\-45 m4 \+\- 50 %, 'calibr\.' \(calibrated fluorescence\)\. The original is not in the library\: its definition, polarisation and photon statistics are not checked; Drag et al\. present it as an integrated cross section in their convention \(their Eq\. 9 'is formula \(1\) of Khambatta et al\. \(1988\)'\)\. It is about a hundred times smaller than shekhtman\_2020's calculated 6p\[3/2\]2 value \(5\.08e\-35 cm4 = 5\.1e\-43 m4, basis set 3 with oscillator strengths\)\. drag\_2021/dakka\_2018\_Kr ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "dakka_2018_Kr", "material": "Kr", "file": "Kr/drag_2021__dakka_2018_Kr.csv", "table": "tbl_e87cefb4180f", "quantity": "two_photon_excitation_cross_section", "unit": "m4", "scale": 1e-43, "abscissa_unit": "nm", "use": "reproduced", "reproduced_from": [ "dakka_2018" ], "uncertainty": { "relative": 0.4, "level": "not stated" }, "parameters": { "frequency_variable": "angular", "polarization": "not stated", "photon_statistics": "as dakka_2018: not measured", "method": "as dakka_2018 (Table 1: 'calibr.')" } } Table 1 \(p\. 5\)\: Kr 5p\[3/2\]2 at 214\.8 nm, 5\.2 x 10^\-43 m4 \+\- 40 %\: dakka\_2018's 5\.2 \+\- 2\.1 x 10^\-35 cm4, correctly converted \(checked by the script\)\. drag\_2021/kroll\_1990\_Xe ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "kroll_1990_Xe", "material": "Xe", "file": "Xe/drag_2021__kroll_1990_Xe.csv", "table": "tbl_e87cefb4180f", "quantity": "two_photon_excitation_cross_section", "unit": "m4", "scale": 1e-43, "abscissa_unit": "nm", "use": "reproduced", "reproduced_from": [ "kroll_1990" ], "uncertainty": { "relative": 0.3, "relative_rows": { "6p[5/2]2": 0.5 }, "level": "not stated" }, "parameters": { "frequency_variable": "angular", "polarization": "linear", "photon_statistics": "as kroll_1990's sigma_tot: corrected, G2(0) = 1.4 assumed", "method": "as kroll_1990 (Table 1: 'calibr.')" } } Table 1 \(p\. 5\)\: Xe 6p\[1/2\]0 \(2p5\), 6p\[3/2\]2 \(2p6\), 6p\[5/2\]2 \(2p9\) at 249\.6, 252\.5, 256\.0 nm\: kroll\_1990's G2\-corrected sigma\_tot \(5\.0, 1\.7, 2\.9 x 10^\-35 cm4\), correctly converted, with the measurement's 30, 30, 50 % \(checked by the script\)\. Table 1 does not say that these values assume G2\(0\) = 1\.4\. 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.