khambatta_1988 ============== N\. M\. Khambatta, J\. A\. Oertel, R\. Silk, L\. J\. Radziemski and J\. M\. Mack, "Absolute excited state and ion densities from two\- and three\-photon processes in some 6p levels of atomic krypton", J\. Appl\. Phys\. 64, 4809\-4814 \(1988\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1063/1\.341226 `__ **Source kind:** measurement **Recorded technique:** \(2\+1\) excitation and ionisation of Kr 4p5 6p\[3/2\]2 by a grating\-tuned ArF excimer laser \(Lambda Physik EMG 150 EST\) at 193\.41 nm, line width 0\.40 \+\- 0\.05 nm \(about 58 % of the energy under a 0\.4 nm FWHM, the rest in the wings; measured with a monochromator and diode array\), 12\.2 \+\- 0\.5 ns, under 20 mJ varying by 100 % shot to shot, 3 Hz, focused by a 100 cm MgF2 lens into flowing krypton at 25\-1000 mTorr and 297 K; multimode, 'top hat' beam profile \(knife edge\)\. Absolute 6p\[3/2\]2 density from the 427\.4 nm fluorescence \(6p\[3/2\]2 \-\> 5s\[3/2\]2\) on a 0\.5 m spectrometer and 1P28 photomultiplier calibrated with a tungsten\-halogen lamp, with Bokor et al\.'s lifetime \(115 ns\) and self\-quenching \(6\.7 x 10^\-10 cm3/s\); absolute ion density from the charge on two parallel wire electrodes \(5\.4 cm, 1 cm apart, \+80 V\), the collection volume from a SIMION simulation \(Tables II, III\)\. sigma\_0^\(2\) and sigma\_pi adjusted so that the rate equations \(Eqs\. 5\-13, square pulse\) reproduce the measured densities\. **Materials in structured entries:** Kr **Dataset quantities:** excited\_state\_photoionization\_cross\_section, two\_photon\_excitation\_cross\_section **Contents:** 4 datasets; 0 formulas. Curation notes -------------- J\. Appl\. Phys\. 64\(10\), 4809\-4814 \(15 November 1988\) = PDF pages 2\-7 \(PDF page 1 is the AIP download cover; journal page = PDF page \+ 4807\)\. Identity checked against the first page of the article \(PDF p\. 2\: title, authors, New Mexico State University and Los Alamos; received 9 May 1988, accepted 9 August 1988\) on 2026\-10\-08\. A scan with a text layer; every number below was read on the rendered pages \(pp\. 4809, 4811, 4813\)\. THE DEFINITION \(p\. 4809\)\. 'The fundamental quantity, the two\-photon absorption cross section sigma\_0^\(2\) \(in cm4\)', Eq\. \(1\); the rate W = sigma\-hat^\(2\) \(I / h nu\)^2, 'sigma\-hat^\(2\) = sigma\_0^\(2\) g\(omega\) G^\(2\), where g\(omega\) is the line\-shape function \(s\), and G^\(2\) is the two\-photon statistical correlation factor, which is assumed 2 for our paper', and on resonance g = 2 sqrt\(ln 2 / pi\) / sqrt\(2 Delta omega\_L^2 \+ Delta omega\_D^2\) \(Eq\. 3, Gaussian laser\)\: a profile of unit area in the two\-photon angular frequency \(its FWHM is that of the two\-photon spectrum, sqrt\(2\) Delta omega\_L with the Doppler width\)\. So sigma\_0^\(2\) is the quantity two\_photon\_excitation\_cross\_section \(TC\-872\) with frequency\_variable = angular and the photon statistics corrected by an assumed G^\(2\) = 2\. The 'two\-photon coupling parameter' alpha = sigma\-hat^\(2\) / h nu \(cm4/W\) is bandwidth\-dependent\: not taken\. CHECKED \(p\. 4811\)\. Delta omega\_L = 2\.014 x 10^13 s\-1 is 2 pi c Delta lambda / lambda^2 for 0\.40 nm \(Table II\) at 193\.41 nm \(2\.0142 x 10^13\); the text's 'a linewidth of 0\.04 nm' gives 2\.014 x 10^12, a slip in the text \(no value of this record depends on it\)\. Delta omega\_D = 1\.313 x 10^10 s\-1 is the one\-photon Doppler width of Kr at 297 K and 193\.41 nm \(1\.3132 x 10^10\), half the two\-photon Doppler width the text names; negligible beside sqrt\(2\) Delta omega\_L\. g = 3\.298 x 10^\-14 s \(printed 3\.3\)\. alpha = sigma\_0^\(2\) g G^\(2\) / h nu\: 5\.59 x 10^\-32 for 8\.7 x 10^\-37 \(printed 5\.6\) and 3\.47 x 10^\-32 cm4/W for 5\.4 x 10^\-37 \(printed 3\.5\)\. Eq\. \(14\), 1\.3931 x 10^\-24 \|M\|^2 with Eq\. \(15\)'s single path \(mu\_1 = 1\.383 D, mu\_2 = 0\.382 D, \|E\_k \- h nu\| = 5\.8034 x 10^\-19 J, in Gaussian units\), gives 8\.68 x 10^\-37 cm4 \(printed 8\.7\)\. Eq\. \(4\) with Z = 1, U\_I = 1\.1805 eV, R = 13\.6058 eV at 6\.4104 eV gives 1\.6961 x 10^\-19 cm2 \(printed 1\.696\)\. WHAT IS TAKEN \(inline points, text only; no table holds them\)\. \(1\) The adjusted sigma\_0^\(2\) of 4p6 1S0 \-\> 4p5 6p\[3/2\]2, 5\.4 x 10^\-37 cm4 \(pp\. 4813 and the conclusions\)\: 'The computed and measured values of N2 agree well on average \(except for the two lowest pressures\) when a value of sigma\_0^\(2\) = 5\.4 x 10^\-37 cm4 \(corresponding to a two\-photon coupling parameter alpha = 3\.5 x 10^\-32 cm4/W\) is used' \(Table III's ratios N2\(theory\)/N2\(expt\) are 0\.59\-1\.9\)\. No uncertainty is given for it; the measured N2 carry '\+\-50%' \(mostly the A coefficient, \+\-50 %, and k\_q, \+\-10 %\), the computed ones \+\-50 % from the irradiance\. \(2\) The single\-path computed sigma\_0^\(2\), 8\.7 x 10^\-37 cm4 \(p\. 4811, intermediate 5s\[3/2\]1, f = 0\.219 from Bokor et al\.\)\: a check\. \(3\) The adjusted 6p\[3/2\]2 photoionisation cross section at 193\.41 nm, 4\.39 x 10^\-19 cm2 \(p\. 4813\)\: 'Disregarding experimental values above 250 mTorr due to the previously mentioned pressure effects, we find that on an average an adjusted sigma\_pi = 4\.39 x 10^\-19 cm2 would bring theoretical results into agreement with the experimental ones'; the measured ion densities carry '\+\-25%'; no uncertainty for sigma\_pi\. \(4\) The quantum\-defect sigma\_pi, 1\.696 x 10^\-19 cm2 \(Eq\. 4\)\: a check\. Krypton two\-photon ionisation \(OEP 6, Q2\)\: the paper has none; 193 nm ionisation of Kr is the three\-photon \(2\+1\) process\. QUOTED, CHECKED AGAINST THE ORIGINALS\. 'two other published values of alpha are 2\.34 x 10^\-31 cm4/W \(Ref\. 4\) and 2 x 10^\-32 cm4/W \(Ref\. 10\), for nearly comparable bandwidth ArF lasers' \(p\. 4813\)\: Ref\. 4 is bokor\_1980 \(Table I, 2\.34 for 6p\[3/2\]2\: matches; it is for a 25 cm\-1 laser, a quarter of this paper's 107 cm\-1, so not comparable without the line\-shape factor\), Ref\. 10 is geohegan\_1986 \(TC\-886; '2 x 10^\-32 cm4 W\-1', an effective cross section averaged over a 140 cm\-1 laser 2\.1 THz off the line\: matches as printed\)\. Bokor et al\.'s sigma\_pi '\(3\.2 \+\- 2\.0\) x 10^\-19 cm2' matches bokor\_1980\. Not taken here \(reproductions; bokor\_1980 holds its own value\)\. NOT TAKEN\. Table I \(computed N1, N2, Ni at 0\.01\-10 Torr and 10^6\-10^9 W/cm2\) and Table III \(computed and measured N2 and Ni against pressure and irradiance\)\: model densities and densities of one apparatus, no quantity\. The Rabi frequency and Stark shifts '\(computed, Ref\. 3\)', Omega ~ 10 I, D0 ~ 2 I, D2 ~ I \(I in W/cm2\)\: an internal report, not a quantity here\. Figs\. 1\-3 \(schemes and apparatus\)\. FINDING\: drag\_2021 \(TC\-891\)\. Its Table 1 reproduces this paper as 'Kr 6p\[3/2\]2 at 193\.5 nm, 5\.4 x 10^\-45 m4 \+\- 50 %, calibr\.'\: the number is right \(5\.4 x 10^\-37 cm4 = 5\.4 x 10^\-45 m4\), and so is drag\_2021's frequency\_variable = angular\. Its polarization and photon\_statistics 'not stated' can now be stated\: linear \(\>80 %\), and corrected with an assumed G^\(2\) = 2 \(not a measured G2\(0\)\)\. The \+\-50 % is not printed for sigma\_0^\(2\) here; it is the stated uncertainty of the measured N2\. The wavelength is the laser's setting, 193\.41 nm \(Table II\: '193\.41 \+\- 0\.4 nm'\)\. The value is about a hundred times smaller than shekhtman\_2020's calculated 6p\[3/2\]2 value \(drag\_2021's notes\) and 1\.6 times below this paper's own single\-path estimate\. TWO\-PHOTON DATA CITED, NOT IN THE LIBRARY\: N\. M\. Khambatta, J\. A\. Oertel, R\. Silk and L\. J\. Radziemski, New Mexico State University Physics Report No\. 88\-1000 \(1988\) \(the model and Rabi frequencies\); J\. A\. Paisner and R\. W\. Solarz, in Laser Spectroscopy and Its Applications \(Dekker, 1987\), ch\. 3 \(three\-photon ionisation of Kr\)\. Its Ref\. 8 \(Payne et al\., Chem\. Phys\. Lett\. 79, 142 \(1981\)\) is curated as payne\_1981\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- khambatta\_1988/sigma0\_6p32\_2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "sigma0_6p32_2", "material": "Kr", "table": "text", "scale": 1e-37, "quantity": "two_photon_excitation_cross_section", "unit": "cm4", "abscissa_unit": "nm", "use": "primary", "uncertainty": { "level": "not stated" }, "parameters": { "frequency_variable": "angular", "polarization": "linear (>80 %, manufacturer's specification, p. 4811)", "photon_statistics": "corrected, G^(2) = 2 assumed (p. 4809), not measured", "method": "absolute 427.4 nm fluorescence of 6p[3/2]2 (calibrated lamp), rate equations (Eqs. 5-13) with a square 12.2 ns pulse; sigma_0^(2) adjusted to the measured densities", "definition": "W = sigma_0^(2) g(omega) G^(2) Phi^2 (p. 4809), Phi the photon flux, g = 2 sqrt(ln 2 / pi) / sqrt(2 Delta omega_L^2 + Delta omega_D^2) on resonance (Eq. 3), unit area in the two-photon angular frequency", "linewidth_nm": 0.4, "linewidth_definition": "FWHM, 0.40 +- 0.05 nm (Table II); about 58 % of the energy under it (p. 4811)", "pulse_ns": 12.2 } } 1 inline points in the source record. pp\. 4813 \(Sec\. III D 1\) and 4814 \(conclusions\)\: the adjusted sigma\_0^\(2\) of 4p6 1S0 \-\> 4p5 6p\[3/2\]2 that makes the rate\-equation N2 agree on average with the measured ones \(Table III, 25\-1000 mTorr, 1\.6\-1\.9 x 10^8 W/cm2\); x is the laser's setting, 193\.41 nm\. No uncertainty is printed for it\: the measured N2 carry \+\-50 % \(A coefficient and k\_q from Bokor et al\.\), the computed ones \+\-50 % from the irradiance\. khambatta\_1988/sigma0\_6p32\_2\_single\_path ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "sigma0_6p32_2_single_path", "material": "Kr", "table": "text", "scale": 1e-37, "quantity": "two_photon_excitation_cross_section", "unit": "cm4", "abscissa_unit": "nm", "use": "check", "uncertainty": { "level": "not stated" }, "parameters": { "frequency_variable": "angular", "polarization": "linear", "photon_statistics": "not applicable (calculated; the definition excludes G^(2))", "method": "single-path approximation, intermediate 4p5 5s[3/2]1, dipole matrix elements from measured oscillator strengths and lifetimes (Bokor et al.)", "definition": "sigma_0^(2) = (2 pi)^3 alpha'^2 (h nu)^2 |M|^2 (Eq. 1), as the measured dataset" } } 1 inline points in the source record. p\. 4811\: sigma\_0^\(2\) computed with Eqs\. \(14\) and \(15\) in the single\-path approximation through 4p5 5s\[3/2\]1 \(mu\_1 = 1\.383 D from f = 0\.219, mu\_2 = 0\.382 D, \|E\_k \- h nu\| = 5\.8034e\-19 J\); reproduced to 8\.68e\-37 \(record notes\)\. An order\-of\-magnitude estimate, not a measurement\. khambatta\_1988/sigma\_pi\_6p32\_2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "sigma_pi_6p32_2", "material": "Kr", "table": "text", "scale": 1e-19, "quantity": "excited_state_photoionization_cross_section", "unit": "cm2", "abscissa_unit": "nm", "use": "primary", "uncertainty": { "level": "not stated" }, "parameters": { "initial_level": "4p5 6p[3/2]2, J = 2, two-photon excited from the ground state by the same light", "method": "absolute ion densities (charge on wire electrodes, SIMION collection volume), rate equations (Eqs. 5-13); sigma_pi adjusted to the data at and below 250 mTorr" } } 1 inline points in the source record. p\. 4813 \(Sec\. III D 2\) and the conclusions\: the photoionisation cross section of 4p5 6p\[3/2\]2 at the laser wavelength, adjusted so that the rate\-equation ion densities agree on average with the measured ones at and below 250 mTorr \(Table III\)\. No uncertainty is printed for it; the measured ion densities carry \+\-25 %\. It also rests on the adjusted sigma\_0^\(2\)\. khambatta\_1988/sigma\_pi\_6p32\_2\_quantum\_defect ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "sigma_pi_6p32_2_quantum_defect", "material": "Kr", "table": "text", "scale": 1e-19, "quantity": "excited_state_photoionization_cross_section", "unit": "cm2", "abscissa_unit": "nm", "use": "check", "uncertainty": { "level": "not stated" }, "parameters": { "initial_level": "4p5 6p[3/2]2, J = 2", "method": "quantum-defect approximation, sigma_pi = 8e-18 / [Z sqrt(U_I / R) (h nu / U_I)^3] cm2 (Eq. 4)" } } 1 inline points in the source record. p\. 4811\: Eq\. \(4\), the quantum\-defect \(hydrogenic\) approximation, with Z = 1, U\_I = 1\.1805 eV and R = 13\.6058 eV; reproduced \(record notes\)\. A model value, the starting point of the adjustment\. 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.