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 · Catalogue · 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#
{
"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#
{
"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#
{
"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#
{
"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 review register for the checks and decisions.