gangopadhyay_1986#
P. Gangopadhyay, X. Tang, P. Lambropoulos and R. Shakeshaft, “Theory of autoionization of Xe under two- and three-photon excitation”, Phys. Rev. A 34, 2998-3002 (1986)
Source record · Catalogue · Review register
Source kind: theory
Recorded technique: Lowest-order perturbation theory of two- and three-photon ionisation of Xe (Eqs. 1-3), the final and intermediate states from multichannel quantum-defect theory in the Lu-Fano form (Eqs. 4-11): jj-coupled channels of the Xe+ 2P3/2 and 2P1/2 cores, eigenchannel quantum defects mu_alpha and frame transformation U_i_alpha ‘obtained from experimental information through the Lu-Fano plots or extrapolations thereof’ (p. 2999); the sum over intermediate states truncated to 27 states for two photons and 59 for three (p. 2999). Dipole operator r . epsilon (length form). Two expressions: in the open continuum above 13.45 eV (Eq. 8, partial cross sections by the core’s J) and in the autoionising region ‘12.13 to 13.45 eV’ (Eq. 11).
Materials in structured entries: Xe
Dataset quantities: multiphoton_ionization_cross_section
Contents: 5 datasets; 0 formulas.
Curation notes#
Journal pp. 2998-3002 = PDF pages 1-5 (a scan: each page one 1-bit image, 5060 x 6898 pixels, about 610 dpi, with a text layer). Identity checked on the first page (Physical Review A, volume 34, number 4, October 1986; P. Gangopadhyay, X. Tang, P. Lambropoulos and Robin Shakeshaft, University of Southern California; received 27 December 1985) on 2026-10-09.
THE DEFINITION (p. 2998, Eq. 1): ‘W^(N) = sigma^(N) F^N, where F is the photon flux density in number of photons/cm2 sec, W^(N) is the rate of the N-photon process, and sigma^(N) is the generalized cross section in cm^2N sec^N-1’; Eq. (2) gives it from the N-th order amplitude. The convention of uiterwaal_1998 and mckenna_2004. POLARISATION: not stated in words; Eq. (3) has one polarisation vector epsilon for all photons and Fig. 3’s caption, ‘The arrow indicates the direction of the photon polarization’, shows a direction: linear (lagutin_2017, TC-880, also reads it as linear). ACCURACY (p. 2999): ‘the error due to truncation alone is not expected to be more than a factor of 2’; no other uncertainty is stated.
THE ENERGY AXES. Every energy the paper prints or draws is the TOTAL energy above the ground state (the text’s regions, ‘12.13 to 13.45 eV’ and ‘above 13.45 eV’, p. 2999; Table I and II: ‘Total energy (eV)’; Fig. 3’s caption: ‘The energies E represent the total energy above the ground state’). Fig. 1’s axis is unlabelled, 12.2 to 13.4 (ticks every 0.2), and lies between those thresholds: the same total energy. The thresholds and the resonance positions come from the MQDT parameters fitted to experimental levels: experimental, J-resolved (jj channels; Fig. 1 labels its peaks by J), not shifted or scaled by the authors. DECISION (the register entry): the data files’ x is the PHOTON energy in eV, the printed total energy divided by the number of photons (2 or 3), exactly (Decimal) for the tables and to 1e-5 eV for Fig. 1; each row’s id is the printed total energy (tables) or the grid’s total energy (Fig. 1), and Fig. 1’s printed cell keeps the total energy at the pixel read.
WHAT IS TAKEN. (1) Table I (p. 3001, tbl_84c11fc5ced5; checked against the table image): the two-photon GCS in the open continuum, cm4 s, with the residual core in J = 3/2 and in J = 1/2 (two partial cross sections; the paper prints no total), total energies 14 to 16.871 eV. Every cell carries its own power of ten (10^-50, and 10^-46 in the last row, ‘as it approaches the first such intermediate resonance’, the 6s(J_c = 1/2), p. 3001): the files hold mantissa e power, as printed. (2) Table II (p. 3002, tbl_8ff4b5716399; checked against the image): the three-photon GCS, cm6 s2, the same two cores, 14 to 14.506 eV. ‘The values of our GCS compare well with those of McGuire’ (p. 3001; mcguire_1981). (3) Fig. 1 (p. 3000, fig_5c0c5705aedd): the two-photon GCS inside the autoionising region, read from the page image (tools/extract/gangopadhyay_1986.py): linear axis in units of 1e-50 cm4 s (ticks 0-6, the top one labelled ‘6 x 10^-50’), every tick found where the script writes it (within 2 pixels); the tick spacing varies (257 to 274.5 pixels per unit up the y axis, 259 to 253 per 0.2 eV along x), so the scale is piecewise linear between ticks (a single line would leave 8.9 and 3.5 pixels at the ticks). 415 values every 0.002 eV of total energy from 12.206 to 13.196 eV where the line is one short run; the resonance peaks and steep flanks (12.264-12.300, 12.738-12.770, 12.974-13.016, 13.108-13.136 eV and narrower gaps) are not read. The overlay of every value on the page image was inspected (2026-10-09): all lie on the line.
CHECKS (the script raises if any fails). Fig. 1’s arrows point at Fig. 3’s printed resonance energies: 12.6023 eV for ‘E = 12.602’ and 12.9463 eV for ‘E = 12.95’ (within 0.006 eV; the curve’s dip and bump there: 12.611 and 12.948 eV). Table I as three later papers draw it, at the photon energy (half the total) and as the SUM of the two cores: lagutin_2017’s Fig. 8 squares (vector) 0.9997-1.0031 of the sums at 7.0-8.25 eV (six squares, the 16.871 eV row not drawn); lhuillier_1987’s Fig. 6 filled circles (TC-883; raster) 0.979-1.043 at 0.5144-0.6065 Ry (six); lhuillier_1989’s Fig. 10(a) crosses (TC-882; raster) 0.94-1.04 at 113.2-125.5e3 cm-1 (four; drawn 0.1-0.4e3 cm-1 above Table I’s energies), the fifth on that paper’s solid line, which is 0.89 of the sum at 16.001 eV. lhuillier_1987b’s Fig. 4 squares are checked by that script. So every later drawing of ‘Gangopadhyay et al.’ is Table I’s total, not values between the thresholds.
COMPARISON WITH McCOWN (mccown_1982, TC-884; a report, not a check). Fig. 1 at McCown et al.’s ArF line centre (two photons 103 466 cm^-1, 12.828 eV) reads 0.458e-50 cm4 s, and at twice the 193 nm photon (12.848 eV) 0.50e-50: 0.11-0.12 of McCown et al.’s alpha hbar omega (4.11e-50). The calculation’s background between the thresholds is 0.3-0.64e-50 cm4 s; its resonances rise to 1.1-6.7e-50 as drawn (peak tops 12.285, 12.750, 12.983 and 13.115 eV). The authors conclude that at 193 nm ‘the two-photon ejection of one electron was an extremely fast process’ (p. 3002).
DOUBT (Fig. 1 against Fig. 3): Fig. 1 labels the dip at 12.60 eV ‘J = 2’; Fig. 3(a) gives the angular distribution at ‘E = 12.602’ as ‘J = 0’. The paper does not resolve it. Fig. 2’s x labels read 12.2, 12.6, 12.6, 12.8: the second ‘12.6’ must be 12.4 (the ticks are evenly spaced); Fig. 2 is not read.
OEP 6, Q3. Between the Xe thresholds this paper is the only calculation drawn: Fig. 1, a RASTER figure (a scanned page) on a linear axis of TOTAL energy, linear polarisation, experimental (MQDT-fitted) J-resolved resonance positions. No table or vector figure exists for that region here.
NOT TAKEN: Fig. 2 (three-photon GCS between the thresholds, raster, a broken axis with two scales, 10^-74 and 10^-76, its spikes unresolved, a mislabelled tick); Figs. 3 and 4 (photoelectron angular distributions, polar plots without scale: no quantity). Further two-photon data the paper cites, not in the library: M. S. Pindzola and H. P. Kelly, Phys. Rev. A 11, 1543 (1975) (Ar, many-body theory); U. Heinzmann, J. Phys. B 13, 4353 and 4367 (1980) (one-photon autoionisation of Xe, the J = 1 resonances).
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
gangopadhyay_1986/tab1_jc32#
{
"id": "tab1_jc32",
"material": "Xe",
"file": "Xe/gangopadhyay_1986__tab1_jc32.csv",
"table": "tbl_84c11fc5ced5",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"polarization_printed": "not stated in words; one polarisation vector (Eq. 3) whose 'direction' Fig. 3 draws",
"channel": "Xe+ 2P3/2 (residual core J = 3/2)",
"method": "MQDT (Lu-Fano, parameters from experimental levels), lowest-order perturbation theory, intermediate sum truncated to 27 states",
"definition": "W^(N) = sigma^(N) F^N (Eq. 1), F the photon flux in photons/cm2 s",
"gauge": "length (r . epsilon, Eq. 3)",
"energy_axis": "photon energy = printed total energy / 2"
}
}
Table I (p. 3001), ‘Two-photon GCS with residual core in angular momentum state J = 3/2 (cm4 sec)’, open continuum: the partial GCS leaving Xe+ 2P3/2, against the photon energy (the printed total energy, the row id, divided by 2). 0.50-0.96e-50 cm4 s from 7.0 to 7.75 eV, rising to 2.84e-46 at 8.4355 eV (16.871 eV total) near the 6s(J_c = 1/2) intermediate resonance. A validator (OEP 6), not a reference.
gangopadhyay_1986/tab1_jc12#
{
"id": "tab1_jc12",
"material": "Xe",
"file": "Xe/gangopadhyay_1986__tab1_jc12.csv",
"table": "tbl_84c11fc5ced5",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"polarization_printed": "not stated in words; one polarisation vector (Eq. 3) whose 'direction' Fig. 3 draws",
"channel": "Xe+ 2P1/2 (residual core J = 1/2)",
"method": "MQDT (Lu-Fano, parameters from experimental levels), lowest-order perturbation theory, intermediate sum truncated to 27 states",
"definition": "W^(N) = sigma^(N) F^N (Eq. 1), F the photon flux in photons/cm2 s",
"gauge": "length (r . epsilon, Eq. 3)",
"energy_axis": "photon energy = printed total energy / 2"
}
}
Table I (p. 3001), ‘Two-photon GCS with core in J = 1/2 (cm4 sec)’, open continuum: the partial GCS leaving Xe+ 2P1/2, against the photon energy (the printed total energy, the row id, divided by 2). 0.74-1.54e-50 cm4 s from 7.0 to 8.0 eV, 6.71e-50 at 8.251 eV and 9.34e-46 at 8.4355 eV near the 6s(J_c = 1/2) intermediate resonance. A validator (OEP 6), not a reference.
gangopadhyay_1986/tab2_jc32#
{
"id": "tab2_jc32",
"material": "Xe",
"file": "Xe/gangopadhyay_1986__tab2_jc32.csv",
"table": "tbl_8ff4b5716399",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm6 s2",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"level": "not stated"
},
"parameters": {
"photons": 3,
"polarization": "linear",
"polarization_printed": "not stated in words; one polarisation vector (Eq. 3) whose 'direction' Fig. 3 draws",
"channel": "Xe+ 2P3/2 (residual core J = 3/2)",
"method": "MQDT (Lu-Fano, parameters from experimental levels), lowest-order perturbation theory, intermediate sum truncated to 59 states",
"definition": "W^(N) = sigma^(N) F^N (Eq. 1), F the photon flux in photons/cm2 s",
"gauge": "length (r . epsilon, Eq. 3)",
"energy_axis": "photon energy = printed total energy / 3"
}
}
Table II (p. 3002), ‘Three-photon GCS with core in J = 3/2 (cm6 sec2)’, open continuum: the partial GCS leaving Xe+ 2P3/2, against the photon energy (the printed total energy, the row id, divided by 3). 2.02e-76 at 4.6667 eV rising to 3.282e-73 at 4.8353 eV (14.506 eV total) near the 6p(J_c = 1/2) intermediate resonance. Doubt: kulander_1988 reports, from a private communication by Lambropoulos, a conversion-factor error in these three-photon results, which would make them about 1e6 too large (TC-949); not corrected here, the paper’s erratum not being in hand.
gangopadhyay_1986/tab2_jc12#
{
"id": "tab2_jc12",
"material": "Xe",
"file": "Xe/gangopadhyay_1986__tab2_jc12.csv",
"table": "tbl_8ff4b5716399",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm6 s2",
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"level": "not stated"
},
"parameters": {
"photons": 3,
"polarization": "linear",
"polarization_printed": "not stated in words; one polarisation vector (Eq. 3) whose 'direction' Fig. 3 draws",
"channel": "Xe+ 2P1/2 (residual core J = 1/2)",
"method": "MQDT (Lu-Fano, parameters from experimental levels), lowest-order perturbation theory, intermediate sum truncated to 59 states",
"definition": "W^(N) = sigma^(N) F^N (Eq. 1), F the photon flux in photons/cm2 s",
"gauge": "length (r . epsilon, Eq. 3)",
"energy_axis": "photon energy = printed total energy / 3"
}
}
Table II (p. 3002), ‘Three-photon GCS with core in J = 1/2 (cm6 sec2)’, open continuum: the partial GCS leaving Xe+ 2P1/2, against the photon energy (the printed total energy, the row id, divided by 3). 3.15e-76 at 4.6667 eV rising to 2.91e-72 at 4.8353 eV near the 6p(J_c = 1/2) intermediate resonance. Doubt: kulander_1988 reports, from a private communication by Lambropoulos, a conversion-factor error in these three-photon results, which would make them about 1e6 too large (TC-949); not corrected here, the paper’s erratum not being in hand.
gangopadhyay_1986/fig1#
{
"id": "fig1",
"material": "Xe",
"file": "Xe/gangopadhyay_1986__fig1.csv",
"table": "fig_5c0c5705aedd",
"digitised": "raster",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"scale": 1e-50,
"abscissa_unit": "eV",
"use": "check",
"uncertainty": {
"absolute": 0.02,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "linear",
"polarization_printed": "not stated in words; one polarisation vector (Eq. 3) whose 'direction' Fig. 3 draws",
"channel": "Xe+ 2P3/2 (the only open core between the thresholds)",
"method": "MQDT (Lu-Fano, parameters from experimental levels; Eq. 11 in the autoionising region), lowest-order perturbation theory, intermediate sum truncated to 27 states",
"definition": "W^(N) = sigma^(N) F^N (Eq. 1), F the photon flux in photons/cm2 s",
"gauge": "length (r . epsilon, Eq. 3)",
"energy_axis": "photon energy = drawn total energy / 2"
}
}
Fig. 1 (p. 3000): the two-photon GCS of Xe inside the autoionising region (between the 2P3/2 and 2P1/2 limits; the core left in J = 3/2), in units of 1e-50 cm4 s, against the photon energy: half the drawn total energy (the row id is the total energy of the sampling grid, 12.206 to 13.196 eV; photon 6.103 to 6.598 eV). Resonance peaks and steep flanks not read (the record’s notes). Uncertainty 0.02 (in 1e-50 cm4 s): one pixel is 0.0037-0.0039, the line 3-6 pixels high, the ticks within 2 pixels; the energy to 0.002 eV of total energy (0.001 eV of photon energy). The calculation’s own truncation error, ‘not expected to be more than a factor of 2’ (p. 2999), is not included.
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.