fink_1989#
M. G. J. Fink and P. Zoller, “Quantum-defect parametrization of perturbative two-photon ionization cross sections”, Phys. Rev. A 39, 2933-2947 (1989)
Source record · Catalogue · Review register
Source kind: theory
Recorded technique: A multichannel quantum-defect (MQDT) parametrisation of two-photon ionisation amplitudes in lowest-order perturbation theory (Eqs. 2.1-2.5; the intermediate sum done as a Dalgarno-Lewis inhomogeneous equation), in which the rapid energy dependence of intermediate and final Rydberg resonances is carried by elementary functions (cot(pi nu), Coulomb phases) and the rest by parameters that are smooth across the series and the thresholds: reaction matrices R^b, R^f of the intermediate and final channels and smooth dipole matrices (Secs. IV-V). Worked numerically only for atomic hydrogen 1s, 2s and 3s with circularly polarised light (Sec. III): the acceleration-form amplitude (Eq. 3.2) split into a standing-wave part t^s, an on-shell part t^o and a first-order term t_3, computed with a cutoff radius r1 = 100 a0 of the 1/r^2 interaction, converged to ‘about one part in 10^4 or better’ for intermediate effective quantum numbers above 10 (p. 2939).
Materials in structured entries: H
Dataset quantities: multiphoton_ionization_cross_section
Contents: 1 dataset; 0 formulas.
Curation notes#
Journal pp. 2933-2947 = PDF pages 1-15 (journal page = PDF page + 2932). Identity checked on the first page (PDF p. 1: ‘PHYSICAL REVIEW A VOLUME 39, NUMBER 6 MARCH 15, 1989’, footer ‘39 2933’; Michael G. J. Fink and Peter Zoller, JILA, Boulder; received 26 September 1988) on 2026-10-09. The PDF is a scan: every page one embedded 1-bit image, 5169 x 7129 pixels (about 600 dpi).
WHAT THE PAPER GIVES. It is a method paper. Its only numbers are for atomic hydrogen: Tables I-III (pp. 2939-2940), the 2PI of H 1s, 2s and 3s with circularly polarised light at nine wavelengths each, with the parameters t^s, t^o, t_3 (a.u.), this paper’s total sigma^(2) (cm4 s) and ‘the same from Ref. 13’ (M. Aymar and M. Crance, J. Phys. B 13, L287 (1980); S. Klarsfeld and A. Maquet, Phys. Lett. 73A, 100 (1979) and J. Phys. B 12, L553 (1979); which of them for which value is not said). Figs. 2 and 3 (H 1s, 2s: sigma^(2), the amplitude and the smooth parameters against the intermediate-state energy near threshold) and Figs. 4 and 5 (a hypothetical two-channel model in arbitrary units, Eqs. 5.5-5.7) are raster figures. There are NO values for any noble gas: krypton and xenon (and He, Ne, Ar) appear in neither a table, a figure nor the text, apart from the remark that for ‘the rare gases, for example’ the matrix diagonalising R ‘may often be approximated satisfactorily by the analytically known recoupling matrix from jj to LS coupling’ (p. 2945).
THE CROSS SECTION (Eq. 2.1, p. 2934): sigma^(2) = 2 pi (2 pi alpha)^2 omega^2 sum_f |T^(2)_f<-a|^2 a0^4 t0 in atomic units, T^(2) the second-order dipole matrix element in length form (Eq. 2.2) for the field E(t) = E0 eps exp(-i omega t) + c.c., converted with a0 = 5.29177e-11 m and t0 = 2.41888e-17 s (printed); the paper does not write the rate, but this is the usual generalised cross section, rate = sigma^(2) F^2, F the photon flux. For s states and circular light T^(2) = Omega (t^(2) + t_3) / omega^4 (Eq. 3.2, acceleration form), Omega = [2/(3 x 5)]^(1/2) (p. 2937), and t^(2) = t^s + i t^o above the one-photon threshold, t^s - cot(pi nu) t^o below it (Eq. 3.9), nu the effective quantum number of the intermediate energy E_a + omega.
CAN A CROSS SECTION BE REPRODUCED FROM THE PARAMETERS? Yes, for hydrogen, by Eqs. 2.1, 3.2 and 3.9 above: the script recomputes every row of Tables I-III from the printed t^s, t^o, t_3 and the wavelength (omega = 2 pi c / lambda in hartree, infinite nuclear mass: 911.25 angstrom is omega = 0.50001, the 1s threshold) and reproduces the printed sigma^(2) within 2e-4 (Table I), 1.2e-3 (II) and 2.0e-3 (III) above the one-photon threshold, and within 0.6 % at the first row of each table, just below it (nu = 8.50). For many-electron atoms the general formulas are Eqs. 4.21, 4.22 and 4.24 (pp. 2942-2943; final-state resonances Sec. IV C, Eqs. 4.25-4.27) and, for two intermediate channels, Eqs. 5.5-5.7 (p. 2944, parameters delta, alpha, tau, q, q’, Q and the thresholds); the parameters are reaction matrices, which the paper says may come from experimental energy levels, and smooth dipole matrices, from one-photon studies, a Coulomb approximation or a fit to ab initio two-photon amplitudes (p. 2945). The paper gives no such parameters for any atom but hydrogen, so for Kr and Xe it provides a formula, not values.
EXTRACTED (tools/extract/fink_1989.py): Table I’s sigma^(2) (H 1s, circular), from the library’s table (tbl_790c596397dd), every cell checked against the table image (all agree, as do Tables II and III’s). The row ids and x are the wavelengths as printed; value the printed number with its bracketed power of ten written as an exponent (printed ‘5.530[-52]’, value 5.530e-52).
THE CHECKS (the script fails if one is missed): the reproduction above; this paper’s sigma^(2) against Ref. 13’s within 1 % wherever both are printed (worst 0.7 % in Table I, 0.9 % in II, 0.4 % in III: Ref. 13 is printed to three digits).
NOT TAKEN: Table I’s t^s, t^o, t_3 (amplitude parameters, no quantity of the vocabulary; they are in the library table and reproduce sigma^(2) as above) and Ref. 13’s column (another paper’s values, used as a check); Tables II and III (2PI from the excited 2s and 3s states: multiphoton_ionization_cross_section is for the ground state and has no initial-level parameter; not bent to hold them); Figs. 2 and 3 (raster figures of H 1s and 2s near the intermediate-state threshold, the resonance structure ‘obtained by interpolation [of the smooth parameters, about 30 grid points] and insertion into Eq. (3.9)’, p. 2939: model curves that Tables I-III’s parameters underlie); Figs. 4 and 5 (a hypothetical two-channel model, arbitrary units); Fig. 1 (a schematic).
TWO-PHOTON REFERENCES the paper cites (data not in this record): A. F. Starace and T. F. Jiang, Phys. Rev. A 36, 1705 (1987) (starace_1987, TC-878); P. Gangopadhyay, X. Tang, P. Lambropoulos and R. Shakeshaft, Phys. Rev. A 37, 2998 (1986) (printed so; the paper is Phys. Rev. A 34, 2998 (1986), gangopadhyay_1986); H: M. Aymar and M. Crance, J. Phys. B 13, L287 (1980); S. Klarsfeld and A. Maquet, Phys. Lett. 73A, 100 (1979), J. Phys. B 12, L553 (1979); E. Karule, J. Phys. B 21, 1997 (1988); B. Gao and A. F. Starace, Phys. Rev. Lett. 61, 404 (1988); none of the H papers is in the library.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
fink_1989/tab1_sigma2_1s#
{
"id": "tab1_sigma2_1s",
"material": "H",
"file": "H/fink_1989__tab1_sigma2_1s.csv",
"table": "tbl_790c596397dd",
"quantity": "multiphoton_ionization_cross_section",
"unit": "cm4 s",
"abscissa_unit": "angstrom",
"use": "check",
"uncertainty": {
"relative": 0.001,
"level": "not stated"
},
"parameters": {
"photons": 2,
"polarization": "circular",
"gauge": "acceleration",
"method": "lowest-order perturbation theory, exact one-electron (hydrogen) Green function decomposed into a standing-wave part, an on-shell part (Coulomb functions) and a first-order term, acceleration form, interaction cut off at r1 = 100 a0 (Sec. III)",
"definition": "sigma^(2) = 2 pi (2 pi alpha)^2 omega^2 sum_f |T^(2)|^2 a0^4 t0 (Eq. 2.1), T^(2) the second-order dipole matrix element; the rate is sigma^(2) F^2, F the photon flux in photons cm^-2 s^-1 (the usual generalised cross section; the paper does not write the rate)",
"wavelength_definition": "lambda = 2 pi c / omega, omega in hartree for an infinitely heavy nucleus"
}
}
Table I (p. 2939), column sigma^(2): two-photon ionisation of atomic hydrogen 1s, circular polarisation, at nine wavelengths from 924.06 to 300 angstrom (photon energy 0.493 to 1.519 hartree). 924.06 angstrom is just below the one-photon threshold (the intermediate state at nu = 8.5); the other eight, 911.25 (the threshold) to 300 angstrom, are above it: two-photon above-threshold ionisation. The wavelengths are omega = 2 pi c / lambda with omega in hartree for an infinitely heavy nucleus (911.25 angstrom is 0.50001 hartree). Uncertainty: the paper’s convergence, ‘about one part in 10^4 or better’ for nu > 10 (p. 2939), and the four printed digits.
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.