pindzola_1981b

M. S. Pindzola, M. G. Payne and W. R. Garrett, “Two-photon excitation of xenon”, Phys. Rev. A 24, 3115-3119 (1981)

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DOI: 10.1103/PhysRevA.24.3115

Source kind: theory

Recorded technique: Lowest-order perturbation theory for the two-photon excitation of the xenon ground state to 5p5 6p 2P3/2 (J = 0) (jjJM coupling; 6p[1/2]0, Paschen 2p5) by one linearly polarised beam, in the dipole approximation, a single-active-electron (frozen-core, single-configuration) model: relativistic Dirac-Fock orbitals (Desclaux’s program), explicit summation over fixed-core bound states to n = 10, the n^-3 rule beyond, and an integral over Dirac-Fock continuum orbitals (iterative exchange), in the length and velocity forms (Eqs. 4, 5); nonrelativistic Hartree-Fock with an implicit summation (Dalgarno-Lewis inhomogeneous equation, Eqs. 7, 8); and average-energy closure (Eqs. 12, 13) with Dirac-Fock, Hartree-Fock, l-averaged Hartree-Fock and Hartree-Slater radial r^2 elements, the average energy set to the experimental 6s 2P3/2 (J = 1) level. ‘The single-particle energies ... were taken from the atomic energy level tables of Moore’ (p. 3117): experimental energies in the denominators. The rate model is that of Payne et al. (Ref. 6): W = alpha I^2 G(omega) (Eq. 1), I the intensity in erg cm-2 s-1, G the bandwidth-dependent line-shape function, rate equations valid when the two-photon Rabi frequency is small against the laser bandwidth.

Materials in structured entries: None recorded.

Dataset quantities: None recorded.

Contents: 0 datasets; 0 formulas.

Curation notes

Phys. Rev. A 24(6), 3115-3119 (December 1981) = PDF pages 1-5 (journal page = PDF page + 3114). Identity checked on the first page (PDF p. 1: ‘PHYSICAL REVIEW A VOLUME 24, NUMBER 6 DECEMBER 1981’, M. S. Pindzola (Auburn University), M. G. Payne and W. R. Garrett (Oak Ridge National Laboratory); received 16 April 1981) on 2026-10-09. The id pindzola_1981b: pindzola_1981 is M. S. Pindzola, Phys. Rev. A 23, 201 (1981), the photoionisation of the same excited level.

Nothing is taken. The paper’s values are the ‘two-photon excitation parameter’ alpha in cm4/erg2 (Table II), the coefficient of W = alpha I^2 G(omega) with I an intensity, not a cross section per photon flux: two_photon_excitation_cross_section holds cm4 or m4 (TC-872), and the conversion (below) rests on reading the line-shape function, which the paper defines only through its Eq. (14). No krypton values (the paper is about xenon only).

THE QUANTITY (pp. 3115-3117). alpha_L = (8 pi^3 / c^2) |sum_n <f|sum_i eps.r_i|n> <n|sum_i eps.r_i|i> / (E_i - E_n + omega)|^2 (Eq. 2, atomic units, omega the line-centre photon energy), alpha_V the velocity form (Eq. 3). For a Gaussian laser at exact resonance G(omega) = (8 ln 2 / pi)^(1/2) / Delta_L, Delta_L the laser FWHM in rad/s (Eq. 14, after Ref. 6). In atomic units alpha has the unit a0^4/E_h^2 = 4.1255 x 10^-13 cm4/erg2 (from Eq. 1, W in 1/t0, I in E_h a0^-2 t0^-1, G in t0); the closure checks below confirm it.

TABLE II (p. 3117; image checked), alpha in cm4/erg2, the ground to 6p 2P3/2 (J = 0) transition: 1. Dirac-Fock explicit summation, length, 2.10 x 10^-12; 2. the same, velocity, 5.89 x 10^-13; 3. Hartree-Fock implicit summation, length, 1.04 x 10^-12; 4. the same, velocity, 4.61 x 10^-13; 5.-8. closure: Dirac-Fock 1.71 x 10^-12, Hartree-Fock 7.53 x 10^-13, l-averaged Hartree-Fock 5.38 x 10^-12, Hartree-Slater 4.11 x 10^-11; 9.-10. ‘Inferred from experiment (Ref. 4)’, with Delta lambda_L = 0.05 and 0.10 A, 2.73 x 10^-12 and 5.46 x 10^-12. The authors’ ‘best estimate is to average the Dirac-Fock explicit summation results to get alpha = 1.4 x 10^-12 cm4/erg2’, uncertain ‘at least [by] the factor of 3.5 found between length and velocity forms’ (p. 3118); the Dirac-Fock 6p (J = 0) state is ‘95% pure’.

CHECKED (2026-10-09, by direct computation from the printed numbers). The four closure rows from Eqs. (12)-(13) with the printed radial elements 3.39 (Dirac-Fock), 2.25, 6.01 and 16.6, omega = 9.9308/2 eV (the paper’s level energy) and epsilon-bar the Xe 6s[3/2]1 level, 68 045.156 cm-1 (nist_asd_2026), converted with a0^4/E_h^2: 1.7105, 0.7535, 5.376 and 41.02 x 10^-12 against the printed 1.71, 0.753, 5.38 and 41.1 x 10^-12 (worst -0.2 %). The experimental rows from W = 2.4 x 10^-23 I^2 (the paper’s quotation of Ref. 4) and Eq. (14) at 2496 A: 2.731 and 5.462 x 10^-12 (printed 2.73, 5.46). The length/velocity ratio 2.10/0.589 = 3.57 (‘3.5’). 9.9308 eV corresponds to 2497.0 A for two photons (vacuum; the paper’s ‘2496 A’).

FINDING: THE CONVERSION TO A CROSS SECTION, AND kroll_1990’s QUOTATION (TC-890). With the photon flux Phi = I/(hbar omega), W = alpha (hbar omega)^2 G Phi^2, so alpha (hbar omega)^2 is a two-photon cross section in cm4 (hbar omega = 4.9654 eV = 7.955 x 10^-12 erg): Dirac-Fock length 1.33 x 10^-34, velocity 3.73 x 10^-35, Hartree-Fock 6.58 and 2.92 x 10^-35, the best estimate 8.9 x 10^-35 cm4. kroll_1990 quotes this paper (its Ref. 12) as ‘4-13’ x 10^-35 cm4 for 2p5: the Dirac-Fock velocity and length values under this conversion. What G is normalised in decides whether that is two_photon_excitation_cross_section with frequency_variable = angular for the two-photon frequency and photon_statistics corrected: Eq. (14)’s (8 ln 2/pi)^(1/2) / Delta_L is twice the peak of a normalised Gaussian of FWHM 2^(1/2) Delta_L, the two-photon line of a Gaussian laser, in the two-photon detuning (Payne et al., Ref. 6, Payne_1981_ResonanceIonizationSpectroscopy, Eqs. 7-8, a multimode model that ‘yields <E^2n> = n! <E^2>^n’, so the factor 2 is the chaotic light’s G2(0) = 2); it is also exactly the peak of a normalised Gaussian of FWHM Delta_L / 2^(1/2) in the laser frequency, without that factor. Read the first way, alpha (hbar omega)^2 is the coherent-light cross section with g in the two-photon angular frequency (kroll_1990’s convention); read the second way it is half of it. The paper does not say which, so the conversion is not made here (a decision for the register, after checking Ref. 6’s normalisation of alpha against the coherent-light rate).

FINDINGS ON THE TEXT. (a) ‘The laser line width ... is estimated to be somewhere between 0.05 and 0.01 A’ (p. 3118), but Table II’s rows 9-10 are computed for 0.05 and 0.10 A (reproduced above; 0.01 A would give 5.46 x 10^-13): the text’s ‘0.01’ is 0.10. (b) ‘the spread in the last two values given in Table I’ means Table II (Table I is orbital energies and radial matrix elements). (c) The ‘average’ of the Dirac-Fock results is 1.34 x 10^-12 (arithmetic) or 1.11 x 10^-12 (geometric), printed 1.4. (d) The experimental W = 2.4 x 10^-23 I^2 (I in erg cm-2 s-1) is attributed to Chen et al. (Ref. 4, Chen_1980_DirectCountingXe in the library): that paper’s fit to its Fig. 3 is ‘R ~ 2 x 10^-9 I^2’ with I in W/cm2 (p. 476), 2 x 10^-23 I^2 in erg cm-2 s-1, and its estimate 3.1 x 10^-9 I^2 (3.1 x 10^-23); neither is 2.4. Not resolved (Chen et al.’s R may be defined differently from W; not curated here).

NOT TAKEN. Table II (alpha in cm4/erg2: no quantity; rows 9-10 are derived from another paper’s measurement and an assumed bandwidth). Table I (orbital energies and radial matrix elements <5p||r||5p>, <6p||r||6p> of eight single-configuration calculations: no quantity). The radial r^2 elements of the closure (3.39, 2.25, 6.01, 16.6). The level energy 9.9308 eV (Moore’s tables, secondary). The text’s percentages (95 % pure Dirac-Fock J = 0 state; the Hartree-Fock 2P 6p 1S0 ‘71% pure’). The paper states no uncertainty beyond the factor 3.5 and ‘better than 25% accuracy will require an extensive study of electron correlation’.

TWO-PHOTON DATA CITED, NOT IN THE LIBRARY: W. Gornik, S. Kindt, E. Matthias, H. Rinneberg and D. Schmidt, Phys. Rev. Lett. 45, 1941 (1980) (two-photon excitation of xenon, E1-E2 contributions). In the library: J. Bokor, J. Zavelovich and C. K. Rhodes, Phys. Rev. A 21, 1453 (1980) (bokor_1980); C. H. Chen, G. S. Hurst and M. G. Payne, Chem. Phys. Lett. 75, 473 (1980) (Chen_1980_DirectCountingXe, uncurated).

Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.

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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.