moccia_1984

R. Moccia and A. Rizzo, “Two-photon transition probability calculations in noble gases. Results for neon and argon”, Mol. Phys. 51, 1095-1108 (1984)

Source record · Catalogue · Review register

DOI: 10.1080/00268978400100701

Source kind: theory

Recorded technique: Second-order (lowest-order) perturbation theory for the bound-bound two-photon amplitude M (Eq. 1), the sum over intermediate states from a random phase approximation (RPA) calculation (Eq. 2): the RPA one-electron transition density matrices of the ground to the 1Po states, the 1Po to final-state matrix elements by the equations-of-motion method (EMM, Eqs. 3-4) or, for the first 1Se and 1De levels, with the final state from a double open shell SCF calculation (DOS). Length (LG) and velocity (VG) forms. Basis (p. 1099): Clementi and Roetti’s augmented with diffuse functions, Ne 12s 10p 5d 2f, Ar 13s 12p 5d 2f (DOS: Ne 8s 9p, Ar 9s 12p). LS coupling, no spin-orbit. ‘The calculations refer to the experimental set-up in which two linearly polarized photons with parallel polarization vectors are used’ (abstract). The experimental energies of the final levels and of the first few 1Po levels (Table 1, LS averages of the jl levels of Bashkin and Stoner) replace the RPA ones in the sums.

Materials in structured entries: None recorded.

Dataset quantities: None recorded.

Contents: 0 datasets; 0 formulas.

Curation notes

Mol. Phys. 51(5), 1095-1108 = PDF pages 2-15 (PDF page 1 is the Taylor & Francis download cover); journal page = PDF page + 1093. A scan with a text layer. Identity checked on the first page (PDF p. 2: ‘MOLECULAR PHYSICS, 1984, VOL. 51, No. 5, 1095-1108’, R. Moccia and A. Rizzo, Pisa; received 29 July 1983, accepted 1 November 1983) on 2026-10-08. Every number below was read against the table images (Tables 1-4).

Nothing is taken: the paper prints two-photon amplitudes M (Tables 2, 3) and rate parameters K in cm4 s (Table 4, Figs. 1-5), and the vocabulary holds neither (two_photon_transition_strength holds delta^TP, TC-872; no quantity holds a rate constant, TC-887). The values and their relation to delta^TP are recorded here.

THE QUANTITIES. ‘K = (2 pi)^3 alpha^2 omega_1^g omega_2^g |M_0^{f,LM}(omega_1, omega_2)|^2’ (Eq. 6, p. 1099) in atomic units of a0^4 hbar/E_h, ‘1.8967 x 10^-50 cm4 s’, g = +1 (LG) or -1 (VG), the photon fluxes in photons per area per time and ‘the density per unit energy range of the final states ... assumed to be a delta function’; M is the matrix element of Eq. (1) for the final level’s component LM with both photons’ operators along the common polarisation, symmetrised in the two photons. For parallel linear polarisation only the M = 0 component of a 1De level is reached, so |M|^2 is the whole level’s strength: for a 1Se level |M|^2 = S_zz^2 = delta^TP (F = G = H = 2), for a 1De level |M|^2 = (4/3) S_xy^2 in terms of the element S_xy of the level’s xy component, which is the delta^TP of the level summed over its components in henriksson_2005’s convention (TC-888) and five times the one-component average of sundholm_1994 and hattig_1998b (TC-887). The printed M (LG, a.u.), Table 3, at omega_1 = omega_2 = half the experimental energy: Ne 2p5 3p 1Se 4.514, 1De 3.836; Ar 3p5 4p 1Se 14.907, 1De 12.149 (|M|^2 = 20.38, 14.71, 222.2, 147.6); VG 0.354, 0.457, 0.641, 0.671. Table 2 adds Ne 2p5 4f 1De 0.56 and Ar 3p5 4f 1De -2.89 (LG). Against henriksson_2005’s TDHF strengths (Ne 1S0 12.850, 1D2 11.060; Ar 1S0 161.45, 1D2 113.40) these |M|^2 are 1.59, 1.33, 1.38, 1.30 times larger: RPA is TDHF, but here with experimental energies in the denominators, which lie closer to the 1Po resonance. A record of these M as delta^TP would need the squaring and the convention above stated as a decision (not made here).

CHECKED (2026-10-08, by direct computation). Every K of Table 4’s EMM rows (Ne and Ar, 1Se and 1De, VG and LG) from Table 3’s M by Eq. (6), with omega_1 = omega_2 = half of Table 1’s experimental energy (Ne 1Se 0.6908, 1De 0.6850; Ar 1Se 0.4954, 1De 0.4841 au) and 1.8967e-50 cm4 s: 2.632, 6.090, 4.460, 4.325 x 10^-52 and 1.678, 3.416, 1.925, 2.167 x 10^-51 against the printed 2.64, 6.10, 4.46, 4.32 x 10^-52 and 1.68, 3.42, 1.92, 2.16 x 10^-51 (worst 0.32 %, the printing). So the energies used are Table 1’s experimental ones. M = M^d + M^c in every column of Table 3; Table 2’s ‘This work’ is Table 3’s LG M rounded. a0^4 hbar/E_h = 1.8968e-50 cm4 s (CODATA).

FINDINGS. sundholm_1994’s Table IV quotes this paper’s argon 1De K as 0.216 x 10^-51 cm4 s (‘HF(omega_1 = 0.242 05)’, Ref. 17 there): Table 4 prints 2.16(-51), ten times larger. hettema_1992 compares the Ne 1De amplitude 3.84 with its S_xy 2.9663 without the factor 2/sqrt 3 between M = 0’s zz element and S_xy (hettema_1992’s notes).

NOT TAKEN. Tables 2-4 (amplitudes and K, above); Table 2’s Lebedev and Yakovleva column (reproduced from I. V. Lebedev and N. S. Yakovleva, Opt. Spectrosc. 46, 3 (1979), not in the library: Ne 3p 4.2, 4f 0.38; Ar 4p 14.0, 4f -1.9, without a final symmetry for the p-p’ rows). Table 4’s DOS rows (K only). Table 1 (RPA energies; the ‘experimental’ column is an LS average of jl levels weighted by first-order spin-orbit coefficients, not a level of the atom). Figs. 1-5, K against omega_1 from 0 to omega_f/2 for the 2p5 3p, 3p5 4p, 2p5 4p, 3p5 5p and p5 4f final levels (LG and VG, scanned images): K is not a quantity of the vocabulary. The paper states no numerical uncertainty; it judges the length form more reliable for these bound-bound transitions (pp. 1104-1107).

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

Datasets

No datasets are recorded.

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.