moccia_1985

R. Moccia and A. Rizzo, “Two-photon transition probability calculations: electronic transitions in the water molecule”, J. Phys. B: At. Mol. Phys. 18, 3319-3337 (1985)

Source record · Catalogue · Review register

DOI: 10.1088/0022-3700/18/16/017

Source kind: theory

Recorded technique: Two-photon excitation of H2O from its ground state to low-lying excited states in the vertical-transition approximation (Born-Oppenheimer, Franck-Condon factors summed, rotational structure neglected), the amplitudes from the random phase approximation (RPA) with excited-to-excited matrix elements by the equations-of-motion method, and from a separated-channels static-exchange approximation (SCA), in a one-centre expansion; length and velocity forms. The appendix derives the rotational average of the squared two-photon amplitude for two photons of any energies and polarisations (Eqs. A1-A9).

Materials in structured entries: None recorded.

Dataset quantities: None recorded.

Contents: 0 datasets; 0 formulas.

Curation notes

J. Phys. B 18(16), 3319-3337 = PDF pages 1-19 (journal page = PDF page + 3318). Identity checked on the first page (PDF p. 1: ‘J. Phys. B: At. Mol. Phys. 18 (1985) 3319-3337’, Roberto Moccia and Antonio Rizzo, Pisa; received 26 November 1984, in final form 27 February 1985) on 2026-10-08.

Nothing is taken: the paper’s values are for water (H2O), which is not a material of the registry (data/materials.toml). It is recorded as the methods reference that hattig_1998b (TC-887) and sundholm_1994 cite for the polarisation factors F, G, H of the rotationally averaged two-photon strength.

THE ROTATIONAL AVERAGE (appendix, pp. 3334-3336). <|M|^2>_rot = sum_J F_{J M1 M2}(cos beta_12) S_gJ (Eqs. 6, A5), with S_g0, S_g1, S_g2 the scalar, antisymmetric and symmetric-traceless parts of the Cartesian amplitude tensor (Eq. A7) and the F_J for photons of spherical polarisation components M1, M2 at angle beta_12 (Eq. A6); related to Monson and McClain’s F, G, H by F = (F_0 - F_2)/3, G = (F_2 + F_1)/2, H = (F_2 - F_1)/2 (Eq. A8). Evaluated here (2026-10-08) from Eqs. (A6) and (A8): parallel linear polarisation (M1 = M2 = 0, beta_12 = 0) gives F_0 = 1/3, F_1 = 0, F_2 = 2/15 and F = G = H = 1/15, which is F = G = H = 2 in the normalisation with 1/30 of hattig_1998b (Eqs. 16-19) and sundholm_1994 (Eqs. 7-10), and F = G = H = 1 in henriksson_2005’s 1/15 (Eq. 6 there); co-rotating circular polarisation (M1 = M2 = 1, beta_12 = 0) gives F_0 = F_1 = 0, F_2 = 1/5 and F = -1/15, G = H = 1/10, that is -2, 3, 3 in the 1/30 normalisation (the values henriksson_2005’s notes use, TC-888). The amplitude is symmetrised in the two photons ((1 + P_12), Eq. 1).

THE RATE (p. 3325). ‘K = a0^4 t0 (2 pi)^3 alpha^2 omega_1^r omega_2^r <|M|^2>_rot’ (Eq. 8), a0^4 t0 = 1.8967e-50 cm4 s, r = +1 (length) or -1 (velocity), a delta-function density of final states: the convention of moccia_1984’s Eq. (6), with the rotational average for a molecule.

NOT TAKEN. Table 2 (K in cm4 s at omega_1 = omega_2 for parallel linear polarisation, H2O final states of A1, B1, B2 and A2 symmetry), Table 1 (calculated and experimental excitation energies of H2O), Figs. 1-7 (K and the polarisation ratios Omega against the photon energy): water is not in the registry, and K is not a quantity of the vocabulary.

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.