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 `__ · :doc:`Catalogue ` · :doc:`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 :doc:`review register ` for the checks and decisions.