Hans U. Stauffer, Sukesh Roy, Waruna D. Kulatilaka, and James R. Gord, "Detailed calculation of hydroxyl (OH) radical two-photon absorption via broadband ultrafast excitation," J. Opt. Soc. Am. B 29, 40-52 (2012)
The theoretical framework for calculation of two-photon absorption cross sections for intermediate Hund’s cases (a) and (b) diatomic species is described in detail and applied toward the hydroxyl (OH) radical. Analytical expressions are derived for the 20 rotational branches that are present in the two-photon A
electronic transition. Calculation of the corresponding line strengths is necessary to permit accurate relative-concentration measurements obtained from the fluorescence induced by a broadband femtosecond excitation pulse. We demonstrate, in particular, that consideration of the temperature-dependent initial-state populations of OH is necessary to obtain accurate relative concentrations from observed two-photon-excitation based laser-induced-fluorescence measurements.
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Factorsa Comprising the Nonvanishing Direction Cosine Matrix Elements for Diatomic Species, , Where (Lab-Fixed Components) and (Molecule-Fixed Components)
(P branch)
(Q branch)
(R branch)
and
and
Table 3
Far-from-Resonance Two-Photon Relative Line Strengths for Transitions [Intermediate Hund’s Coupling Case (a)/(b) Molecule]
J is the initial state () total orbital angular-momentum quantum number excluding nuclear spin.
Corresponding Hund’s case (b) limit quantum numbers: for transitions out of the initial state; for transitions out of the initial state.
Variables associated with state mixing {, U [Eq. (20)], [Eq. (22)]} defined in the text.
Tables (3)
Table 1
Important Symbols/Notation Introduced in the Text
Symbol
Definition
Symbol/Notation
Definition
J
Total angular momentum excluding nuclear spin
Σ
Projection QN of S onto molecular z axis
Ω
Projection quantum number (QN) of J onto molecular z axis
Factorsa Comprising the Nonvanishing Direction Cosine Matrix Elements for Diatomic Species, , Where (Lab-Fixed Components) and (Molecule-Fixed Components)
(P branch)
(Q branch)
(R branch)
and
and
Table 3
Far-from-Resonance Two-Photon Relative Line Strengths for Transitions [Intermediate Hund’s Coupling Case (a)/(b) Molecule]
J is the initial state () total orbital angular-momentum quantum number excluding nuclear spin.
Corresponding Hund’s case (b) limit quantum numbers: for transitions out of the initial state; for transitions out of the initial state.
Variables associated with state mixing {, U [Eq. (20)], [Eq. (22)]} defined in the text.