Electric-Quadrupole and Magnetic-Dipole Radiation in Linear Molecules. Applications to 1Π—3Π Transitions

Abstract

The electric-quadrupole and magnetic-dipole operators of a rotating, linear molecule interacting with a radiation field are formulated, in the space-fixed and in the molecular-coordinate systems, as contractions of irreducible spherical tensors. Radiative transition probabilities are obtained for the initial and final rotation-electronic states that are in Hund's Coupling Case a or b, using the normalized rotation matrix as the separated rotational wavefunction in the Born—Oppenheimer approximation. Line-strength formulas are derived for (1) transitions between singlet Case b states, in the case of an electric quadrupole, the 1Σ—1Σ, 1Π—1Σ, 1Δ—1Σ, 1Π—1Π, 1Δ—1Π, 1Φ—1Π, 1Δ—1Δ, 1Φ—1Δ, and 1Γ—1Δ transitions; in the case of a magnetic dipole, the 1Π—1Σ, 1Π—1Π, 1Δ—1Π, 1Δ—1Δ, and 1Φ—1Δ transitions; (2) the 1Π—3Π(a) transitions; (3) the 1Π—3Π(b) transitions. The master line-strength formula as well as intensity distribution for different branches are given. In (2) and (3), some of the transitions are found to be dependent on the absolute Kronig reflection symmetry, giving, for molecules of unequal nuclei, an intensity alternation for the two Λ-doubling components. A discussion of this reflection symmetry and the inversion symmetry is given and a consistent set of molecular wavefunctions of a given symmetry is constructed for (1) singlet Case b states and triplet Case a states (2) triplet Case b states expressed as a linear combination of Case a state wavefunctions through angular momentum coupling. The rotation—vibration spectra due to these higher multipole radiations are briefly discussed. A new point of view for the possibility of ΔΛ=0 (for Λ≠0) magnetic-dipole pure rotation spectra is advanced.

Quantitative determination of singlet oxygen density and temperature for Oxygen-Iodine Laser Applications

“…In order to estimate the absolute transition probability for the b-a (0,0) band based solely on this observation, Noxon assumed that this feature essentially encompassed the Q-branch of the b-a (0,0) band and that the Q-branch represented one fifth of the total band intensity. Considering the line-strength factors derived by Chiu [19] and verified by Fink et al [25], the Qbranch actually represents approximately one third of the band intensity. Therefore, the value reported by Noxon should be multiplied by a factor of 3/5 yielding a transition probability of 1 · 10 À3 s À1 .…”

Theoretical study on the low-lying excited states of the phosphorus monoiodide (PI) including the spin–orbit coupling

“…For the aforementioned transitions, the transition probabilities of the selected vibrational level v' of the upper state has been computed by the following formulae [40][41][42]:…”

Quantitative detection of singlet O_2 by cavity-enhanced absorption

“…However, an additional correction should be made at this point because Noxon assumed that the Q branch represented one f ifth of the total band intensity. In light of the line-strength factors derived by Chiu 16 and verified by Fink et al, 13 the Q branch actually represents approximately one third of the band intensity. Therefore, the A coefficient measured by Noxon should be scaled down by a factor of 3͞5 yielding a value of 1.0 3 10 23 s 21 .…”

“…All observed line positions are within 0.01 cm 21 of the predicted values. The line-strength factors for this transition were derived by Chiu 16 and experimentally verified for the ͑0, 0͒ band by emission in the work of Fink et al 13 These line-strength factors are used to produce the f itted spectrum in Fig. 2.…”

“…The entire Q branch is fitted simultaneously with Voigt line shapes with common Doppler width but varying Lorentzian widths. The line strengths are taken from Chiu, 16 and the only adjustable parameters are the temperature and the individual Lorentzian widths. As can be seen from Fig.…”