Relationship between bipolar moments and molecule-frame polarization parameters in Doppler photofragment spectroscopy

• Published in: The Journal of chemical physics 1999-11, Vol.111 (19), p.8751-8754
• Main Authors: Rakitzis, T. Peter, Hall, Gregory E., Costen, Matthew L., Zare, Richard N.
• Format: Article
• Language: English
• ISSN: 0021-9606; 1089-7690
• DOI: 10.1063/1.480223

In terms of the molecular-frame polarization parameters aq(k)(p), an equation is derived that describes the shape of a photofragment Doppler profile as a function of the three angles Γ, Δ, and Φ that specify the photolysis and probe laser polarizations about the detection axis. This expression is specialized to linearly polarized photolysis and probe laser beams. For the particular value of the angle between the probe laser polarization and the detection axis, Δ=π/2, this equation can be reduced to the form of well-known laboratory-frame expressions that use the bipolar moment formalism introduced by Dixon. Comparison of these forms shows the equivalence of the two formalisms and gives the relationships between the bipolar moments βQK(k1k2) and the molecule-frame aq(k)(p) parameters. We show that linear combinations of the bipolar moments completely describe photofragment polarization in the molecular frame and possess distinct quantum mechanical significance. In particular, it is shown that the coherent contribution to the photofragment alignment is proportional to the linear combination (1/5)β02(02)−(1/7)β02(22)−(12/35)β02(42).