Photofragment angular distribution

Let us begin with the scheme for measuring differential photodissociation cross sections using a beam of unpolarized radiation propagating in the +Z direction as defined by Fig. 7.8. Photofragments are detected along k which has spherical polar coordinates 8, fi 8 is the inclination relative to Z, f is the angle relative to X made by the projection of k into the XOY plane). The differential photodissociation cross section dcr/d l can be written (Beswick, 1993) 

Another equation, analogous to Eq. (7.2.13), may be derived for experiments in which a beam of linearly polarized light (propagating along X, polarized along Z ) is used to photodissociate a diatomic molecule. For this scheme, the photofragment ejection direction O, j is defined relative to the linear polarization direction, Z, and the resultant photofragment distribution is described by 

As will be seen in Chapter 8, equations identical to Eq. (7.2.13) and Eq. (7.2.17) describe the photoelectron angular distributions observed in photoionization processes. However, owing to the difference in photofragment masses (atom vs. electron), the photoelectron angular distributions sample the photofragmentation dynamics very differently from photodissociation angular distributions. 

For photodissociation, when it is assumed that the dissociation is rapid relative to the rotational period of the molecule (axial recoil approximation) (Zare and Herschbach, 1963) a limiting value of (3 = +2 is obtained when dissociation is induced by a transition (AQ = 0, /i parallel to the internuclear axis) and (3 = — 1 when the dissociative transition is -L (Afi = 1, /i perpendicular to the internuclear axis). 

Similar information can also be provided by fast beam photofragment translational spectroscopy where the two photofragments from the same fragmentation event are detected in coincidence (Leahy, et al., 1995). 

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Figure 2-1. A schematic diagram of the apparatus used to record photofragment angular distributions of complexes. An F-center laser is used to pump transitions in the parent complex which leads to dissociation. A second F-center laser is used as a probe to state selectively detect the fragments. The electrodes are used to orient the parent molecules prior to excitation.

Eqs. (6.4) and (6.5) lead to the cylindrical symmetry of the final photofragment angular distribution W(0f, pf) in the form of a dumbbell and a toroid, which are symmetrical with respect to the E-vector (the 2-axis). The distribution W(0f,ipf) is proportional to a differential photodissociation cross-section in the laboratory frame, f(0f,(fif) = daph/dO. For a proper description of its symmetry properties it is usually [376, 402] expanded in a set of spherical harmonics Ykq The cylindric symmetry in this case means that only spherical functions Too and Y20 appear with non-zero coefficients, and then... 

Zare, R.N. (1989). Photofragment angular distribution from oriented symmetric-top precursor molecules, Chem. Phys. Lett., 156, 1-6. 

The photofragment angular distribution can indicate the electronic symmetry of the predissociating state (Zare, 1972). 

As pointed out in our previous paper on the state-to-state photodissociation of HF dimer , photofragment angular distributions can be used in favorable cases to determine the final internal state distribution of the fragments. The kinematics also can be used to determine the correlations between the rotational states of the two fragments. That is to say the relative rates can be determined for... 

D. C. Dayton, K. W. Jucks, and R. E. Miller,/. Chem. Phys., 90,2631 (1989). Photofragment Angular Distributions for HF Dimer. Scalar J-J Correlations in State-to-State Photodissociation. 

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