Photodissociation cross section differential

The state-to-state differential photodissociation cross section is given by... 

Let us, for illustration purposes, consider the dissociation of a triatomic molecule as sketched in Figure 1.4. In an ideal experiment one would measure differential photodissociation cross sections with full specification of the initial state and full resolution of the final state,... 

Next we outline the calculation of fully resolved differential photodissociation cross sections for any arbitrary initial rotational state of the parent... 

It is not difficult to surmise that the final expression for the fully resolved differential photodissociation cross section is extremely complicated (Balint-Kurti and Shapiro 1981). It contains vast quantities of sums and angular momentum coupling elements. Note that the cross section depends explicitly on the magnetic quantum numbers Mi and mj. Somewhat simpler cross section expressions can be derived by averaging over the initial projection quantum number Mi and summing over the final projection quantum number of the rotor, mj. As shown by Balint-Kurti and Shapiro, the angle-resolved cross section then takes on the general form... 

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... 

Ugh scenarios for interference between an JV-photon route and an M-photon -Where N, M are of the same parity, allow for control over both the differential -gral photodissociation cross sections, this is not the case when N and M are rent parity. In this case only control over the differential cross section is fe. [However, the control is such that it leads to the breaking of the usual StdMbrward symmetry, This is but one example of the breaking of svmmetrv... 

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, 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)... 

Owing to the symmetry property of an optical dipole transition, the data analysis for a photodissociation study is greatly simplified. The center-of-mass differential cross-section for a single-photon, dissociative process can be expressed as38,39... 

The first part of the review deals with aspects of photodissociation theory and the second, with reactive scattering theory. Three appendix sections are devoted to important technical details of photodissociation theory, namely, the detailed form of the parity-adapted body-fixed scattering wavefunction needed to analyze the asymptotic wavefunction in photodissociation theory, the definition of the initial wavepacket in photodissociation theory and its relationship to the initial bound-state wavepacket, and finally the theory of differential state-specific photo-fragmentation cross sections. Many of the details developed in these appendix sections are also relevant to the theory of reactive scattering. 

We can regard the two components and fi2 as inducing two independ excitation routes. Choosing e, and 2 parallel and perpendicular to the quantize (z) axis, respectively, the differential cross section is composed of three terras) corresponds to photodissociation of E ) by the gj component, one by the- component, and one being the cross term between these two contributions. Ex) tion by the parallel component allows AM, = 0 transitions, while excitation by)... 

The theory of tirnc-dcpciidciit wavcpackct calculations of reactive scattering and photodissociation is briefly reviewed and some illustrative results presented. Particuhir attention will be j)aid to the theory- of differential scattering cross sections, cirising from both types of process, and to the symmetry of iuigular dependent scattering in a photodissociation process. Electronically non-adiabatic i)ro-cesses will be discussed mid illustrations from the reactive scattering of 0( D) + H2 cuid from the photodissociation of HF are presented. 

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