Angular momentum coupling general

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... 

The mechanism by which spin-orbit coupling can impact molecular bonding becomes more obvious if the wave function is reformulated in terms of molecular spinors (Hund s case c coupling). One should keep in mind, however, that even for the heaviest elements the angular momentum coupling is generally intermediate between case a and case c, and the following picture is therefore an oversimplification. 

It is possible, of course, to write the general result for two irreducible representations [A i,0] and [A 2>0] of U(2) by means of quite simple formulas related to angular momentum coupling schemes. 

In chapter 3, the complete set of molecular constants is collected behind a listing of reliable experimental transition frequencies, separately for each species. Radicals require greatly differing angular momentum coupling schemes and therefore different kinds of effective hamiltonians for fitting spectra. Consequently, in contrast to chapter 2, the tabulations in chapter 3 show generally more individual character per molecule. 

More generally, further complications arise for angular momentum couplings when the fragments show electronic angular momentum, but the fundamental symmetry rules are not affected by this. Early examples for detailed correlations include triatomic systems, and another more recent example is the correlation for atom + linear molecule. While for such simple cases, and planar molecules in general, parity is... 

The individual J,Mj) multiplets cannot be, in principle, described by a single Slater determinant. This is a consequence of the general rules of coupling of two angular momenta eigenfunctions of all projections of the total angular momentum which is lower than the maximal possible (L + S), are represented as linear combinations of several determinants [36]. 

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