Asymptotic equations for angular momenta

As mentioned in the preceding section, the law of conservation of angular momentum in the process of optical pumping of molecules is reflected in the coefficients kFXk, kFxk, KA K, K Ax and CK in Eqs. (5.28), (5.29), (5.30), (5.31) and (5.32). For optical transitions between states with large angular momentum quantum numbers J, J the explicit form of these coefficients is considerably simplified [15, 39]. These simplifications are due to the possibility of employing asymptotic expressions of the 6j-symbols presented in Appendix C. Applying Eq. (C.12) for the coefficients KA K and K Ax we obtain 

The asymptotic expressions for the coefficients CK may be found with the aid of (C.13) and are of simple form, namely 

introducing unified notation for coinciding coefficients  

Owing to the coincidence between a number of coefficients, the symmetry of the equations obtained is considerably higher, as compared to (5.22) and (5.23). In addition, the terms responsible for the dynamic Stark effect disappear, which agrees perfectly with the analysis performed in the preceding section concerning the influence of the dynamic Stark effect on optical polarization of molecules. 

A new circumstance, in comparison with Eqs. (5.22) and (5.23), is the fact that the asymptotic system (5.87), (5.88) contains an infinite number of equations (0 K oo, 0 k oo). If the solution for polarization moments is found by way of expansion into a series over a small parameter, then the argument produced in Section 5.4 can be applied here without change. However, if the system of equations (5.87) and (5.88) is solved by computer, then we are deprived, in principle, of the possibility of accounting for all emerging polarization moments. What could be done in this case  

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Asymptotic equations for angular momenta 5.6 Asymptotic equations for angular momenta... 

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