Coupling of four and more angular momenta

The coupling of four angular momenta again can be performed by different routes using a different set of intermediate spins. For example, we can select two coupling schemes  

These two states are interrelated through the recoupling coefficients 

In the last formula the index j runs over all the meaningful values for which the triangular conditions of 67-symbols are satisfied. For better transparency we use the property that the 67-symbol remains invariant under the interchange of columns so that 

The evaluation of Clebsch-Gordan coefficients, 3/-, 67- and 97-symbols can be performed on the basis of special formulae (Appendix 3) or a computer program (Appendix 5). 

In coupling of five, six, etc. angular momenta the 12/-, 15/-, etc. symbols may appear but these are not used here. 

---