Angular momentum theory for relativistic case

While calculating matrix elements of various items of the energy operator or electron transition quantities in relativistic approximation we shall 

It plays a fundamental role in relativistic theory, therefore, below we shall present its algebraic values for j = f 7/2 (Table 7.1) and for k 9, j = = j (Table 7.2). These values are sufficient for the calculation 

Such presentation is necessary, because both these forms of the Clebsch-Gordan coefficient occur in relativistic formulas. They appear also in non-relativistic expressions while adopting j j coupling. 

As was mentioned in the previous paragraph, the Wigner-Eckart theorem (5.15) is fairly general, it is equally applicable for both approaches considered, for tensorial operators, acting in various spaces (see, for example, Chapters 15,17 and 18, concerning quasispin and isospin in the theory of an atom). 

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The Dirac equation for a particle in the electromagnetic field contains the interaction of the spin magnetic moment with the magnetic field. In this way, spin angular momentum appears in the Dirac theory in a natural way (as opposed to the non-relativistic case, where it has had to be postulated . 

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