Atomic Spectra and Coupling Schemes

In this section we wish to discuss the relationships between the stationary electronic states of free atoms and ions. The quantum mechanical derivation of these relationships is to be found in almost any required depth in several texts so that we shall be content to classify the states and list expressions for their energies. 

Electronic states are conveniently classified in terms of the electronic configuration, as described by the principal and orbital quantum numbers, and the interactions between orbital and spin momenta of the electrons 

The most common coupling scheme is known as LS—or Russell-Saunders—coupling. In this it is considered that all the orbital momenta of the electrons, represented by vectors 1, combine to form a resultant L and all the spin momenta, represented by vectors Sj, combine to form a resultant S. The vectors L and S then combine to form the total angular momentum vector J, taking all integral values from iL + ltolL — 5. The stationary states are then labeled in terms of the multiplicity, 25+1, the L value, as shown by a capital letter  

In jj coupling the individual and are coupled to form and then the various are coupled together to form states again characterized by J. Interactions such as Ij + l t h + and Si + Sf. are neglected to a first approximation and L and 5 are no longer good quantum numbers. States 

TABLE II. Allowed J Values for Groups of nly-Equivalent Electrons  

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