Multiplets with magnetic angular momentum

The zero-order energy accounting for the equivalence coefficients adopts the form of 

It leads to the following zero-order van Vleck coefficient 

The first-order perturbation correction to the energy is given by the electronic Zeeman term as follows 

M) = VLBBzgyj[jM jz jM)[r ] = iiBBzgYjM yields the Lande factor modified to the form 

Consequently the first-order van Vleck coefficients become 

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