Effects of J Mixing

In some ions, such as Sm3+ and Eu3+, because of the close proximity of the excited multiplets to the ground state, it is necessary to include one or more of the higher multiplets in evaluating the magnetic and related properties. Recent papers by Malik et al. (2) and de Wijn et al (2) provide excellent information on the details of the calculations. However, we give below some salient features of the effects of J mixing. 

In calculations involving higher J multiplets, matrix elements of the crystal field Hamiltonian between states belonging to different J multiplets are needed. Although these can be calculated by the method of operator equivalents extended to elements non-diagonal in J, it is convenient to use a more general approach, utilizing Racah s tensor operator technique (26). In this method the crystal field interaction may be written as 

The expression for the matrix elements of UJJ, can be written in terms of the Wigner 3—j and 6—j symbols as follows  

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