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Numerical Example: 4FJ States of Nd3+ (4f3)

1988; Springer Nature; Linguagem: Inglês

10.1007/978-3-642-93376-9_11

2192-6603

Carole A. Morrison,

Spectral Theory in Mathematical Physics

As a numerical example of the calculation of the crystal-field splitting, we calculate the splitting for Nd3+ (4f3) in a field of S4 point symmetry. We assume that the levels are pure 4FJ. We assume that L, S, and J are all good quantum numbers; then we consider matrix elements of H3 in equation (9.9) with J’ = J and L’ = L. Thus, (11.1) $$ =\sum\limits_{kq}{B_{kq}^* } <\ell(0)k(0)|\ell(0)>$$ . The values of the reduced matrix elements for the 4F state of Nd3+ are as in table 11.1. In obtaining these values we have used Nielson and Koster’s results (1963) in equations (9.9) and (9.10) for the reduced matrix elements, (LS|Uk|LS), for L = 3 and S = 3/2; the Racah coefficients (6-j symbols) are found in Rotenberg et al (1969).