Matrix Elements of the Spin–Orbit Coupling for an ln Configuration in a Crystalline Electric Field
- 15 January 1972
- journal article
- Published by Canadian Science Publishing in Canadian Journal of Physics
- Vol. 50 (2) , 78-83
- https://doi.org/10.1139/p72-016
Abstract
A general expression for the matrix elements of the spin–orbit coupling for an ln configuration in a crystalline electric field of arbitrary symmetry is derived using Racah formalism. This calculation is an extension of Lulek's treatment of this problem for an l1 configuration. This general expression is used to calculate the contribution to the ground-state splitting for the S-state lanthanide ion Gd3+ (4f7; 8S7/2)in an axial crystalline electric field of a second-order perturbation mechanism involving the matrix element of the spin–orbit coupling. It is shown that this mechanism, which was proposed by Lulek is incapable of explaining the observed ground-state splitting.Keywords
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