The S-J exchange interaction under the influence of the crystalline field

A magnetic impurity, having the s-j interaction with conduction electrons, under the crystalline field of host metals is investigated. The Hamann integral equation for the t-matrix can be derived and solved by the method of Zittartz and Müller-Hartmann for the cases of (1) small splittings, yielding the Kondo anomaly and decrease of the Kondo temperatureT _K compared with no splittings, (2) a large splitting from the crystalline ground doublet state, producing the higherT _K by the exicited level, and (3) a large splitting from the ground singlet state giving no Kondo effect. The macroscopic properties are calculated for (1) and (2).