Oscillatory long-range interactions

In conclusion, the origin and nature of the long-range interactions in semiconductors seem to be fairly well understood, though accurate inclusion of its effects has only been accomplished for simple situations. It is interesting that the same method, Eq. (9-15), can be used to calculate the interaction between atoms in metals, where there is no gap we shall in fact do just that when we discuss metals. Where there is no gap, the evaluation of the asymptotic form is different, and the evaluation gives an oscillatory form cos(2/<,. r)/(/c,./ ) rather than the exponential decay. 

The materials are all metallic (except possibly for some of the nitrides) and possess the NaCl structure. The exchange interaction between the lanthanide ions is thus probably of the RKKY type and involves oscillatory long range... 

In metallic systems with 4f atoms the most prominent source of long-range interaction between magnetic moments is the mechanism first described by Ruderman and Kittel (1954), Kasuya (1956) and Yosida (1957), which involves the conduction-electron sea as mediator of the interaction. Distinctive features of the RKKY-interactions are its long range and oscillatory nature ... 

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