Divergences and Phonons in the Indirect Interaction

Divergences arising in the third-order perturbation-theory derivation of the indirect interaction between nuclear or ionic spins in a metal are avoided if the recoil of the localized spin is taken into account by including the phonon degrees of freedom. When this is done the form of the usual Ruderman-Kittel function is altered, particularly at small $R$, where the singularity at the origin is removed.