Indirect exchange interaction, effect

It is well known that a Mossbauer-active nucleus senses its local environment via direct and indirect exchange mechanisms (see Fig. 18.28) [I 1,94]. Direct interactions include (i) interaction between atomic shell and nucleus of a Mossbauer-active atom (interaction of Type I), (ii) interaction between the nucleus of the Mossbauer-active atom and its surrounding lattice (interaction of Type III), and (Mi) interaction between Bext nd nucleus of the Mossbauer-active atom (interaction of Type V). On the other hand, indirect interactions involve (i) interaction between the lattice and atomic shell of the respective nucleus of the Mossbauer-active atom (interaction of Type II) and (ii) interaction between Bgxt and atomic shell of the respective nucleus of the Mossbauer-active atom (interaction of Type IV). Thus, Bgxt can act directly or indirectly on the nucleus of the Mossbauer-active atom and affects its nuclear levels. Beside this, Bgxt can magnetically induce a quadrupole interaction that frequently happens, for example, in the case of Fe " " having a cubic environment. Interaction of Type IV and Type V can be effectively described by Hamiltonians in the form of [94]... 

The interactions of the RE-ions with phonons and conduction electrons cause indirect interactions between different RE-ions. Phonons and conduction electrons serve as medium for these interactions. In the effective-interaction model they are eliminated and replaced by an ion - ion interaction. Since the latter is an instantaneous interaction all retardation effects are lost which are connected with the dynamical properties of the medium. This shows the limitations of the effective interaction model. The isotropic exchange interaction as described by eq. (17.40) leads to an effective ion-ion interaction of the form... 

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