Multipolar exchange interaction: Difference between revisions

Revision as of 17:55, 24 August 2015

Revision as of 17:55, 24 August 2015

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:<math> Y_{2}^{+1}=\sqrt{2}(Y_{1}^{0}Y_{1}^{+1}+Y_{1}^{+1}Y_{1}^{0}) </math>

:<math> Y_{2}^{+2}=2Y_{1}^{+1}Y_{1}^{+1} </math>

If so, a quadrupole-quadrupole interaction can be considered as a two step dipole-dipole interaction (see next section), e.g <math> Y_{2_{i}}^{+2_{i}}Y_{2_{j}}^{-2_{j}}=4Y_{1_{i}}^{+1_{i}}Y_{1_{i}}^{+1_{i}}Y_{1_{j}}^{-1_{j}}Y_{1_{j}}^{-1_{j}} </math>. However, it is not a perturbation expansion but just a mathematical technique. The high rank multi-exchange terms are necessarynot necessarily smaller than low rank terms. In many cases, high rank terms are often more important than low rank terms<ref name="Review"/>.

== Multipolar Exchange Interactions ==