Content deleted Content added
No edit summary |
No edit summary |
||
Line 129:
:<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 (see next section) can be considered as a two steps dipole-dipole interaction. For example, <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>, so the one step quadrupole transiton <math> Y_{2_{i}}^{+2_{i}} </math> on site <math> i </math> now becomes a two steps of dipole transition <math> Y_{1_{i}}^{+1_{i}}Y_{1_{i}}^{+1_{i}} </math>. Hence not only inter-site-exchange but also intra-site-exchange terms appear (so called multi-exchange). If <math> J </math> is even larger, one can expect more complicated intra-site-exchange terms would appear. However, one has to note that it is not a perturbation expansion but just a mathematical technique. The high rank multi-exchange terms (four or more dipole terms) are not necessarily smaller than low rank terms (two dipole terms). In many cases, high rank terms are more important than low rank terms.<ref name="Review"/>
== Multipolar Exchange Interactions ==
| |||