Quadrupole interaction in high field.
Contributor: Y. Millot
Quadrupole interaction in high magnetic field
The first two terms in the Magnus expansion of the quadrupole
interaction are:
(1) the first-order quadrupole interaction
(一階四極矩作用力),
and (2) the second-order quadrupole interaction
(二階四極矩作用力),
where V(2,i) are the spherical components of the
second-rank EFG tensor. In its principal-axis system, the components
of this tensor are:
The direct products of the EFG second-rank irreducible
tensors can be expressed as higher rank spherical tensors
W using the Clebsch-Gordan coefficients.
Since V(2,2)V(2,-2) =
V(2,-2)V(2,2) and V(2,1)V(2,-1)
= V(2,-1)V(2,1), we simply have
where W(3,0) = W(1,0) = 0.
The second-order quadrupole interaction becomes:
The eigen values of the fourth-rank EFG tensor W in the spherical tensor representation are:
