quadrupole operator

[Art Willems]

1) First of all, the most important part of the EFG expression is the matrix. As we can see, it is symmetric, meaning taking the transpose of the matrix does not change a thing. We have symmetry in the x-y direction. Secondly, the determinant of the matrix is zero.The determinant is actually the measure for the span of a 3D shape. This means that the EFG must be axially symmetric.

2) From the figure we can derive that the flipping the configuration from the x-axis to the y-axis will not make a difference. Vice versa yields a similar conclusion. The same can be said if we flip the z-axis. Therefore the EFG tensor is axially symmetric.

[Art Willems]

Pardon me, when I said determinant, I meant trace. In the trace we can shift the terms around, so we can see this as a way of mirroring.

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