That the Electron Field Gradient tensor has axial symmetry in its
Principle Axis System can be determined from:
– the equation: Because the representation of the EFG tensor is a
diagonal matrix, the tensor itself as a mathematical object is invariant
to rotations and space translations.
– the picture of a toy model presents two fixed -e charges, equidistant from OZ origin;
moreover the dumb-bell is mounted at (0,0,0) point and while rotating it draws cone-like
currves, that are surely axially symmetric.