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1)The matrix symmetry reveals the PAS. It is diagonal, which means that the chosen axis is PAS (tensor of rank 2 has vanishing elements from the 5 elements in total (specifically +/-1 terms)).
2)The EFG will have the smallest magnitude when nucleus dumbbell is orientated parallel to the electron cloud, and has maximum magnitude when it nucleus dumbell is parallel to the xy plane (I try to visualize the electric field lines and make this conclusion).
The axial symmetry would disappear if the charge distribution along the nucleus dumbell wouldn’t be equal, similarly if one of the electrons would instead be muon (but I’m not exactly sure about these statements).
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