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a) By looking at the V^(2) tensor one sees that it is diagonal, thus the chosen axis system is already a principal axis system. Also V_xx = V_yy, so the system has axial symmetry.
b) The axial symmetry corresponds to rotation around the z-axis and the EFG is a property of the electrons. When we rotate the system around the z-axis, nothing happens to the electrons as they lie on the z-axis, thus the EFG doesn’t change.
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