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What is the magnetic quadruple moment of a nuclei in cylindrical coordinates?

The quadrupole moment of a nucleus is zero in spherical coordinates but in the cylindrical coordinates it can't be vanished. In cylindrical coordinates we are not able to use jlms and its very difficult to solve the integral as the expectation value of the magnetic quadrupole operator.

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This doesn't sound right to me. A quadrupole moment can be expressed as a tensor, and a tensor can't be zero in one set of coordinates and nonzero in another. If you can express a tensor in one set of coordinates, you can always reexpress it in some other set of coordinates just by using the tensor transformation law. –  Ben Crowell May 18 '13 at 22:21
    
can you introduce a reference to me to find the topic about this tensors? –  Hamid Ghaffari May 18 '13 at 22:24
    
In general, the static quadrupole moment of a nucleus, in the body-fixed frame, can be found just by using the nucleus's deformation and the classical definition of the quadrupole moment. E.g., many nuclei in their ground states are nearly ellipsoidal, so you can use the classical equation for the quadrupole moment of a uniformly charged ellipsoid. No quantum mechanics is required. –  Ben Crowell May 18 '13 at 22:25
    
en.wikipedia.org/wiki/Tensor –  Ben Crowell May 18 '13 at 22:25
    
Quadrupole moments make little sense in cylindrical coordinates, and treating an atomic nucleus as a cylindrical object can only get you in trouble. What makes you think the quadrupole moment is zero to begin with? –  Emilio Pisanty May 19 '13 at 1:16

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