Several Physics SE questions/answers note the difference between intrinsic and spectroscopic electric quadrupole moments:
- Why do spin-1/2 nuclei have zero electric quadrupole moment?
- Measurement of (intrinsic) electric quadrupole moment of neutron?
- Can an electron have an electric quadrupole moment?
Also, and even more commonly, questions/answers simply refer to "electric quadrupole moments" or "nuclear quadrupole moments" which I think usually refers to spectroscopic electric quadrupole moments, especially when the Wigner-Eckart theorem is invoked.
Could someone please explain mathematically and conceptually the difference between intrinsic and spectroscopic electric quadrupole moments?
