- #1
kelly0303
- 579
- 33
Hello! I am confused about the definition of the quadrupole moment in nuclei. One definition I found, in Wong, says that the quadrupole moment of a nucleus is given (ignoring some numerical constant) by: $$<J,M=J|r^2Y_{20}|J,M=J>$$ so the expectation value of a second order spherical harmonic (times ##r^2##) in the state with maximum M of the nucleus. However, given that we have a second order tensor (##Y_{20}##), for a nucleus with ##J=0## we can't have a quadrupole moment (this follows from the addition rules of angular momentum). However, there are several nuclei that have a (pretty big) quadrupole deformation in the ground state (for example they show a clear rotational spectrum, which is possible only if the nucleus is deformed), yet their ground state has ##J=0## (for example Hf). How is this possible, shouldn't a ##J=0## state indicate a spherical nucleus? Can someone explain this to me? Thank you!