Three-quadrupole-phonon multiplet
= Three-quadrupole-phonon multiplet
{title2=$S^3(V_2)=V_0\oplus V_2\oplus V_3\oplus V_4\oplus V_6$}
Three identical quadrupole quanta occupy the third <symmetric power> of the five-dimensional spin-two space. Its dimension is $\binom73=35$, and its <irreducible representations> have $J=0,2,3,4,6$, each once. All have positive <parity>. This counts allowed angular states in the ideal harmonic <nuclear quadrupole vibration>; anharmonic interactions can split their energies.