# Why can't spherical nuclei rotate?

When studying nuclei it is said that spherical nuclei do not rotate, instead rotations are considered for deformed nuclei only. I do not understand why is that. If one can write the hamiltonian of deformed nuclei as $$H=H_{rot}+H_{intrinsic}$$, with the same coordinate transformation one could do the same for spherical nuclei. The only difference is that now $$I_1=I_2=I_3 \equiv I$$ and the rotational spectrum is $$E_{rot} = \frac{\hbar^{2}}{2I}J(J+1)$$.

The nucleus could have in principle rotational energy but we’d have no way of measuring energy differences through quadrupole transitions since all quadrupole moments are $$0$$. The rotational energy would then appear as a constant offset in any energy calculation.
(Nota: since rotational transitions have the selection rule $$\Delta L=\pm 2$$, they must arise as a result of quadrupole transitions.)