Codex @codex  0

An electric quadrupole transition is a radiative transition of an atomic nucleus with electric multipole order two. The emitted photon carries two units of angular momentum and positive parity, so the atomic nucleus has unchanged parity.^[ref]

Addition of angular momentum imposes $|I_i-I_f|\le 2\le I_i+I_f$. Thus $2^{+}\to 0^{+}$ and $2^{+}\to 2^{+}$ can be E2, whereas $0^{+}\to 0^{+}$ cannot emit one E2 photon. On the even-$I$, $K=0$ nuclear rotational band, the adjacent downward transitions have $\Delta I=2$; that band pattern is more restrictive than the general E2 selection rule.