= Electric quadrupole transition
{title2=$E2$}
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>.<NuDat 3 Glossary by National Nuclear Data Center>[Multipolarity, E2 entry]{ref}
<Addition of angular momentum> imposes $|I_i-I_f|\le2\le I_i+I_f$. Thus $2^+\to0^+$ and $2^+\to2^+$ can be E2, whereas $0^+\to0^+$ 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>.
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