 Nuclear gamma-ray multipole selection rules

A real photon emitted in gamma decay carries a radiation multipole of integer angular momentum $L\ge 1$. The triangle rule gives the displayed range. An electric multipole $EL$ requires ${\pi }_f/{\pi }_i=(-1{)}^L$, while a magnetic multipole $ML$ requires ${\pi }_f/{\pi }_i=(-1{)}^{L+1}$. There is no real single-photon $E0$ decay; an electric monopole transition can instead proceed through internal conversion or, above threshold, pair creation. In the long-wavelength regime $kR\ll 1$, increasing $L$ usually strongly suppresses the rate, but nuclear transition matrix elements and collective enhancement can make an allowed lower multipole weaker than a higher one.