Nuclei with zero-spin and high excitation energies (more than about 1.022 MeV) also can't rid themselves of energy by (single) gamma emission due to the constraint imposed by conservation of momentum, but they do have enough decay energy to decay by pair production. In this type of decay, an electron and positron are both emitted from the atom at the same time, and conservation of angular momentum is solved by having these two product particles spin in opposite directions.