Shell theorem for spontaneous emission

We investigate spontaneous emission from excitons beyond the point source dipole approximation and show how the symmetry of the exciton wave function plays a crucial role. We find that for spherically symmetric wave functions, the Purcell effect is independent of the wave function size and therefore is given exactly by the dipole approximation theory. This surprising result is a spontaneous emission counterpart to the shell theorems of classical mechanics and electrostatics and provides insights into the physics of mesoscopic emitters as well as great simplifications in practical calculations.