Observation of quantum supershells in clusters of sodium atoms

ATOMIC clusters of sodium and other simple metals are known to exhibit a shell structure, giving rise to enhanced stability at certain 'magic numbers' of constituent atoms1–3. Balian and Bloch have shown4 that such shells are the likely result of particularly stable electronic structures: electrons in a spherical cavity (approximating the potential in the clusters) follow semiclassical triangular or square orbits, leading to a shell structure similar to that in atoms5, and stable configurations occur at magic numbers proportional to the cube root of the number of electrons. Balian and Bloch4 also predicted that the existence of both triangular and square orbits, with slightly different periodicities of their magic numbers, should lead to a 'quantum beating' effect that imposes a low-frequency envelope on the periodic variation in cluster stability with increasing size, in effect creating an additional 'supershell' structure. Here we report the observation of this supershell effect in sodium clusters with up to 3,000 constituent atoms.