Depolarisation of spherical-membrane quantum well: Gap renormalisation for closed-shell fullerenes

An anomalous large level shift is newly found to correct the one-electron spectrum of a closed-shell carbon nanocluster, for example, the spectrum which was described within the model of a thin quantum well rolled into a sphere. As a result of the interaction with zero-point oscillations of the confined modes of the electric field, the one-electron energy levels heighten. The depolarization depends on the electron momentum, why it does not shift the rotational spectrum as a whole. Surprisingly the shift in a spherical closed-shell cluster of an arbitrary size is described by an universal law. The non-equidistant shift of the levels results in an increase of an one-electron gap by 1.4 times.