Quantum dot shell closure

Filling a degenerate orbital shell produces a larger addition energy for the next electron. In a circular two-dimensional harmonic potential, shell $q=n_x+n_y$ has $q+1$ orbitals and capacity $2(q+1)$ including spin. Cumulative closed-shell occupancies are $(q+1)(q+2)=2,6,12,20,\dots$. Charging and orbital contributions must be separated, and anisotropy or exchange can split the ideal shells.