Supershell quantization of staggering patterns in the rotational bands of the iodine molecule

In this paper we recall the description of molecular spectral staggering in terms of transition energies between neighboring rotational states and then describe the fitting procedure used to derive these energies from available experimental data, making use of theoretical models involving both Dunham-type expansions and q-deformed rotators. Using this procedure, we investigate $\Delta J=2\mathrm{}$ staggering in a few rotational bands of the homonuclear iodine molecule and analyze the quasiperiodic patterns that appear from the lowest to the highest values of angular momentum J. In addition to parity splitting, these patterns disclose a supershell structure involving magic numbers formally similar to those occurring in atom clusters. We propose to relate molecular staggering to tiny oscillations in the electron-level density induced by the rotating nuclear frame.