Coherently rotating hyperdeformed quasimolecules in 12C +24Mg scattering?

We present an interpretation of oscillations in the energy autocorrelation functions for [Formula Presented] scattering assuming that the scattering process can be treated in terms of formation and decay of a dinucleus with strongly overlapping resonances. It is shown that these oscillations can be interpreted in terms of a slow spin decoherence and time-space localization of a coherently rotating hyperdeformed intermediate system. This coherent rotation allows us to reconstruct the time evolution of the long-lived intermediate dinucleus back into the past as far as the moment of its formation. Our analysis indicates that for spin values [Formula Presented] and at ≃50 MeV excitation energy hyperdeformation (3:1) of [Formula Presented] terminates and is replaced by (2:1) deformation. New experiments are proposed to test our interpretation.