A quantal toy model for heavy-ion collisions

A one-dimensional toy model of two moving finite boxes is analysed with respect to quantal phenomena associated with heavy-ion dynamics at low and intermediate energies. Special attention is payed to the relation between energy and momentum of the nucleons inside and outside the time-dependent mean field. A Wigner transformation of the one-body density matrix in space and time allows for a unique comparison with classical phase-space dynamics. It is found that high momentum components of the nuclear groundstate wave function approximately become on-shell during the heavy-ion reaction. This leads to the emission of energetic nucleons which do not appear classically. It is furthermore shown, that the low lying eigenstates of the dinuclear system for fixed time are only partly occupied throughout the reaction at intermediate energies. This opens up final phase space for nucleons after producing e.g. a pion or energetic photon. Though the present model does not allow for a reliable calculation of double differential nucleon spectra, pion or photon cross sections, it transparently shows the peculiar features of quantum dynamics in heavy-ion collisions.