The Two-Center-Shell-Model for Analyzing the Dynamics of Heavy Ion Collisions

Current findings from using the shell model in nuclear fission and heavy-ion collisions are discussed. Since Nilsson-style one-centre oscillators are incapable of producing the scission configuration seen in fission, a new model based on a two-centre shell has been developed to account for it. The discovery of the compound nucleus in fission and its subsequent creation as a byproduct of heavy-ion collisions has led to the formulation of a hypothesis of fragmentation. The well-established Cranking model and the two-centre shell model (in the Stutinsky style) both show this to be the case. Under certain limiting circumstances, the time-dependent Schroedinger equation is solved for the fission and heavy-ion collision trajectories by using the mass and charge asymmetries of the two components as dynamical coordinates in the Hamiltonian. The concept has significantly increased the yields from binary fission and the methods for creating new elements, including super-heavy elements, by the fusion of two heavy ions. In light of the recent discovery of fissioning of a heavy (compound) nucleus produced in heavy-ion collisions, extensions of the shell model to two and more centers have also been conducted. Based on current trends in experimental data, it seems that characterizing nuclear fission and heavy ion collisions properly requires treating the nucleus as a multi-centre shell. In this article, we take a look back at the two-centre shell model and the main theoretical challenges in describing heavy-ion collisions at high energies.