Abstract
Superheavy elements (SHE) are defined as elements with proton number Z ≥ 104, and were predicted to exist as early as 1966 using the nuclear shell model. One of the most effective experimental techniques for producing SHE is via the cold fusion of heavy ions. Currently, there is no fully quantum mechanical description that addresses scattering and fusion phenomena involved in the formation of SHE in the cold and hot fusion scenarios. From our literature review, we have determined that a few body quantum dynamical method is a sensible approach to describing collisions that lead to the formation of SHE, in particular for the ability of these methods to incorporate dynamical effects, such as nuclear friction, and quantum effects such as tunnelling.
Our goal is to develop a quantum dynamical method that includes quantum tunnelling, and can be expanded upon in the future to describe nuclear friction and multi-nucleon transfer phenomena. In order to build and test our dynamical model, we model a simpler nuclear collision which will allow us to properly explore the strengths and weaknesses of our approach. In this feasibility study, we benchmark the time-dependent coupled-channel wave-packet (TDCCWP) method results for 16O + 152,154Sm collisions, to those from solving the time- independent Schrödinger equation (TISE) using the iso-centrifugal approximation. Comparisons to experimental data are also present. We generate the transmission coefficients, S-matrix elements, inelastic transition probabilities and differential cross sections for the elastic 0+, and inelastic 2+ and 4+ states in the ground state rotational band of the 152,154Sm targets.
We find that the TDCCWP results reproduce the TISE results for a wide range of energies (including many below the Coulomb barrier) and angular momenta. However, the TDCCWP method has technical limitations when trying to explain results deep (> 5 MeV) below barrier, and results at high angular momenta, which are needed to describe the scattering differential cross sections. We address the former by using a simple yet justified extrapolation method into deep below barrier energies. For the 16O + 152Sm inelastic scattering differential cross sections at 59 MeV, the nearly converged TDCCWP method results are a significant underestimate of the experimental data, but are qualitatively similar to the TISE results. This can be improved by relaxing the iso-centrifugal approximation. Overall, we find that the TDCCWP method is a robust method that can be expanded upon to address more complicated problems such as SHE formation and heavy-ion collisions in general.