Impact of Shell Structure on Fusion and Fission

Abstract

Fusion and fission are fundamentally important processes to both technology and as probes for the dynamics of quantum many-body systems. Both processes are understood to result from the movement of the system over a potential energy surface. The structure of this potential energy surface arises from the interplay of the nuclear and coulomb potentials and the structure of the quantum shell states. The trajectories over the potential energy surface differ due to the probabilistic nature of single particle transitions at level crossings; raising or lowering the available energy for the trajectory.

To calculate level crossings as a function of internuclear separation, a new implementation of the Asymmetric Two-Centre Shell Model (ATCSM) has been developed, named Orthrus. A brief description of the model is followed by details of the implementation. Errors in the original publication were identified and corrected, including modifications to the defined operators and a full rederivation of the matrix elements. Novel improvements to both parameter selection for the basis elements and the calculation of the non-integer principle quantum numbers, a unique feature of this model, are also discussed in detail.

This work also developed and tested a Monte Carlo-based model of shell occupancy. This model was used to examine the transition between the initial diabatic behaviour near the barrier and the adiabatic regime reached when the system has lost the majority of its kinetic energy, using the Landau-Zener transition model. This novel approach enables an ensemble of trajectories to be generated for a single reaction. Initial tests of the model show that the minimum separation distance reached by the fusing dinuclear system can be attributed to specific outcomes in diabatic transitions between certain levels, which differ between 50 Ti and 48 Ca; relevant to the search for new superheavy elements. Insights into the role of shell structure in fission are obtained from experimental measurements; extracting both the position and number of fission modes.

Recent experimental efforts to measure multimodal mass-asymmetric fission in the preactinides triggered my development of a new analysis method, Panther, for fitting fission-mass distributions. Panther provides an iterative approach to determining the minimum number of fission modes present. In conjunction, a method of pseudodata generation was developed to benchmark the accuracy and precision of fitted results. This analysis showed high precision when determining the positions of mass-asymmetric fission modes, but low precision in their relative yields. The results of a subsampling-based approach to determining the uncertainties from fitting procedures were found to be consistent the local behaviour of the chi-square hypersurface in most cases, and an improvement in cases where the local behaviour differs from observed global behaviour.

The fission of 220 Ra was analysed using low- and high-statistics measurements with Panther and with robustness testing via pseudodata generation. The fission mass distribution was found to contain clear evidence of both the standard-I and standard-II fission modes from the actinides. This agrees with historic measurements of the same reaction but disagrees in the yield of the asymmetric fission. Show more