The statistical model of nuclear fission: from Bohr-Wheeler to heavy-ion fusion-fission reactions

Abstract: The first theory of the rate and temperature dependence of nuclear fission reactions was put forward as early as 1939 by Niels Bohr and John A. Wheeler. Their theory uses a transition-state argument, well known especially to physical chemists, that was already being used to rationalise the temperature dependence of the rates of chemical reactions since the 1930's. Their model however relies on equilibrium statistical mechanics, and neglects two important, if not essential, aspects of fission. The first aspect is the nonequilibrum decay process of the parent nucleus which can be described as the decay of a thermodynamically metastable state. The second aspect is the effect of "viscous" dissipation in the deformation of the unstable nucleus which is especially important for large nuclei. These problems were addressed by Kramers in a remarkable 1940 paper where he derived expressions for generic decays of metastable states in the presence of dissipation. This line of research to include dissipation in the description of nuclear fission has been intensively pursued in the last decades. After briefly outlining the fundamentals of theoretical modelling of nuclear fission of heavy nuclei from the point of view of statistical models, I will discuss some recent developments in the regime of high-excitation energy, which is encountered for example in heavy-ion induced fusion-fission reactions. In this regime, the exp(U/T) Kramers-Arrhenius dependence of fission time on nuclear temperature is shown to break down dramatically. A recent model [Eccles, Roy, Gray, Zaccone, Phys. Rev. C 96, 054611 (2017)] solves this problem and leads to the correct temperature dependence also in the high energy regime. An application to the example of heavy-ion induced fusion-fission of Thorium will be presented.

Short bio - Dr Alessio Zaccone (PhD ETH Zurich, 2010) is a University Lecturer at the University of Cambridge in the Department of Chemical Engineering and Biotechnology, and the Head of the Statistical Physics Group, since 2015. Previously he has been a Professor of Theoretical Physics at the Technical University Munich, Germany. He is also the Anthony L. Lyster Fellow in Physics at Queens' College.