Dynamical Effects in Fission Process by the Langevin Equation

 After the discovery of nuclear fission by Hahn and Strassmann in 1939, Petrzhak and Flerov discovered the spontaneous and low-energy fission of ²³⁸U in 1940. In the 1960s, studies on fission became prevalent with the development of new devices and experimental techniques. Strutinsky reported the precise estimation of nuclear energy by considering microscopic shell effects, which drastically alter the landscape of the potential energy surface. Various kinds of fission phenomena become prominent.

 Many theoretical attempts have been made to quantitatively explain this exotic phenomenon. The precise introduction of shell correction energy in the potential energy landscape in the fission process has been found to be inevitable. The study of the dynamical model calculation to describe the fission process commenced at the end of the 1980s. In the model using the Langevin equation, the time evolution of nuclear shape was analyzed. We noticed the characteristic nuclear-shape oscillation in the Langevin trajectories.

 The main motivation of this analysis is to elucidate the characteristic nuclear-shape oscillation induced by a random force in the Langevin equation and its impact on the fission process. The characteristic random oscillation originates from the requirement of an overdamped condition. The properties of the friction tensor in the equation reveal that the directional nuclear shape fluctuations originate in the subspace of nuclear deformation. Our calculations exhibit a good agreement with the fission data for fermium isotopes, where the fission-fragment mass distribution changes dramatically from the asymmetric shape to the sharp symmetric shape as the masses of the fissioning Fm isotopes increase.