Langevin model of low-energy fission

Background: Since the earliest days of fission, stochastic models have been used to describe and model the process. For a quarter century, numerical solutions of Langevin equations have been used to model fission of highly excited nuclei, where microscopic potential-energy effects have been neglected. Purpose: In this paper I present a Langevin model for the fission of nuclei with low to medium excitation energies, for which microscopic effects in the potential energy cannot be ignored. Method: I solve Langevin equations in a five-dimensional space of nuclear deformations. The macroscopic-microscopic potential energy from a global nuclear structure model well benchmarked to nuclear masses is tabulated on a mesh of approximately 107 points in this deformation space. The potential is defined continuously inside the mesh boundaries by use of a moving five-dimensional cubic spline approximation. Because of reflection symmetry, the effective mesh is nearly twice this size. For the inertia, I use a (possibly scaled) approximation to the inertia tensor defined by irrotational flow. A phenomenological dissipation tensor related to one-body dissipation is used. A normal-mode analysis of the dynamical system at the saddle point and the assumption of quasiequilibrium provide distributions of initial conditions appropriate to low excitation energies, and are extended to model spontaneous fission. A dynamical model of postscission fragment motion including dynamical deformations and separation allows the calculation of finalmass and kinetic-energy distributions, along with other interesting quantities. Results: The model makes quantitative predictions for fragment mass and kinetic-energy yields, some of which are very close to measured ones. Varying the energy of the incident neutron for induced fission allows the prediction of energy dependencies of fragment yields and average kinetic energies. With a simple approximation for spontaneous fission starting conditions, quantitative predictions are made for some observables which are close to measurements. Conclusions: This model is able to reproduce several mass and energy yield observables with a small number of physical parameters, some of which do not need to be varied after benchmarking to U-235(n, f) to predict results for other fissioning isotopes.