A Langevin equation description of dynamic nuclear deformation

A model of dynamic nuclear deformation is developed in which the collective degrees of freedom of a nucleus are coupled to subcollective degrees of freedom by means of friction and fluctuation forces in the equations of motion for the collective degrees of freedom. The Langevin equation is a stochastic differential equation that includes friction and fluctuation terms, so it is used as the equation of motion in this model. The necessary inertia and friction parameters are obtained using the Werner-Wheeler approximation, and the fluctuation parameter is obtained by applying the fluctuation-dissipation theorem. It is shown that a second order Runge-Kutta method for numerical solution of the Langevin equation is much better than the commonly employed Euler method. Poor random number generators are shown to have serious negative effects in a Langevin simulation. Several case studies are described, including a model employing the (c, h, α) shape parameterization with h set equal to zero to reduce it to two dimensions. This parameterization allows scission into fragments of varying relative sizes, providing a suitable model for study for mass distributions, transient times, and the importance of dynamics on distributions and scission rates