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We apply a Langevin model by imposing additive and multiplicative noises to study thermally activated diffusion over a fluctuating barrier in underdamped dynamics. The barrier fluctuation is characterized by Gaussian colored noise with exponential correlation. We present the exact solutions for the first and second moments. Furthermore, we use direct simulations to calculate the asymptotic probability for a Brownian particle passing over the fluctuating barrier. The results indicate that the correlation of the fluctuating barrier is crucial for barrier crossing dynamics. [ABSTRACT FROM AUTHOR]

The three-dimensional Langevin model plus a constraint on the heavy fragment deformation is used to study the fission dynamics for uranium and plutonium isotopes at low excitation energies. The potential energy surface is calculated with the macroscopic-microscopic model based on the two-center shell model. The Werner-Wheeler approximation is used to calculate the inertia tensor and the wall-and-window model is applied to calculate the friction tensor. In this work, the influence of the model parameters on the fission fragment mass distribution is investigated. The fission fragment mass distributions for 234,236,239U and 240Pu at low excitation energies are calculated and compared with the results of gef code as well as the evaluated data of ENDF/B-VIII.0. A nice agreement is found in the comparison, in which the incorporation of the constraint on the heavy fragment deformation plays an important role. In addition, the dependence of the mass distribution on the excitation energies for n+235U fission is also studied within the model. Furthermore, the correlation between the elongation and mass asymmetry at the scission point and the correlations of the fission time with both the elongation and mass asymmetry are studied. This study may shed light on understanding the dynamics of the superlong channel for symmetric fission and the standard channels for asymmetric fission in the gef model and other phenomenological fission models. [ABSTRACT FROM AUTHOR]