Analytical Solution of Smoluchowski Equation in Harmonic Oscillator Potential

Non-equilibrium fission has been describrd by diffusion model. In order to describe the diffusion processanalytically,the analytical solution of Smoluchowski equation in harmonic oscillator potential is obtained. This analyticalsolution is able to describe the probability distribution and the diffusive current with the variable x and t. The resultsindicate that the probability distribution and the diffusive current are relevant to the initial distribution shape,initialposition,and the nuclear temperature T;the time to reach the quasi-stationary state is proportional to friction coefficientβ,but is independent of the initial distribution status and the nuclear temperature T. The prerequisites of negativediffusive current are justified. This method provides an approach to describe the diffusion process for fissile process incomplicated potentials analytically.