NON-EQUILIBRIUM STATISTICAL THEORY OF NUCLEAR FISSION MASS DISTRIBUTION

Abstract：

We consider the fission process from saddle point to scission point as a non-equili-brium transport process obeying the Master equation, which can be reduced into theform of Fokker-Planck equation approximately. Taking the mass asymmetry coordinatex as the macrovariable, the nuclear fission can be considered as a diffusion process inx space, the drift velocity v(x,t), which is a non-linear. function of x, is proportionalto the gradient of the potential surface of fission nucleus in x space. The kinetics ofnuclear deformation from saddle point to scission point is represented by the variationof v(x,t) with time t phenomenologically. Assuming the mass distribution at saddlepoint is a symmetric one, and to solve the Fokker-Planck equation by means of Su-zuki's scaling limit approximation method, we get a solution which becomes a double-Gaussian asymmetric distribution on the potential valley after a time interval longenough, the width of mass distribution is proportional to nuclear temperature and in-versely proportional to relative depth of the potential valley. In the case of ²³⁵U(n,f),the time interval evaluated from saddle point to scission point would be larger than1.6×10^-21 second, while it has arrived at the statistical equilibrium state. The Fong'sstatistical theory of nuclear fission is proved to be the case of stationary solution of theFokker-Planck equation exactly.