Statistical description of a point reactor in the absence of delayed neutrons

The effect of finite correlation time of the stochastic reactivity on the moments of the neutron density for a point reactor is studied in the absence of delayed neutrons. The time development of the moments is calculated. The exact form of the Fokker-Planck equation is derived for a delta-correlated reactivity from the stochastic Liouville equation. The stationary probability distribution is obtained from the Fokker-Planck equation. The probability distribution so obtained comes out to be non-Gaussian in agreement with the result of Williams. The distribution in the absence of deterministic source reduces to Cauchy distribution under some conditions. (orig.)