The transport of short-lived fission products close to the fuel surface

The diffusion equation is an approximate description of fission-product transport in UO2. Although it is an extremely good approximation for stable and long-lived products its use is suspect for short-lived species when the frequency of diffusive jumps becomes comparable with the decay constant. An alternative treatment of the transport of short-lived fission products is presented in which an integral equation is developed by assuming only that transport takes place by isotropic jumps of a fixed length. This equation is solved numerically. The solution shows both diffusional and knock-out characteristics, and provides a method for linking these processes. A diffusion equation is solved with a 'zero inward current' boundary condition to obtain similar features analytically. The formulation explains why diffusion theory should always be valid for thermally activated diffusion at high temperatures. It also offers new prospects for gaining information on the poorly understood in-pile phenomenon of athermal diffusion, and provides a general mathematical framework for discussing near-surface transport. (orig.)