(An) analytic relations method for the calculation of actinides concentrations

Abstract

Two methods are in general use for the solution of the nuclide rate equations:one is the numerical integration method and the other is the analytic relations method. In the numerical integration method, three principal difficulties are encountered in employing this method to solve a large system of equations. First, a large amount of memory is required to store the transition matrix and the matrix exponential functions, and second, computational problems are encountered in applying matrix exponential method to a system of equations with widely separated eigenvalues, and third, the results contain truncation errors due to discrete time steps. A typical example that is based on this method is the ORIGEN2 code. The analytic relations method directly integrates the linear differential equations governing radioactive transformation and mass transfer using analytic relations and recursion relations. Thus, the computation is efficient and fast and involves no truncation errors. The code KIGEN was developed on the basis of this method with the assumption of no backward decay reactions in the case of fission products and with the assumption of purely forward or backward decay reactions in the case of actinides. Under the above assumptions, the analytic relations are obtained for each nuclide in terms of decay chain paths, which make it possible to compute the concentration of each nuclide in a relatively short computer time with an acceptable accuracy. However the whole decay paths cannot be considered in KIGEN due to the above assumptions, and, in particular, the errors in the concentrations of actinides become significant after long cooling periods. The accurate calculation of the concentrations of the actinides is of importance because they are major contributors to the health effects to the human body. To calculate the concentrations of actinides accurately, the computer program KIGEN2 was developed in this study by improving KIGEN. It allows both forward and bac...