Transition Matrix Approach to the Solution of the Bateman Equations

The Bateman system of differential equations describes serial radioactive decay. By tracing atoms through the decay chain, one can decompose the original system into a more elementary system. A concise formulation of this elementary system can be given through the use of a transition matrix. The solution to the system can then be derived in matrix form. The simplicity of this latter expression motivated the use of the transition matrix in the development for Portland General Electric of a computer code for activity calculations. The transition matrix approach together with a strategy for minimal storage requirements produced a very efficient code.