Solution of depletion chain equations using nonsingular Bateman coefficients

The exact solution of the depletion chain equations for arbitrary values of depletion constants is obtained. New nonsingular coefficients are introduced, and recurrence formulas that provide an efficient and accurate method of calculation are derived. Generality and simplicity of the method are found to be useful in evaluating depletion chains with one hundred or more nuclides in the chain, such as the s-process chain in studies of nucleosynthesis by neutron capture. The method can also be used to check the validity of approximate solutions