The Determination of the Activity of Serially Transforming Radionuclides by a Recursive Technique

The recursive formalism is a neat, compact and efficient way to express the analytical solution to non-feedback compartment models involving time-independent transfer coefficients. In problems dealing with radioactive decay, build-up and mass transfer, the complete time dependence is given by recursive functions which are easy to calculate, interpret and memorise. The objectives of this paper are to show how the recursive formalism can be applied to air-sampling of radon daughters and to illustrate the use of suitable computer programming codes for an efficient calculation of the involved functions. The mathematics involves three different functions describing decay of activity, build-up of activity and cumulated number of decays during sampling. Once the time dependence of a mother nuclide activity is known, the time behaviour of the daughter activity is obtained recursively as a relative difference. This simple scheme of calculation is applicable to an arbitrary number of consecutive generations. Different air-sampling regimes will be treated and the recursive formalism as coded in different program languages will be exemplified. It is concluded that the recursive formalism is well suited for use with computers and that the formalism greatly simplifies the mathematics describing decay, build-up and mass transfer of serially decaying nuclides.