A formulation of the linear equations of the Thomas method into simple matrices

The Thomas method for the determination of the air concentrations of each of the short half-life descendants of radon is a standard method for the determination of those quantities. The set of three linear equations which arise in the method have coefficients which depend on the sampling time, the waiting time between the end of sampling and the start of counting as well as on the three independent counting times used in determining the alpha activity of the sample. A consistent formulation of the equations which describe the collection, decay and counting of the sample allows a matrix factorisation of the equations and a simplified determination of the coefficients for different sampling, waiting and counting times. Use of this matrix method will allow researchers and radiation safety personnel to vary the sampling and counting schedules of the Thomas method to fit the experimental or environmental conditions of their measurement. Total counting times less than one thousand seconds may, however, introduce significant statistical uncertainty in the results and care should be taken in interpretation when short total counting times are used. 3 refs., 1 fig