Optimisation of efficiency extrapolation functions in radioactivity standardisation

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When radioactivity is measured by 4πβ-γ efficiency extrapolation the data is commonly fitted to a linear function, but also to a polynomial function of second or third order if this proves necessary. In order to justify the empirical fitting procedure, we compared the experimental results with some functions which could be expected theoretical grounds. The most suitable function was a linear function at high 4π counting efficiencies joined on to a second-order function at low 4π counting efficiencies, while a third-order polynomial function without second-order term produced accurate results regardless of the fitting region.