Improved Čerenkov counting techniques based on a free parameter model

•The TDCR-Čerenkov method was extended and improved.•The model comprises the light dispersion in water.•The wavelength-dependent PMT response is taken into account.•Potential differences of the PMT efficiencies are taken into account.

In the past few years, two Čerenkov methods were developed to make activity measurements of high-energy beta emitters in liquid scintillation counters with two or three photomultiplier tubes (PMTs) possible. Both methods are based on a free parameter model and make use of the Frank and Tamm theory for the emission of Čerenkov light. In this article, additional effects are discussed and further improvements are presented. The dependence of the refractive index of water on the wavelength can now be taken into account, which has also an influence on the upper limit of the wavelength region for the production of Čerenkov light. In addition, the dependence of the PMT response on the wavelength is taken into account. Finally, it is possible to take a potential asymmetry of efficiencies in a system with three PMTs into account. To this end, three free parameters are assigned to each individual PMT and then determined by means of a downhill simplex optimization algorithm. The computed counting efficiencies for a triple-to-double coincidence ratio (TDCR) system were compared with experimental data for 32P, 89Sr, and 90Y.