Use of the GEANT4 code in precise measurements of $\beta^+$-branching-ratios

In order to determine the vector coupling constant and to test the unitarity of the Cabibbo-Kobayashi-Maskawa matrix one has to make precise measurements of nuclear masses, $\beta$-branching ratios and halflives~[1]. The measurements of halflives and branching ratios are performed in a simple, but very precise counting station at our institute. A typical ``on-line'' branching ratio experiment consists of collection of the accelerator-produced radioactive nuclei with a tape transport station that rapidly moves the collected sample to a location between a scintillaton detector and a well-calibrated high-volume HPGe $\gamma$-detector. Data are collected with a PC station for all $\beta$-$\gamma$ coincident events. In order to completely understand all systematic effects contributing to the branching ratio measurements one must determine the relative efficiency of the scintillator as a function of $\beta$-particle energy, because the various $\gamma$-ray peaks correspond to $\beta$-transitions with different end-point energies and their observed relative intensities will be affected by the slight differences in $\beta$ detection efficiency. Previous work~[2] has reported a response function of $\beta$-particles from standard open $\beta$-sources. Here we present a comparison with measurements obtained in the ``on-line'' geometry configuration. [1] J.~C.~Hardy and I.~S.~Towner. {\em PRC}, 71(5):055501, 2005. [2] V.V.~Golovko et. al. {\em BAPS 59}, no~6, p.~DH4 83, 2006.