Monte Carlo studies of $\beta$-detector efficiency with GEANT4 for precise $\beta^+$-branching-ratio experiments

We previously reported Monte Carlo (MC) studies of the efficiency of a 1-mm-thick plastic detector to few-MeV electrons with various programs: Geant4, EGSnrc and Penelope. The simulated results were also compared with measured data from standard conversion-electron sources: $^{133}$Ba, $^{137}$Cs and $^{207}$Bi.~[1] These studies were part of our program to test the Electroweak Standard Model via precise measurements of lifetimes, branching ratios and Q-values of superallowed $0^+\rightarrow0^+$ nuclear transitions~[2], which in turn yield the value of the up-down quark-mixing element of the Cabibbo-Kobayasshi-Maskawa (CKM) matrix. The MC studies of the $\beta$-detector efficiency are important for the measurement of precise $\beta^+$-branching-ratios since there is a slight difference in the efficiency of the $\beta$-detector for different $\beta$-branches. This has an additional affect on the number of observed $\beta-\gamma$ coincidences over and above the well known efficiency of our $\gamma$-ray detector. We report here an extension of the comparison between MC calculations and experiment to a $^{60}$Co $\beta$-source, and a study of the influence of peripheral objects on the $\beta$-detector efficiency. [1]~V.V.~Golovko \textit{et. al.} \newblock {\em BAPS 59}, no~6, p.~DH4 83, 2006; \newblock {\em BAPS 52}, no~3, p.~C16 53, 2007; \newblock {\em BAPS 52}, no~9, p.~EH8 83, 2007. [2]~J.C.~Hardy and I.S.~Towner. \newblock {\em PRC}, 71(5):055501, 2005.