Absolute fraction of emitted Ps determined by GEANT4 supported analysis of gamma spectra

The fraction of positronium (Ps) emitted from a surface of a germanium single crystal at high temperature is usually assumed to approach unity at zero positron implantation energy. In the experiment, however, the determination of the absolute Ps fraction is not straightforward since recording a reference spectrum with $100%$ Ps formation remains demanding. We use geant4-simulated detector responses to $2\ensuremath{\gamma}$ and $3\ensuremath{\gamma}$ radiation sources mimicking positron and Ps annihilation inside the (coincidence) Doppler-broadening spectrometer at NEPOMUC, FRM II, in order to derive a reliable value for the Ps fraction reemitted from a Ge(100) target heated close to its melting point. Analysis of the measured spectra by fitting the simulated spectra shows an absolute value of $72\ifmmode\pm\else\textpm\fi{}4%$ maximum Ps formation, contradicting the $100%$ assumption.