Background Estimation Studies for Positron Double Beta Decay

The study of neutrinoless double beta decay has attracted much attention as it can provide valuable information about the mass and the nature of the neutrino. The double beta decay (DBD) itself is also of interest in nuclear physics. While DBD has been observed in about a dozen nuclei, the positron double beta decay ($\beta^{+}\beta^{+}$/EC-$\beta^{+}$) continues to be an elusive. An important signature for $\beta^{+}\beta^{+}$ decay is the simultaneous emission of four 511 keV gamma rays and the coincident detection of these gamma rays can improve the measurement sensitivity. This paper presents an estimation of sensitivity for EC-$\beta^{+}$ and $\beta^{+}\beta^{+}$ employing coincidence measurement with two high purity Ge (HPGe) detectors. Simulations for coincident detection efficiency (${\epsilon}_c$) of 511 keV gamma rays with two HPGe detectors have been carried out using GEANT4 for different source geometries to optimize the mass efficiency product (M${\epsilon}_c$). The source of size $55\,mm \times 55\,mm \times 5\,mm$ (thickness) sandwiched between the front faces of the detectors were found to be optimal for 2 pairs of 511 keV gamma rays in the present detector setup. The coincident background is estimated at the sea level with moderate Pb shielding. With this setup, the sensitivity for T$_{1/2}$ measurement of EC-$\beta^{+}$ in $^{112}$Sn and $\beta^{+}\beta^{+}$ in $^{106}$Cd is estimated to be $\sim$10$^{19}$ - 10$^{20}$ y for 1y of measurement time.