The $^{76}$Ge(n,p)$^{76}$Ga reaction and its relevance to searches for the neutrino-less double-beta decay of $^{76}$Ge

The $^{76}$Ge(n,p)$^{76}$Ga reaction and the subsequent $\beta $ decay of $^{76}$Ga to $^{76}$Ge has been used to excite the 3951.9 keV state of $^{76}$Ge, which decays by emission of a 2040.7 keV $\gamma $ ray. Using HPGe detectors, the associated pulse-height signal may be undistinguishable from the potential signal produced in neutrino-less double-beta decay of $^{76}$Ge with its Q-value of 2039.0 keV. In the neutron energy range between 10 and 20 MeV the production cross section of the 2040.7 keV $\gamma $ ray is approximately 0.1 mb. In the same experiment $\gamma $ rays of energy 2037.9 keV resulting from the $^{76}$Ge(n,$\gamma $)$^{77}$Ge reaction were clearly observed. Adding the $^{76}$Ge(n,n${'}$$\gamma $)$^{76}$Ge reaction, which also produces the 2040.7 keV $\gamma $ ray with a cross section value of the order of 0.1 mb clearly shows that great care has to be taken to eliminate neutron-induced backgrounds in searches for neutrino-less double-beta decay of $^{76}$Ge.