Neutron-capture cross-section measurements of $^{74}$Ge and $^{76}$Ge in the energy region 0.4-14.8 MeV for neutrinoless double $\beta $ decay applications

Fast neutron capture cross sections for the reactions $^{74}$Ge(n,$\gamma $)$^{75}$Ge and $^{76}$Ge(n,$\gamma $)$^{77}$Ge have been measured in the neutron energy region 0.4-14.8 MeV with the activation method. The results are important to identify backgrounds in the neutrinoless double-$\beta $ decay experiments GERDA and MAJORANA, which use germanium as both source and detector. Isotopically enriched targets which consisted of 86\% of $^{76}$Ge and 14\% of $^{74}$Ge were irradiated with mono-energetic neutrons produced via $^{3}$H(p,n)$^3$He, $^2$H(d,n)$^3$He and $^3$H(d,n)$^4$He reactions. The cross sections were determined relative to $^{197}$Au(n,$\gamma $)$^{198}$Au, $^{115}$In(n,n$^{'}$)$^{115m}$In and $^{197}$Au(n,2n)$^{196}$Au standard cross sections. The activities of the products were measured using high-resolution $\gamma $-ray spctroscopy. The present results are compared with the evaluated data from ENDF/B-VII.1 and TALYS.