Measurement of the Electron capture of $^{76}$As into the first excited state of $^{76}$Ge
The neutrinoless double beta decay of $^{76}$Ge is searched for in the large-scale experiment LEGEND. The measurement of the half-life of this process would give access to the neutrino mass using the nuclear matrix element. Experimentally the contribution of the $^{76}$As ground state to the nuclear matrix element can be investigated via the branching ratios of its $β^-$ and electron capture decay. While energetically, the electron capture of $^{76}$As into the first excited state of $^{76}$Ge is possible and was measured once before this work, the electron capture into the $^{76}$Ge ground state was not observed yet. The present study investigates the branching of $^{76}$As that is produced via $^{75}$As(n,$γ$) on a thin As$_2$O$_3$ sample. A silicon drift detector measures characteristic X-rays emitted by the germanium atoms caused by an inner vacancy after the electron capture. A high-purity germanium detector is used to measure the 562.9$\,$keV $γ$-rays emitted after electron capture into the excited state. Investigation of coincident signals in both detectors leads to the branching ratio of the $^{76}$As electron capture into the first excited state of $^{76}$Ge of $ν_{\mathrm{EC}^\ast} = (0.0572 \pm 0.0029 (\mathrm{stat.}) \pm 0.0074(\mathrm{syst.}))\%$. This is the first measurement with the full uncertainty budget quantified.