Lawrence Berkeley National Laboratory

A search for neutrinoless ββ$$\beta \beta $$ decay processes accompanied with Majoron emission has been performed using data collected during Phase I of the GERmanium Detector Array (GERDA) experiment at the Laboratori Nazionali del Gran Sasso of INFN (Italy). Processes with spectral indices n=1,2,3,7$$n = 1, 2, 3, 7$$ were searched for. No signals were found and lower limits of the order of 1023$$^{23}$$ yr on their half-lives were derived, yielding substantially improved results compared to previous experiments with 76$$^{76}$$Ge. A new result for the half-life of the neutrino-accompanied ββ$$\beta \beta $$ decay of 76$$^{76}$$Ge with significantly reduced uncertainties is also given, resulting in T1/22ν=(1.926±0.094)×1021$$T^{2 u }_{1/2} = (1.926 \pm 0.094)\times 10^{21}$$ yr.