Two neutrino double beta decay of $^{76}$Ge to excited states of $^{76}$Se has been studied using data from Phase I of the GERDA experiment. An array composed of up to 14 germanium detectors including detectors that have been isotopically enriched in
$^{76}$Ge was deployed in liquid argon. The analysis of various possible transitions to excited final states is based on coincidence events between pairs of detectors where a de-excitation $gamma$ ray is detected in one detector and the two electrons in the other. No signal has been observed and an event counting profile likelihood analysis has been used to determine Frequentist 90,% C.L. bounds for three transitions: ${0^+_{rm g.s.}-2^+_1}$: $T^{2 u}_{1/2}>$1.6$cdot10^{23}$ yr, ${0^+_{rm g.s.}-0^+_1}$: $T^{2 u}_{1/2}>$3.7$cdot10^{23}$ yr and ${0^+_{rm g.s.}-2^+_2}$: $T^{2 u}_{1/2}>$2.3$cdot10^{23}$ yr. These bounds are more than two orders of magnitude larger than those reported previously. Bayesian 90,% credibility bounds were extracted and used to exclude several models for the ${0^+_{rm g.s.}-0^+_1}$ transition.
An optimized digital shaping filter has been developed for the GERDA experiment which searches for neutrinoless double beta decay in 76Ge. The GERDA Phase I energy calibration data have been reprocessed and an average improvement of 0.3 keV in energy
resolution (FWHM) at the 76Ge Q value for 0 ubetabeta decay is obtained. This is possible thanks to the enhanced low-frequency noise rejection of this Zero Area Cusp (ZAC) signal shaping fillter.
A search for neutrinoless $betabeta$ 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 were searched for. No signals were found and lower limits of the order of 10$^{23}$ yr on their half-lives were derived, yielding substantially improved results compared to previous experiments with $^{76}$Ge. A new result for the half-life of the neutrino-accompanied $betabeta$ decay of $^{76}$Ge with significantly reduced uncertainties is also given, resulting in $T^{2 u}_{1/2} = (1.926 pm 0.095)cdot10^{21}$ yr.
