Cross section of the induced neutrinoless double β decay

The neutrinoless double β decay is a process, that would prove the Majorana nature of neutrinos. But the process has not been measured yet. Therefore, the cross section and the expected number of events for the neutrinoless double β decay induced with energetic neutrinos was calcu- lated in this report. The evaluation of the expected number of events in 10 yr is smaller than $10^{−15}$ for energies of the inducing neutrinos up to 100 MeV. However, the cross section grows more than linearly with the energy, so the interaction could be measurable at higher energies. Indu- cing the decay with a scalar dark matter particle also does not lead to a measurable rate, as the expected number of events in 10 yr is smaller than $10^{−43}$ for the dark matter mass $m_{DM}$ = 1 MeV.