  The data of the Heidelberg-Moscow double beta decay experiment for the
measuring period August 1990 - May 2000 (54.9813 kg y or 723.44 molyears),
published recently, are analyzed using the potential of the Bayesian method for
low counting rates. First evidence for neutrinoless double beta decay is
observed giving first evidence for lepton number violation. The evidence for
this decay mode is 97% (2.2\sigma) with the Bayesian method, and 99.8% c.l.
(3.1\sigma) with the method recommended by the Particle Data Group. The
half-life of the process is found with the Bayesian method to be T_{1/2}^{0\nu}
= (0.8 - 18.3) x 10^{25} y (95% c.l.) with a best value of 1.5 x 10^{25} y. The
deduced value of the effective neutrino mass is, with the nuclear matrix
elements from [Sta90,Tom91] < m >= (0.11 - 0.56) eV (95% c.l.), with a best
value of 0.39 eV. Uncertainties in the nuclear matrix elements may widen the
range given for the effective neutrino mass by at most a factor 2. Our
observation which at the same time means evidence that the neutrino is a
Majorana particle, will be of fundamental importance for neutrino physics.
PACS. 14.69.Pq Neutrino mass and mixing; 23.40.Bw Weak-interaction and lepton
(including neutrino) aspects 23.40.-s Beta decay; double beta decay; electron
and muon capture.
