  The Neutrinoless double beta Decay allows to determine the effectice Majorana
electron neutrino mass. For this the following conditions have to be satisfied:
(i) The neutrino must be a Majorana particle, i. e. identical to the
antiparticle. (ii) The half life has to be measured. (iii)The transition matrix
element must be reliably calculated. (iv) The leading mechanism must be the
light Majorana neutrino exchange. The present contribution studies the accuracy
with which one can calculate by different methods: (1) Quasi-Particle Random
Phase Approach (QRPA), (2) the Shell Model (SM), (3) the (before the variation)
angular momentum projected Hartree-Fock-Bogoliubov method (PHFB)and the (4)
Interacting Boson Approach (IBA). In the second part we investigate how to
determine experimentally the leading mechanism for the Neutrinoless Double Beta
Decay. Is it (a) the light Majorana neutrino exchange as one assumes to
determine the effective Majorana neutrino mass, ist it the heavy left (b) or
right handed (c) Majorana neutrino exchange allowed by left-right symmetric
Grand Unified Theories (GUT's). Is it a mechanism due to Supersymmetry e.g.
with gluino exchange and R-parity and lepton number violating terms. At the end
we assume, that Klapdor et al. have indeed measured the Neutrinoless Double
Beta Decay(, although contested,)and that the light Majorana neutrino exchange
is the leading mechanism. With our matrix elements we obtain then an effective
Majorana neutrino mass of: <m(nu)> = 0.24 [eV], exp (pm) 0.02; theor. (pm) 0.01
[eV]
