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Assuming mixing of three massive Majorana neutrinos, we study theimplications of the neutrino oscillation solutions of the solar and atmosphericneutrino problems and of the results of the CHOOZ experiment for thepredictions of the effective Majorana mass in neutrinoless double beta decay,|< m >|. The general case of CP-nonconservation is investigated. The predictedvalues of |< m >|, depend strongly on the type of the neutrino mass spectrum,on the solution of the solar neutrino problem, as well as on the values of thetwo Majorana CP-violating phases, present in the lepton mixing matrix. We findthat i) $|< m >| \lesssim 0.02 $eV for a hierarchical neutrino mass spectrum,ii) $|< m >| \lesssim 0.09 $eV if the spectrum is of the inverted hierarchytype, and iii) $|< m >| \leq m$ in the case of three quasi-degenerateneutrinos, m > 0 being the common neutrino mass scale which is limited by thebounds from the $^3$H $\beta-$decay experiments, $m < 2.5 $eV. The observationof the $(\beta \beta)_{0\nu}-$decay with a rate corresponding to $|< m >|\gtrsim 0.02 $eV can provide unique information on the neutrino mass spectrumand on the CP-violation in the lepton sector, and if CP-invariance holds - onthe relative CP-parities of the massive Majorana neutrinos.Comment: 51 pages, LATEX; 33 pages of text, 28 eps-files; the text includes 6  tables and 28 figures; results and conclusions unchanged, a reference to the  KATRIN project and Comments concerning its physics potential added; version  to be published in Physical Review

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Majorana neutrinos, neutrino mass spectrum,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>CP</mml:mi></mml:math>violation, and neutrinoless double<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>β</mml:mi></mml:math>decay: The three-neutrino mixing case

Majorana neutrinos, neutrino mass spectrum,CPviolation, and neutrinoless doubleβdecay: The three-neutrino mixing case