Abstarct: Double beta ( ) decay is a rare transition between two nuclei of the same mass number having a change of two units of nuclear charge. In cases of interest, ordinary single beta decay is forbidden because of the energy conservation or angular momentum mismatch. There are two modes of double beta decay. One involving the emission of two antineutrinos and two electrons ( mode), occurs in second order of the standard weak interaction theory and is independent of a possible small neutrino mass. The other involving no neutrinos and two electrons ( mode) violates the lepton number conservation and requires the neutrino to have a nonzero mass. Analysis of the experimental result to determine the character of the neutrino in decay strongly depends on the precise calculation of the nuclear matrix elements. In particular, agreement between experiment and theory for the standard mode is one of the prerequisites for a reliable interpretation of the more exotic mode. In this thesis, we study the decay of and . The nuclear wave functions are obtained by solving the radial Schrödinger equation with Woods-Saxon and Harmonic Oscillator potentials for an eight-body system by using the Supersymmetry method. Then we use the Fermi Golden Rule for obtain half-life. Our result is in good agreement with experiment and the work done by others.