  The zero neutrino mode of the double beta decay in heavy deformed nuclei is
investigated in the framework of the pseudo SU(3) model, which has provided an
accurate description of collective nuclear structure and predicted half-lives
for the two neutrino mode in good agreement with experiments. In the case of
$^{238}U$ the calculated zero neutrino half-life is at least three orders of
magnitude greater than the two neutrino one, giving strong support of the
identification of the radiochemically determined half-life as being the two
neutrino double beta decay. For $^{150}Nd$ the zero neutrino matrix elements
are of the order of magnitude of, but lesser than, those evaluated using the
QRPA. This result confirms that different nuclear models produce similar zero
neutrino matrix elements, contrary to the two neutrino case. Using these pseudo
SU(3) results and the upper limit for the neutrino mass we estimate the
$\beta\beta_{0\nu}$ half-lives for six nuclei. An upper limit for majoron
coupling constant is extracted from the experimental data.
