  The two neutrino and neutrinoless double beta decay of $^{94,96}$Zr,
$^{98,100}$Mo, $^{104}$Ru, $^{110}$Pd, $^{128,130}$Te and $^{150}$Nd isotopes
for the $0^{+}\to 0^{+}$ transition is studied within the PHFB framework along
with an effective two-body interaction consisting of pairing,
quadrupole-quadrupole and hexadecapole-hexadecapole correlations. It is found
that the effect of hexadecapolar correlations can be assimilated substantially
as a renormalization of the quadrupole-quadrupole interaction. The effect of
deformation on nuclear transition matrix elements is investigated by varying
the strength of quadrupolar correlations in the parent and daughter nuclei
independently. The variation of the nuclear transition matrix elements as a
function of the difference in deformation parameters of parent and daughter
nuclei reveals that in general, the former tend to be maximum for equal
deformation and they decrease as the difference in deformation parameters
increases, exhibiting a very similar trend for the $(\beta^{-}\beta
^{-})_{2\nu}$ and $(\beta^{-}\beta ^{-})_{0\nu}$ transition matrix elements.
