  The two neutrino double beta $(\beta ^{-}\beta ^{-})_{2\nu}$ decay of $
^{94,96}$Zr, $^{98,100}$Mo, $^{104}$Ru, $^{110}$Pd, $^{128,130}$Te and
$^{150}$Nd nuclei for the $0^{+}\to 0^{+}$ transition is studied in the PHFB
model in conjunction with the pairing plus quadrupole-quadrupole plus
hexadecapole-hexadecapole effective two-body interaction and the effect of the
latter is investigated on the calculation of nuclear transition matrix elements
$M_{2\nu}$. The reliability of the intrinsic wave functions of parent and
daughter nuclei involved in the $(\beta ^{-}\beta ^{-})_{2\nu}$ decay of above
mentioned nuclei is established by obtaining an overall agreement between a
number of theoretically calculated spectroscopic properties, namely the yrast
spectra, reduced $B(E2$:$0^{+}\to 2^{+})$ transition probabilities, static
quadrupole moments $Q(2^{+})$ and $g$-factors $g(2^{+})$ and the available
experimental data. The effect of deformation on $M_{2\nu}$ is also investigated
to inveterate its inverse relation with nuclear deformation.
