  Four nuclei which are proved to be $2\nu\beta\beta$ emitters ($^{76}$Ge,
$^{82}$Se, $^{150}$Nd, $^{238}$U), and four suspected, due to the corresponding
Q-values, to have this property ($^{148}$Nd, $^{154}$Sm, $^{160}$Gd,
$^{232}$Th), were treated within a proton-neutron quasiparticle random phase
approximation (pnQRPA) with a projected spherical single particle basis. The
advantage of the present procedure over the ones using a deformed Woods Saxon
or Nilsson single particle basis is that the actual pnQRPA states have a
definite angular momentum while all the others provide states having only K as
a good quantum number. The model Hamiltonian involves a mean field term
yielding the projected single particle states, a pairing interaction for alike
nucleons and a dipole-dipole proton-neutron interaction in both the
particle-hole (ph) and particle-particle (pp) channels. The effect of nuclear
deformation on the single beta strength distribution as well as on the double
beta Gamow-Teller transition amplitude (M$_{{\rm GT}}$) is analyzed. The
results are compared with the existent data and with the results from a
different approach, in terms of the process half life T$_{1/2}$. The case of
different deformations for mother and daughter nuclei is also presented.
