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The two neutrino double beta decay of $^{124,126}$Xe,$^{128,130}$Te, $^{130,132}$Ba and $^{150}$Nd isotopes is studied in the ProjectedHartree-Fock-Bogoliubov (PHFB) model. Theoretical 2$\nu $ $\beta^{-}\beta ^{-}$half-lives of $^{128,130}$Te, and $^{150}$Nd isotopes, and 2$\nu\beta^{+}\beta^{+}$, 2$\nu $ $\beta^{+}EC$ and 2$\nu $ $ECEC$ for $^{124,126}$Xe and $^{130,132}$Ba nuclei are presented. Calculated quadrupolartransition probabilities B(E2: $0^+\to 2^+$), static quadrupole moments and $g$factors in the parent and daughter nuclei reproduce the experimentalinformation, validating the reliability of the model wave functions. Theanticorrelation between nuclear deformation and the nuclear transition matrixelement $M_{2\nu} $ is confirmed.

Nuclear deformation and the two neutrino double-\beta decay in ^{124,126}Xe,^{128,130}Te, ^{130,132}Ba and ^{150}Nd isotopes