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The two neutrino positron double beta decay of $^{106}$Cd for 0$^{+} \to $0$^{+}$ transition has been studied in the Hartree-Fock-Bogoliubov model inconjunction with the summation method. In the first step, the reliability ofthe intrinsic wave functions of $^{106}$Cd and $^{106}$Pd nuclei has beentested by comparing the theoretically calculated results for yrast spectra,reduced $B(E2$:$0^{+}\to 2^{+})$ transition probabilities, quadrupole moments$Q(2^{+})$ and gyromagnetic factors $g(2^{+})$ with the available experimentaldata. In the second step, the nuclear transition matrix element $M_{2\nu}$ andthe half-life $T_{1/2}^{2\nu}$ for 0$^{+}\to$ 0$^{+}$ transition have beencalculated with these wave functions. Moreover, we have studied the effect ofdeformation on nuclear transition matrix element M$_{2\nu}.$Comment: 20 page

Two-neutrino positron double-beta decay of 106Cd for the 0+ → 0+ transition