Two neutrino positron double beta decay of ${}^{106}$Cd for $0^{+}\to 0^{+}$ transition

Abstract

The two neutrino positron double beta decay of ${}^{106}$Cd for 0${}^{+}\to$ 0${}^{+}$ transition has been studied in the Hartree-Fock-Bogoliubov model in conjunction with the summation method. In the first step, the reliability of the intrinsic wave functions of ${}^{106}$Cd and ${}^{106}$Pd nuclei has been tested 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 experimental data. In the second step, the nuclear transition matrix element $M_{2\nu }$ and the half-life $T_{1/2}^{2\nu }$ for 0${}^{+}\to$ 0${}^{+}$ transition have been calculated with these wave functions. Moreover, we have studied the effect of deformation on nuclear transition matrix element M${}_{2\nu }.$

Comments: 20 pages