Half-life and the nuclear matrix element of the 2 nu beta beta decay in Ge-76

We apply the shell-model wave functions of Ge-76 to calculate the nuclear matrix elements and the half-life of the 2 nu beta beta decay of Ge-76. Our result is comparable to the recent observed 2 nu beta beta decay half-life of Ge-76. Furthermore it provides the upper limit of the effective neutrino mass is about 0.4eV with the recent experimental data of the 0 nu beta beta decay half-life.