Approximate symmetries in nuclei and the 2νββ-decay rate

A nonstandard method for calculating the nuclear $2\nu\beta\beta$ - decay amplitude is proposed. The method is based on the explicit use of those approximate symmetries of a nuclear hamiltonian, which correspond to the operators of allowed $\beta$ -- transitions. Within the framework of the proposed method the mentioned amplitude is calculated for a wide range of nuclei. The model parameters used in calculations are taken from independent data. Calculated \bb half-lifes are compared with known experimental data.