Based on Pyatov's method, the low-lying Gamow–Teller (GT) 1⁺ state energies and log($f_{t}$) values for ^128,130,132Sb and ^132,134,136I isotopes have been calculated. In this method, the strength parameter of the effective spin–isospin interaction is found by providing the commutativity of the GT operator with the central part of the nuclear Hamiltonian. The problem has been solved within the framework of RPA. The calculation results have been compared with the corresponding experimental data.

The violated commutation condition between the total shell model Hamiltonian and Gamow–Teller operator (GT) has been restored by Pyatov method (PM). The considered nuclear model Hamiltonian in PM includes the separable GT residual interaction in ph and pp channels and is differentiated from the traditional schematic model by $h_{0}$ (restoration term). The influence of the h0 effective interaction on the $2\nu\beta\beta$ decay of ⁴⁸Ca, ⁷⁶Ge, ⁸²Se, ⁹⁶Zr, ¹⁰⁰Mo, ¹¹⁶Cd, ^128,130Te and ¹³⁶Xe is investigated. All the calculations have been done within the framework of standard QRPA. The results obtained by PM are compared with those of other approaches and experimental data. The influence of the restoration term on the stability of the $2\nu\beta\beta$ decay nuclear matrix elements is analysed.