We derive an approximate expression for a "radiative potential" which can be used to calculate QED strong Coulomb field radiative corrections to energies and electric dipole (E1) transition amplitudes in many-electron atoms with an accuracy of a few percent. The expectation value of the radiative potential gives radiative corrections to the energies. Radiative corrections to E1 amplitudes can be expressed in terms of the radiative potential and its energy derivative (the low-energy theorem): the relative magnitude of the radiative potential contribution is similar to alpha(3)Z(2)ln(1/alpha(2)Z(2)), while the sum of other QED contributions is similar to alpha(3)(Z(i)+1)(2), where Z(i) is the ion charge; that is, for neutral atoms (Z(i)=0) the radiative potential contribution exceeds other contributions similar to Z(2) times. The advantage of the radiative potential method is that it is very simple and can be easily incorporated into many-body theory approaches: relativistic Hartree-Fock, configuration interaction, many-body perturbation theory, etc. As an application we have calculated the radiative corrections to the energy levels and E1 amplitudes as well as their contributions (-0.34% and +0.43%, respectively) to the parity nonconserving (PNC) 6s-7s amplitude in neutral cesium (Z=55). Combining these results with the QED correction to the weak matrix elements (-0.41%) we obtain the total QED correction to the PNC 6s-7s amplitude, (-0.32 +/- 0.03)%. The cesium weak charge Q(W)=-72.66(29)(exp)(36)(theor) agrees with the Standard Model value Q(W)(SM)=-73.19(13), the difference is 0.53(48).
