We use a simple two-electron model introduced previously in the literature Phys. Rev. Lett. 78 1884 to study the process of non-sequential double ionization of atoms. In particular, we discuss the phenomena of non-sequential double ionization of helium and we show that there is a definite relationship between the dipole radiation of the outermost (strongly ionized) electron and the ionization of the inner electron. We also investigate in detail the effect of quantum interference of the outer-electron wavefunction on the non-sequential ionization.