## Left: greyscale representation (colourscale in the online version) of the variation of the TDCS in atomic units equation (2), scaled by 10^{4}, of the photo-double ionization of the 3σ_{g} level of N_{2} obtained by the velocity gauge in terms of the two ejection angles θ_{1} and θ_{2}

**Figure 6.** Left: greyscale representation (colourscale in the online version) of the variation of the TDCS in atomic units equation (2), scaled by 10^{4}, of the photo-double ionization of the 3σ_{g} level of N_{2} obtained by the velocity gauge in terms of the two ejection angles θ_{1} and θ_{2}. Here *E*_{1} = *E*_{2} = 10 eV, and the vectors **k**_{1}, **k**_{2}, lie in the same plane. Right: the equivalent representation obtained by the Gaussian parametrization fit.

**Abstract**

We have determined the multiply differential cross sections (MDCS) of the vertical photo-double ionization of diatomic nitrogen with coincidence detection of the ejected electrons, for fixed and random orientations of the internuclear axis, using the correlated product of two two-centre continuum Coulomb functions for the description of the two ejected electrons, which satisfies the exact asymptotic conditions. To verify our procedure, we have applied it to the photo-double ionization of diatomic hydrogen for which many experimental and theoretical results are available. Our results on diatomic hydrogen show the influence of the initial state correlation. In the case of diatomic nitrogen only, the photo-double ionization of the 3σ_{g} orbital is considered resulting in the ^{1}Σ_{g} state of the residual N_2^{2+} dication. The case of the nearby ^{3}Π_{u} final state having an open shell configuration will be considered in a future paper. Our results confirm the symmetry properties of the MDCS and give the optimal ejection angles. A comparison is also made with results obtained by the Gaussian parametrization method.