**Figure 1.** The variation, in polar representation, of the fourfold differential cross section in atomic units equation (1), scaled by 10^{5}, of the photo-double ionization of H_{2} obtained by the velocity gauge (left) and the length gauge (right). The polar angle represents the ejection angle θ_{2}. Here *E*_{1} = *E*_{2} = 10 eV and the polarization vector is parallel to the internuclear axis ρ; **k**_{2}, , **ρ** are coplanar and **k**_{1} is perpendicular to them. (cf [20] figure 8(a).) The solid line gives the results obtained by the Turbiner–Guevara wave function, the dotted line those obtained by the Mueller–Eyring wave function and the dashed line those obtained by the Heitler–London wave function.

**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.