Mutual angular distribution for the two photoelectrons with (a) odd and (b) even parities at different energy sharings in the laser-assisted XUV double ionization process. Here the black solid line is for ε = 0.01, the red dashed line is for ε = 0.1, and the blue dashed line is for ε = 0.5. The XUV laser pulse is at 89 eV with an intensity of 10¹⁴ W/cm², and the IR laser field is at 1.61 eV with an intensity of 10¹² W/cm². (c) Schematic of causes of (a), (b). Here (i) and (ii) show the splitting of mutual angular distributions, and (iii) enables the side-by-side emission. The green solid arrowed lines stand for the momentum without laser assistance. The red dashed arrowed lines stand for the extra momentum obtained from the assisting laser field. The final superposition momenta are plotted in blue dotted dashed lines.