 Solution

Only ${}^1{\Delta }_g\to {}^1{\Delta }_u$ is electric-dipole allowed within the listed terms. For a diatomic molecule, the electric-dipole selection rule requires $\Delta S=0$, $g\leftrightarrow u$, and $\Delta \Lambda =0,\pm 1$. The lower singlet of part (a) is ${}^1{\Delta }_g$. Every candidate from the same configuration fails the inversion rule, while the ${}^1{\Sigma }_u^{\pm }$ terms of part (b) require $|\Delta \Lambda |=2$. Triplet destinations fail the spin rule. The surviving $\Delta \to \Delta$ transition uses the axial dipole component, so it is a parallel electronic transition. Weak spin-orbit or other intensity-borrowing transitions are outside this leading electric-dipole classification.