On the role of potential features in fine-structure transitions with application to H⁺+F(²P _{1 2}→F(²P _{3 2})

The first order functional sensitivity densities δln σ _{1 2→ 3 2}(E)/δln W_|Λ|(R) are employed to assess the role of structure in potential energy curves W₀(R) and W₁(R) involved in the fine-structure transition H⁺+F(²P _{1 2})→H⁺+F(²P _{3 2}). The results reveal that the fine-structure transition cross-section draws on the W₀(²Σ) and W₁(²Π) potentials in a highly correlated fashion and a measurement of σ _{1 2→ 3 2}(E) for H⁺+F will primarily allow information to be extracted only on the potential function difference W₀(R)-W₁(R) for moderate to large internuclear distances (R≳3 a₀). While there is a marginal preference for the π alignment in the region where splitting between the ²Π and ²Σ curves is equal to the fine-structure transition energy, the oscillatory nature of the sensitivity densities with respect to R indicates that the alignment effects may disapper upon averaging over many impact parameters. The results from both functional sensitivity and adiabatic analysis isolate the region of potential energy curves centered at R≈7.8 a₀ where the potential function difference W₀(R)-W₁(R) is equal to the fine-structure splitting, to be of maximum significance to the collisional fine-structure transition in this system.