Isolation of the regions of potential significance in fine-structure transitions using adiabatic and functional sensitivity analyses: a comparative investigation with application to Na(²P_1/2)+He→Na(²P_3/2)+He and Na(²P_1/2)+Ar→Na(²P_3/2)+Ar

Abstract

The first-order functional sensitivity densities δ lnσ_1/2→3/2(E)/δ lnW_||Λ||(R) are employed to assess the role of structure in the potential-energy curves W₀(²Σ) and W₁(²Π) mediating the fine-structure transition Na(²P_1/2)+He→Na(²P_3/2)+He and Na(²P_1/2)+Ar→Na(²P_3/2)+Ar. The sensitivity density profiles δ lnσ_1/2→3/2(E)/δ lnW???(R) for the two systems reveal that regions of significance differ widely for the ²Σ and ²Π curves. The results suggest that prevalent mechanistic explanations from adiabatic analyses have limitations in terms of the ultimate significance of the identified kinematic coupling over well demarcated radial and angular coupling regions. The functional sensitivity analysis is shown to permit a full deconvolution of the collision cross section's dependence on the features in the individual ²Σ and ²Π curves as opposed to the adiabatic analysis where only the features in [W₀(R)-W₁(R)] are deemed critical to the collisional outcome.