Role of potential structure in nonadiabatic collisions

The role of structure in crossing potential-energy curves upon nonadiabatic collisions is probed by means of functional sensitivity analysis. The inelastic transition ${}_{}{}^2{}_{}{}^{}[{\mathrm{He}}^{+}+\mathrm{N}\mathrm{e}(3\mathrm{}{p}^6\left)\right]$ →${\mathrm{}}^2$Σ[${\mathrm{He}}^{+}$+Ne(3$p^5$4s)] modeled by a crossing of the corresponding diabatic potential-energy curves ($V_{11}$ and $V_{22}$) is used as an illustration. The functional derivatives δ${\sigma }_{12}$(E)/δ$V_{11}$(R), δ${\sigma }_{12}$(E)/δ$V_{22}$(R), and δ${\sigma }_{12}$(E)/δ$V_{12}$(R) of the corresponding nonadiabatic collision cross section ${\sigma }_{12}$ are calculated using the exponential distorted-wave approximation. These functional derivatives offer a quantitative measure of the importance of different regions of the potential [$V_{11}$(R) and $V_{22}$(R)] and coupling [$V_{12}$(R)] functions to the nonadiabatic collision cross section ${\sigma }_{12}$. The prominent Gaussian-like feature of the δ${\sigma }_{12}$(E)/δ$V_{12}$(R) curve in the crossing point region (R∼$R^{\mathrm{*}}$) is found to be in qualitative accord with the δ(R-$R^{\mathrm{*}}$) function idealization of the Landau-Zener-Stueckelberg (LZS) theory.