Molecular Theory of Atomic Collisions: Fine-Structure Transitions

Abstract

The theory of fine-structure transitions in atom-atom collisions is formulated in terms of the molecular states of the diatomic collision complex. The Born-Oppenheimer (BO) electronic wave functions are implicit functions of the interatomic coordinate $R$, and the molecular theory is analogous to the "perturbed-stationary-state" method. Expansion in molecular channel states incorporates the effects of polarization, exchange, and valence forces on the electronic portion of the scattering wave function and embodies the "adiabatic" contribution of the entire set of closed-channel excited states that are generated in the more usual asymptotic-atomic-state expansion. The channel states are expressed explicity in terms of the body-fixed molecular wave functions, and the resultant interaction matrix elements in the close-coupling scattering formalism are related to the molecular potentials. The theory is developed specifically for proton collisions with the fluorine atom in its ground ${}_{}{}^2{}_{}{}^{}P_{j,\mathrm{mj}}^{}{}_{}{}^{}$ state, with explicit account being taken of the spin-orbit splitting between the $j=\frac{3}{2}$ and $j=\frac{1}{2}$ multiplet states. Use is made of the accurate H${\mathrm{F}}^{+}$ (${}_{}{}^2{}_{}{}^{}\mathrm{II}$) and ${\mathrm{HF}}^{+}\left({}_{}{}^2{}_{}{}^{}\Sigma \right)$ wave functions calculated by Wahl, Julienne, and Krauss. These molecular states asymptotically approach ${\mathrm{H}}^{+}$ +F(${}_{}{}^2{}_{}{}^{}\mathrm{P}$), and accurate quadrupole and induced-dipole interaction parameters which describe the asymptotic interaction potentials are obtained from the calculations. Estimates are made of the BO coupling terms and they are found to be negligible compared to the spin-orbit couplings. In the following paper close-coupling calculations are made of the cross sections for the fine-structure transitions ($j,m_j\to j^{\prime },m_j$).