Quantum mechanical calculations for charge transfer processes in slow ion-atom collisions are difficult due to the fact that there is not a single coordinate system which is suitable for describing all different rearrangement channels. The well known perturbed stationary state (PSS) approximation, based on the adiabatic Born-Oppenheimer (BO) approximation, have deficiencies originating from the fact that molecular orbitals do not satisfy correct asymptotic boundary conditions. The fundamental defects associated with the PSS model have been well documented, including incorrect dissociation thresholds, non-vanishing asymptotic couplings and lack of Galilean invariance.

We recently developed a quantum mechanic theory for ion-atom collisions at low energies based on the hyperspherical close coupling method (HSCC) [1]. In the hyperspherical coordinates the wavefunction is expanded in analogy to BO approximation. The slow/smooth variable discretization (SVD) technique combined with the R-matrix propagation method allows us to solve the coupled hyperradial equation and to avoid calculating the nonadiabatic coupling matrix elements. Also, efficient procedures have been implemented in order to account for a large number of partial waves. It has been shown that this method can be used to study low-energy ion-atom collisions without the need to introduce the ad hoc electron translation factors, and results are free from the ambiguities associated with the traditional MO expansion approach [1].

Collisions involving hydrogen atoms and C⁶⁺ ions have been studied extensively in the last few decades, but controversies remains. Particularly, the predicted C⁵⁺(n=5) capture cross sections from various theoretical studies show different energy dependence and their magnitudes differ by as much as one order in the energy range below 1 keV [2]. In an effort to resolve this controversy, we apply the HSCC method to calculate the charge transfer cross section for C⁶⁺+H collisions at low energies.

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