Hyperspherical close-coupling calculations for charge-transfer cross sections in ${\mathrm{He}}^{2+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ collisions at low energies

A theory for ion-atom collisions at low energies based on the hyperspherical close-coupling (HSCC) method is presented. In hyperspherical coordinates the wave function is expanded in analogy to the Born-Oppenheimer approximation where the adiabatic channel functions are calculated with B-spline basis functions while the coupled hyperradial equations are solved by a combination of R-matrix propagation and the slow/smooth variable discretization method. The HSCC method is applied to calculate charge-transfer cross sections for ${\mathrm{He}}^{2+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to {\mathrm{He}}^{+}\mathrm{}(n=2\mathrm{})+{\mathrm{H}}^{+}$ reactions at center-of-mass energies from 10 eV to 4 keV. The results are shown to be in general good agreement with calculations based on the molecular orbital (MO) expansion method where electron translation factors (ETF’s) or switching functions have been incorporated in each MO. However, discrepancies were found at very low energies. It is shown that the HSCC method can be used to study low-energy ion-atom collisions without the need to introduce the ad hoc ETF’s, and the results are free from ambiguities associated with the traditional MO expansion approach.