Full Ambiguity-Free Quantum Treatment of $D^{+}+H\left(1\mathit{s}\right)$ Charge Transfer Reactions at Low Energies

Cross sections for the nonresonant charge transfer process ${\mathrm{D}}^{+}+\mathrm{H}\left(1s\right)\to \mathrm{D}\left(1s\right)+{\mathrm{H}}^{+}$ at low energies are calculated in hyperspherical coordinates. The method is free from all the inherent ambiguities associated with the conventional Born-Oppenheimer approach, such as the incorrect asymptotic energies and spurious couplings. However, like the Born-Oppenheimer approach, we show that hyperspherical potential curves and coupling terms have to be calculated only once to obtain results for all partial waves. Feshbach and shape resonances of ${\mathrm{HD}}^{+}$ near the $\mathrm{H}\left(1s\right)$ threshold are also calculated.