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Ab initio calculation of H + He$^+$ charge transfer cross sections for plasma physics

The charge transfer in low energy (0.25 to 150 eV/amu) H($nl$) + He$^+(1s)$ collisions is investigated using a quasi-molecular approach for the $n=2,3$ as well as the first two $n=4$ singlet states. The diabatic potential energy curves of the HeH$^+$ molecular ion are obtained from the adiabatic potential energy curves and the non-adiabatic radial coupling matrix elements using a two-by-two diabatization method, and a time-dependent wave-packet approach is used to calculate the state-to-state cross sections. We find a strong dependence of the charge transfer cross section in the principal and orbital quantum numbers $n$ and $l$ of the initial or final state. We estimate the effect of the non-adiabatic rotational couplings, which is found to be important even at energies below 1 eV/amu. However, the effect is small on the total cross sections at energies below 10 eV/amu. We observe that to calculate charge transfer cross sections in a $n$ manifold, it is only necessary to include states with $n^{\prime}\leq n$, and we discuss the limitations of our approach as the number of states increases.