The character of resonant charge exchange involving highly excited atoms

We study the process of resonant charge exchange involving excited helium atoms with the principal quantum number n = 5 colliding with the helium ion in the ground state in the collision energy range from thermal up to 10 eV. This information may be important for the analysis of planet atmospheres containing helium, in particular, for Jupiter's atmosphere, but our basic interest is the transition from the quantum to classical description of this process, where, due to large cross sections, evaluations of the cross sections are possible. For the chosen process, quantum theory allows determining the cross section as a result of a tunnel electron transition, while classical theory accounts for over-barrier electron transitions. The classical theory additionally requires effective transitions between states with close energies. The analysis of these transitions for helium with n = 5 shows that electron momenta and their projections are mixed for a part of the states, while for other states, the mixing is absent. A simple criterion to separate such states is given. In addition, the main contribution to the cross section of resonant charge exchange follows from tunnel electron transitions. As a result, the quantum theory is better for calculating the cross sections of resonant charge exchange than the classical one and also allows finding the partial cross sections of resonant charge exchange, while the classical approach gives the cross section of resonant charge exchange in a simple manner with the accuracy of 20%.