[en] The adiabatic spectrum of potential energy curves, corresponding to the ²Σ⁺ and ²Pi states of the molecular complex, have been calculated using an ab initio configuration-interaction method. Curve-crossing phenomena are found in all the curves with the exception of the lowest ²Σ⁺ state, corresponding to the Ne⁺(²P) + He(¹S) asymptotic level. An approximate threshold of 22 eV is predicted for the neon ¹S to ¹P excitation, which is in good agreement with available experimental predictions. The charge-exchange excitation of Ne in the Ne⁺ + He collision occurs at about 29 eV in the ²Pi state for an internuclear separation of 1.5a₀. Three additional crossings for the ²Pi spectrum are also found at lower energy and larger separation. The cross section for the first ²Σ⁺ crossing is calculated as a function of collision energy using the Landau-Zener-Stueckelberg method, and including the phase-interference effect. Phase-interference (''Stueckelberg'') oscillations are found in the cross section and are in qualitative agreement with oscillations found in the experimental cross sections