Two-state curve crossing processes involving rotational coupling in the Na 2 + molecular ion

We examine the relative utility of the Landau-Zener, phase integral, and semiclassical Magnus approximations for processes involving a real crossing of two potential curves. As an example we consider rotational coupling in Na ₂ ⁺ . Numerical calculations for the ¦3p〉→¦3s〉 quenching process and for ¦3p〉→¦3d〉 excitation agree well with recent experiments in the energy range 20 eV≦E_K≦50 eV. Simple expressions forS-matrix elements, differential and total cross sections in these approximations depend only on accurate evaluation of a few JWKB phases. For the total cross section further simplification of the Magnus results yields a useful semiempirical formula.