Muonic atom formation using the two-state approximation in different energy regions

Using the two-state approximation within a time-dependent formalism, differential charge-exchange collision cross sections in the formation of muonic (μ-p, μ-d, μ-t), muonium (e-μ+) and positronium (e-e+) atoms have been calculated. The effect of non-orthogonality at different energies for muonium and positronium atom formation has also been studied. Our estimations indicate that the non-orthogonality effect can be neglected at higher energies.