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Inelastic collisions of protons with rubidium atoms are treated for the first time within the framework of the three channel coupled static, and frozen core approximations. The method is used for calculating partial and total cross sections with the assumption that only three channels (elastic; non-excited hydrogen, 1s-state; and excited hydrogen, 2s-state) are open. We have used the Lipmann–Schwinger equation and the Green’s functions iterative numerical method technique to solve the derived coupled integro-differential equations to obtain the computer code. The present results for total hydrogen formation cross sections are in agreement with results of other available ones in a wide range of incident energy.

The collisions of a proton with a lithium atom are treated for the first time as a three-channel problem under the assumption that the elastic and hydrogen formation in non-excited, H(1s), and excited, H(2s), channels are open. The effect of polarization potentials of the target and hydrogen formation is considered. A one-valence-electron model for the target, based on the Clementi–Roetti Slater-type basis functions, as well as a modified coupled-static approximation are used to calculate the partial and total cross sections of seven partial waves (0 ≤ ℓ ≤ 6, where ℓ is the total angular momentum) at incident energies between 50 and 500 keV. Our values of the total cross section are in good agreement with previous results.

The inelastic scattering of a proton with a caesium atom is treated for the first time as a three-channel problem within the framework of the improved coupled static approximation with the assumption that the ground (1s state) and excited (2s state) hydrogen formation channels are open for seven values of the total angular momentum, [Formula: see text] at energies between 50 and 500 keV. The Green’s function iterative numerical method is used to obtain the computer code to calculate iterative partial cross sections. This can be done through calculating the reactance matrix at different values of considered energies to obtain the transition matrix that gives partial and total cross sections. Present results give reasonable agreement with previous results.

This work deals with the effect of polarization potential on inelastic scattering of muons by hydrogen atom, μ+-H, as a two-channel problem in which the elastic and muonium (in 1s state) formation channels are open for seven values of the total angular momentum at energies between 1 and 10 keV. For this purpose, we improved the coupled static approximation by “switching on” the polarization potential of hydrogen atom (in 1s state) to calculate elastic and muonium formation cross-sections of μ+-H inelastic scattering. We use the Lipmann–Swinger equation and an iterative numerical method to obtain the computational code. This can be done through calculating the reactance matrix, then obtaining the transition matrix that gives partial and total cross-sections. Our results and those determined by previous authors are in reasonable agreement.