We present triple differential cross sections (TDCS) for single ionization of atoms by proton and highly charged bare ions impact by means of the three-body formalism of the fi rst Born, two-Coulomb wave and three-Coulomb wave methods, respectively. The TDCS has been calculated both in the scattering and perpendicular planes. The purpose of this work is to investigate the validity of different methods as well as the role of interaction between projectile and residual target-ion in the fi nal state for weak perturbation strength with low electron emission energy at several momentum transfers. By comparing our calculations with experimental data, overall, the 3CW predicts better agreement with experiments than other calculations in the scattering plane. In the perpendicular plane, all calculations deviate from experimental data with increasing transverse momentum transfer for p - He collision. At low momentum transfer, the location of binary peak obtained by the FBA calculation is well established with the experiment for proton impact. On the other hand, the 3CW model is in much better agreement with experiments, both in absolute values and peak position for highly charged impact. Finally, the strong influence of the inter nuclear Coulomb distortion on TDCS has been observed at low and intermediate momentum transfer.

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