Application of Haar multi-resolution analysis in subspace V2 to calculate Faddeev partial amplitudes of electron transfer in three-body proton-hydrogen scattering

The exact or projected form of the off-the-energy-shell Coulomb transition matrix (T-matrix), in the Daubechies first scalet basis, is used to calculate the Faddeev-Watson-Lovelace (FWL) amplitudes up to the second order, in the electron capture channel for the scattering of high-energy protons by atomic hydrogen. The phase, angular and energy dependence of the FWL partial amplitudes and differential cross sections are constructed. An analytical expression for the differential cross sections is presented as a function of energy and scattering angle. Finally, differential cross sections obtained by the exact and approximate Coulomb off-the-energy-shell T-matrix are compared with the available experimental results.