Polarization of Lyman-α and Balmer-α emission in proton-hydrogen collisions: a study using first-order Born-Faddeev-type equations

A three-body Born-Faddeev model is devised to calculate the total cross sections of Balmer-alpha and Lyman-alpha emissions, for the excitation of hydrogen atoms by proton impact in the energy range of 100 keV-7 MeV. In addition, the polarization alignment factor A(20) is calculated and compared against available experimental data to further test the theory. Specifically, here we use the Faddeev-Watson-Lovelace formalism to study the excitation of atomic hydrogen from its ground state to the excited states of n = 2 and 3 and magnetic sublevels l = 0, 1 and 2, wherever applicable. The first-order electronic, A(e)((1)), and the first-order nuclear, A(n)((1)), amplitudes are considered in order to calculate the excitation transition matrix (T-PT), while a near-the-shell condition is assumed throughout. In addition, our results were used to calculate the first-order form factors. The present results are compared, where possible, with those of other theoretical and experimental works that are currently available in the literature.