Differential cross sections for excitation of atomic hydrogen by proton impact

The differential cross section for the excitation of the hydrogen atom to the $2s$ and $2p$ states are calculated by applying the Coulomb-projected-Born (CPB) method as proposed by Geltman. The results for the excitations of the hydrogen atom for the incident proton energies of 25, 50, 100, and 150 keV and for the scattering angles $\theta$ varying from 0 to 1.5 (in ${10}^{-3\mathrm{}}$ rad c.m.) obtained by the present CPB approach are compared with the experimental observations and other existing theoretical calculations. At the incident energy 100 keV the present CPB results, except at large scattering angles, are found to be in good agreement with the observed results and are as reliable as the calculated results obtained by applying the many-state close-coupling (CC) approximation. For 50 keV and for scattering angles varying from 0.4 to 1.0 (in ${10}^{-3\mathrm{}}$ rad c.m.) the present CPB results agree with the observed data and are as reliable as the CC and the Glauber results, however with the decrease of scattering angle ($\theta \le 0.4$ in ${10}^{-3\mathrm{}}$ rad c.m.) the results obtained by the CPB method become less reliable compared to the CC or the Glauber results. At 25 keV the present CPB results for the differential cross sections underestimate the observed values throughout the angular region considered except at the large angles, where $\theta \ge 0.5$ in ${10}^{-3\mathrm{}}$ rad c.m. On the other hand, the Glauber results at this energy give quite good agreement throughout the angular region, whereas the Born results grossly overestimate the observed differential cross sections.