Total cross sections for elastic and inelastic scattering of charged particles by hydrogen atoms

A new method has been developed in order to calculate the total cross section for particle-atom collisions. For hydrogen we have found the explicit expression of the first three terms of the cross section for large incident momentum. The calculation is performed in momentum space. The propagator of the scattering amplitude is expanded in powers of the atomic energy levels, and use is made of the optical theorem. The polarization and distortion effects have been taken into account by calculating the contributions of the scattering amplitude up to the fourth order. The latter was evaluated using the Glauber amplitude. Thus the explicit dependence of the cross section on $Z^2$, $Z^3$, and $Z^4$, where $\mathrm{Ze}$ is the charge of the particle, has been obtained. An estimate of the precision of our result is given. The total elastic cross section has also been calculated.