The Effect of Atomic Polarizability in Electron-Hydrogen Excitation

In the perturbation series treatment of scattering, the effect of atomic polarizability first appears in the second-order term. Consequently, the atomic polarizability does not contribute to the scattering amplitudes in the usual first-order distorted-wave treatment without making approximations. However, it is known that this effect is important and including it in a first-order treatment is desirable. This paper investigates different methods for including the effect of polarizing the target atom in a first-order treatment for electron-hydrogen scattering. In particular, we examine approximations for including the effect of atomic polarizability on the projectile wavefunction as well as the effect of distortion of the atomic wavefunction. For the latter case, we approximate the polarized atomic states as Stark states, and have used these states for both the determination of the final-state potential and the evaluation of matrix elements. The accuracy of the various methods is ascertained by comparing their results with those obtained from a second-order distorted-wave Born approximation using the real part of the Green's function. The results also are compared with available experimental data for electron-hydrogen scattering.