Alignment creation by elastic electron scattering by ions in a plasma was described in the past (Petrashen, Rebane, Fujimoto, Kazantsev) mainly by the application of the impact parameter method assuming straight-line trajectories. This theory gave, for the alignment created by elastic electron scattering on a single isolated fine-structure level a zero value. Nikitin and Dashevskaya used the multiple trajectory method and obtained non-zero value for the alignment created. If the same formula for the created alignment is used with a complete quantum mechanical calculation, then an infinite value is obtained for the alignment. Consequently, in order to obtain finite results in a quantum-mechanical calculation plasma-screening effects need to be introduced. Furthermore, the whole problem was formulated within the impact-parameter formalism, the development of a completely quanum-mechanical formalism is now called for. This new formalism will be introduced and discussed and applied to alignment creation by elastic scattering of electrons off laser excited barium atoms.