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We present the formalism of Time-dependent Exchange Perturbation Theory(TDEPT) built to all orders of perturbation, for the arbitrary time dependencyof perturbation. The theory takes into account the rearrangement of electronsamong centres. We show how the formalism can be reduced to the standard form ofinvariant perturbation theory by 'switching off' the re-arrangement ofelectrons among centres. The elements of the scattering S-matrix andtransitions T-matrix and the formula for the electron scattering differentialcross section are derived. The application of the theory to scattering andcollision problems is discussed. As an example, we apply the theory to protonscattering on a Lithium atom, calculating the differential and totalcross-sections.

Invariant Time-Dependent Exchange Perturbation Theory and its Application to the Particles Collision Problem