Multiple electromagnetic excitation in fast peripheral heavy ions collisions

We study the corrections of first order electromagnetic excitation due to higher order electromagnetic interactions. An effective operator is introduced which takes these effects into account in the sudden approximation. Evaluating the matrix elements of this operator between the relevant states corrections to the first order result are obtained in a simple way. As an example we discuss the excitation of the first excited state in 11Be. It tends to improve the agreement between experiment and theory.