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We use quantum scattering theory to study a fixed quantum system Y subject to collisions with massive particles X described by wave packets. We derive the scattering map for system Y and show that the induced evolution crucially depends on the width of the incident wave packets compared to the level spacing in Y. If Y is nondegenerate, sequential collisions with narrow wave packets cause Y to decohere. Moreover, an ensemble of narrow packets produced by thermal effusion causes Y to thermalize. On the other hand, broad wave packets can act as a source of coherences for Y, even in the case of an ensemble of incident wave packets given by the effusion distribution, preventing thermalization. We illustrate our findings on several simple examples and discuss the consequences of our results in realistic experimental situations.