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The effect pointed out by A. B. Migdal in the 40’s (hereafter named Migdal effect) has so far been usually neglected in the direct searches for WIMP Dark Matter candidates. This effect consists in the ionization and the excitation of bound atomic electrons induced by the recoiling atomic nucleus. In the present paper the related theoretical arguments are developed and some consequences of the proper accounting for this effect are discussed by some examples of practical interest.

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