Probing the electron charge distribution via Kapitza-Dirac diffraction

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We analyze the diffraction of elementary systems as the electron by light gratings when they are described by charge distributions instead of the usual point-like form. The treatment of the problem is based on the introduction, in analogy with atomic polarizability, of state-dependent non-permanent multi-pole moments for the charge. The diffraction patterns can provide bounds on these moments. With this approach we can experimentally explore some aspects of the interpretation of the wave picture of single charges.