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Metallic magnetic calorimeters have been used for several years for the determination of the shapes of beta spectra. Experimental spectra of the beta decays of $$^{63}$$ Ni and $$^{241}$$ Pu exhibit, at very low energy, strong deviations from standard theoretical calculations including corrections for screening, radiative, and nuclear size effects. These discrepancies can be attributed to the atomic exchange effect. In particular the spectrum of $$^{63}$$ Ni measured with an electroplated $$^{63}$$ Ni source is in excellent agreement with theory including the exchange effect. This underlines the quality of the experimental spectrum as well as the correctness of the calculation of the exchange effect. [ABSTRACT FROM AUTHOR]