Searches for new physics in the coherent elastic neutrino-nucleus scattering require a precise knowledge of the neutrino flux and energy spectrum. In this paper we investigate the feasibility and the performances of an experiment based on a $^{51}$Cr source, whose neutrino spectrum is known and whose activity can be heat-monitored at few permil level. With a 5 MCi source placed at ~ 25 cm from the detector, under an exposure of two $^{51}$Cr half-lives (55.4 days), we evaluate 3900 (900) counts on a 2000 cm$^3$ target of germanium (sapphire) featuring an energy threshold of 8 (20) eV. To further increase the exposure, multiple activations of the same source could be possible.
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