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The search for coherent elastic neutrino nucleus scattering (CE$\nu$NS) usingreactor antineutrinos represents a formidable experimental challenge, recentlyboosted by the observation of such a process at the Dresden-II reactor siteusing a germanium detector. This observation relies on an unexpectedenhancement at low energies of the measured quenching factor with respect tothe theoretical Lindhard model prediction, which implies an extra observableionization signal produced after the nuclear recoil. A possible explanation forthis additional contribution could be provided by the so-called Migdal effect,which however has never been observed. Here, we study in detail the impact ofthe Migdal contribution to the standard CE$\nu$NS signal calculated with theLindhard quenching factor, finding that the former is completely negligible forobserved energies below $\sim 0.3\,\mathrm{keV}$ where the signal isdetectable, and thus unable to provide any contribution to CE$\nu$NS searchesin this energy regime. To this purpose, we compare different formalisms used todescribe the Migdal effect that intriguingly show a perfect agreement, makingour findings robust.

On the impact of the Migdal effect in reactor CE$\nu$NS experiments