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It is in principle possible to measure directly the electron neutrino mass(or masses and mixing angles) in weak electron-capture decays. The optimalnuclide in this respect is $^{163}$Ho. The favoured experimental technique,currently pursued in various experiments (ECHo, HOLMES and NuMECS) is"calorimetric". The calorimetric energy spectrum is a sum over the unstablevacant orbitals, or "holes", left by the electrons weakly captured by thenucleus. We discuss the current progress in this field and analize thepreliminary data. Our conclusion is that, as pointed out by Robertson, thecontribution of two-hole states is not negligible. But --in strongcontradistinction with the tacit conclusion of previous comparisons of theoryand observations-- we find a quite satisfactory agreement. A crucial point isthat, in the creation of secondary holes, electron shakeoff and not onlyelectron shakeup must be taken into account.

The calorimetric spectrum of the electron-capture decay of $^{163}$Ho. A preliminary analysis of the preliminary data