  Three decades ago, the measurement of the electron neutrino mass in atomic
electron capture (EC) experiments was scrutinized in its two variants: single
EC and neutrino-less double EC. For certain isotopes an atomic resonance
enormously enhances the expected decay rates. The favoured technique, based on
calorimeters as opposed to spectrometers, has the advantage of greatly
simplifying the theoretical analysis of the data. After an initial surge of
measurements, the EC approach did not seem to be competitive. But very
recently, there has been great progress on micro-calorimeters and the
measurement of atomic mass differences. Meanwhile, the beta-decay neutrino-mass
limits have improved by a factor of 15, and the difficulty of the experiments
by the cube of that figure. Can the "calorimetric" EC theory cope with this
increased challenge? I answer this question affirmatively. In so doing I
briefly review the subject and extensively address some persistent
misunderstandings of the underlying quantum physics.
