Examination of the calorimetric spectrum to determine the neutrino mass in low-energy electron capture decay

Background: The standard kinematic method for determining neutrino mass from the beta decay of tritium or other isotope is to measure the shape of the electron spectrum near the endpoint. A similar distortion of the "visible energy" remaining after electron capture is caused by neutrino mass. There has been a resurgence of interest in using this method with Ho-163, driven by technological advances in microcalorimetry. Recent theoretical analyses offer reassurance that there are no significant theoretical uncertainties. Purpose: The theoretical analyses consider only single vacancy states in the daughter Dy-163 atom. It is necessary to consider configurations with more than one vacancy that can be populated owing to the change in nuclear charge. Method: The shakeup and shake-off theory of Carlson and Nestor is used as a basis for estimating the population of double-vacancy states. Results: A spectrum of satellites associated with each primary vacancy created by electron capture is presented. Conclusions: The theory of the calorimetric spectrum is more complicated than has been described heretofore. There are numerous shakeup and shake-off satellites present across the spectrum, and some may be very near the endpoint. The spectrum shape is presently not understood well enough to permit a sensitive determination of the neutrino mass in this way.