Determination of the neutrino mass by electron capture in 163 Holmium and the role of the three-hole states in 163 Dysprosium

TL;DR

This paper investigates the impact of three-hole states on the electron capture spectrum of 163 Dysprosium to assess their effect on neutrino mass determination, concluding they are not significantly influential.

Contribution

It presents the first calculation of three-hole state effects on the Dysprosium deexcitation spectrum using a relativistic Dirac-Hartree-Fock approach.

Findings

Three-hole states have minimal impact on the spectrum.

Relativistic calculations improve accuracy of electron wave functions.

Three-hole states are not crucial for neutrino mass measurement.

Abstract

163 Holmium to 163 Dysprosium is probably due to the small Q value of about 2.5 keV the best case to determine the neutrino mass by electron capture. The energy of the Q value is distributed between the excitation of Dysprosium (and the neglected small recoil of Holmium) and the relativistic energy of the emitted neutrino including the restmass. The reduction of the upper end of the deexcitation spectrum of Dysprosium below the Q value allows to determine the neutrino mass. The excitation of Dysprosium can be calculated in the sudden approximation of the overlap of the electron wave functions of Holmium minus the captured electron and one-, two-, three- and multiple hole-excitations in Dysprosium. Robertson and the author have calculated the influence of the two-hole states on the Dysprosium deexitation spectrum. Here for the first time the influence of the three-hole states on the deexcitation bolometer spectrum of 163 Dysprosium is presented. The electron wave functions and the overlaps are calculated selfconsitently in a fully relativistic and antisymmetrized Dirac-Hartree-Fock approach in Holmium and in Dysprosium. The electron orbitals in Dysprosium are determined including the one-hole states in the selfconsistent iteration. The influence of the three-hole states on the deexcitation (by X-rays and Auger electrons) spectrum is hardly visible. The three-hole states seem not to be important for the determination of the neutrino mass.