Using krypton-83m to determine the neutrino-mass bias caused by a non-constant electric potential of the KATRIN source

Precision spectroscopy of the electron spectrum of the tritium $\beta$ decay near the kinematic endpoint is a direct method to determine the effective electron antineutrino mass. The KArlsruhe TRItium Neutrino (KATRIN) experiment aims to determine this quantity with a sensitivity of better than $0.3\,\mathrm{eV}$ ($90\,\%$~C.L.). An inhomogeneous electric potential in the tritium source of KATRIN leads to a distortion of the $\beta$ spectrum, which directly impacts the neutrino-mass observable. This effect can be quantified through precision spectroscopy of the conversion electrons of co-circulated metastable $^{83\mathrm{m}}Kr$. This work perturbatively describes the effect of the source potential on the recorded spectra, and thus establishes the leading-order observables of this effect.