Computed total β-electron spectra for decays of Pb and Bi in the 220,222Rn radioactive chains

Abstract

The radon radioactivity is an unavoidable background in present and future underground experiments attempting to detect the neutrinoless double β decay, WIMP-nucleus interactions in direct dark-matter searches, etc. In particular, the Rn220,222 radioactive chains lead to β-decays of Pb212,214 and Bi212,214, notorious backgrounds in the mentioned experiments. In this paper, we compute the total β-electron spectral shapes of these decays by including next-To-leading-order terms and other correction factors in the β spectral shape. The studied β-decays involve strong allowed and first-forbidden β transitions, the nonunique first-forbidden transitions being nuclear-structure dependent through the numerous involved nuclear matrix elements (NMEs). We compute these NMEs by using the nuclear shell model with the khpe Hamiltonian. This Hamiltonian renders a very nice description of the level energies of the daughter nuclei Bi212,214 and Po212,214 of the mentioned mother nuclei. We adopt experimental endpoint energies and engage the small relativistic NMEs (sNME), to accurately describe the measured branching ratios, a necessary prerequisite for a precise description of the total β spectra. We also discuss the uncertainties of our computed spectra and hope that these computations will be of help for present and future rare-decays and dark-matter experiments.