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We present high-precision theoretical predictions for the electron energyspectra for the ground-state to ground-state $\beta$ decays of $^{214}$Pb,$^{212}$Pb, and $^{85}$Kr most relevant to the background of liquid xenon darkmatter detectors. The effects of nuclear structure on the spectral shapes aretaken into account using large-scale shell model calculations. Final spectraalso include atomic screening and exchange effects. The impact of nuclearstructure effects on the $^{214}$Pb and $^{212}$Pb spectra below $\approx100$keV, pertinent for several searches for new physics, are found to becomparatively larger than those from the atomic effects alone. We find that thefull calculation for $^{214}$Pb ($^{212}$Pb) predicts 15.0-23.2% (12.1-19.0%)less event rate in a 1-15 keV energy region of interest compared to thespectrum calculated as an allowed transition when using values of the weakaxial vector coupling in the range $g_{\rm A}=0.7-1.0$. The discrepancyhighlights the importance of both a proper theoretical treatment and the needfor direct measurements of these spectra for a thorough understanding of$\beta$ decay backgrounds in future experiments.

Improved calculations of beta decay backgrounds to new physics in liquid xenon detectors