Precision measurement and modelling of the threshold-free 210Pb β spectrum

Abstract

Beta decay is a fundamental process that governs nuclear stability and serves as a sensitive probe of the weak interaction and possible physics beyond the Standard Model of particle physics. However, precise measurements of complete $β$ decay spectra, particularly at low energies, remain experimentally and theoretically challenging. Here we report a high-precision, threshold-free measurement of the full $β$ decay spectrum of 210Pb to excited states of 210Bi, using a transition-edge sensor (TES)-based micro-calorimeter. This approach enables the detection of $β$ particle energies from 0 keV up to their endpoint by coincidence summing with subsequent de-excitation energy, thereby eliminating reconstruction artifacts near zero energy that have traditionally limited low-energy spectral accuracy. To our knowledge, this is the first complete, high-precision $β$ decay spectrum from 0 keV. The data resolve theoretical uncertainties associated with the atomic quantum exchange (AQE) effect. An accompanying ab initio theoretical framework, incorporating atomic, leptonic, and nuclear components, predicts a statistically significant (7.2 {$σ$}) enhancement in $β$ emission probability near zero energy, in agreement with the measurement and in contrast to models that omit AQE corrections. These results provide a new benchmark for $β$ decay theory at low energies, deepen our understanding of the weak interaction, and establish a critical foundation for searches for new physics, including dark matter interactions and precision studies of neutrinos.

Figures (7)

• Figure 1: Illustration of the atomic quantum exchange (AQE) effect. (Left) In addition to direct decay to the continuum (green dashed line), a $\beta$ particle can be exchanged with an atomic electron (green solid lines) of the parent atom with the same angular momentum. The bound electron is then ejected into the continuum (blue solid lines) and cannot be distinguished from the created $\beta$ particle by any detection system. (Right) Representation of the AQE process in the form of Feynman diagrams. The double lines indicate bound atomic electrons.
• Figure 2: Schematic drawing of the experimental setup. The micro-calorimeter is operated in the dilution refrigerator at a base temperature of 20 mK. The Pb-Sn ball acts both as the $^{210}$Pb source and the energy absorber for the TES micro-calorimeter. An $^{241}$Am $\gamma$ source is placed 22 cm from the absorber with a copper shielding in between to stop $\alpha$ particles from $^{241}$Am.
• Figure 3: Illustration of the threshold-free measurement. The inset presents the decay scheme of $^{210}$Pb disintegration based on the evaluated data from ENSDF2014, except for the quantities marked with an asterisk, which are from this study. For most of the time, $^{210}$Pb decays to the excited state of $^{210}$Bi with an excitation energy $\Delta E = 46.539~(1)$ keV released in the form of internal conversion electrons or $\gamma$ rays within a time frame of nanoseconds. In the micro-calorimeters, the $\beta$-ES pulse is shifted up because of $\Delta E$. The shift would lift small $\beta$-ES signals away from the electronics and detector noise. In the energy spectrum, the $\beta$-ES spectrum is shifted by $\Delta E$, from a range of [0, 17.0] keV to [46.5, 63.5] keV, enabling an entirely threshold-free measurement of the $\beta$-ES spectrum.
• Figure 4: The measured energy spectrum from 8 to 70 keV. The most prominent signal peak from 46.5 to 63.5 keV is the $\beta$-ES + $\Delta E$. The spectrum is fitted with the signal peak, Gaussian peaks of $K_\alpha$ of Ag, $^{241}$Am Compton continuum, and escape peaks in Sn, $^{210}$Pb $\beta$-GS, $^{210}$Bi $\beta$, and a flat background spectrum. The full absorption peak of $^{241}$Am is excluded from the fit. The bottom panel shows the residual plot.
• Figure 5: The measured $\beta$-ES spectrum after shifting back to 0 keV starting point and theoretical $\beta$-ES calculations with (red curve) and without (green) AQE effect considered. The spectrum bin width is 80 eV. The fit curves include the $\beta$-ES signal and backgrounds, detailed in the appendix. The bottom panel shows residuals between theories and data. For each bin, the residual is calculated as (data-theory)/$\sqrt{\textrm{data}}$.