Precision measurement and modelling of the threshold-free 210Pb {\beta} spectrum

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 $\beta$ decay spectra, particularly at low energies, remain experimentally and theoretically challenging. Here we report a high-precision, threshold-free measurement of the full $\beta$ decay spectrum of 210Pb to excited states of 210Bi, using a transition-edge sensor (TES)-based micro-calorimeter. This approach enables the detection of $\beta$ 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 $\beta$ 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 {$\sigma$}) enhancement in $\beta$ 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 $\beta$ 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.