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The atomic exchange effect will lead to a significant increase in theprobability density of $\beta$ decays below a few keV. This effect is veryimportant for scientific experiments that performed by low-energy electronspectroscopy measurements. However, the atomic exchange effect involvesmulti-electron interactions, especially for a system with 82 electrons such aslead. Different parameters will lead to different trends in the energy spectrumpredicted by the theory, so it is urgent to carry out experimental measurementsto provide parameter limits for the theory. The probability increase broughtabout by the atomic exchange effect is most obvious near 0keV, and the $\beta$energy spectrum is accurately measured near this energy point, so as to provideconstraints for the physical model of atomic exchange. However, it is extremelydifficult to measure the $\beta$ energy spectrum at 0keV due to the limitationsof electronic noise and internal conversion effects. The excited decay path of$^{210}$Pb was taken as the observation object,by measuring the total energyspectrum of $\beta$ rays and cascaded gamma rays, the precise measurement ofthe $\beta$ energy spectrum near 0keV has been completed. The analysis of the$\beta$ energy spectrum of $^{210}$Pb gives the following conclusions. Theexperimental results first verified the theory that the exchange effect causesthe probability increase at the low energy end near 0keV. At the same time, theexperimental results are higher than the existing predictions of the atomicexchange effect. At least for Pb element, all the electron shells have played arole in improving the probability density of the low end of the $\beta$ energyspectrum. This discovery will promote the theoretical calculation of the$\beta$ energy spectrum of $^{214}$Pb, at the same time, it also indicates thatthe reactor neutrinos have a higher probability density at the omnipotent end.

Precise determination of $^{210}$Pb $\beta$ Decay Spectrum at 0 keV and its Implication to Theoretical Calculations