Development of a Dual Cryogenic Detection System for the Forbidden Non-unique $$\beta$$ -Decay Spectrum Study

We present the development of a dual-detector system designed for investigating the spectral shape of forbidden non-unique beta decays. Two PbMoO\(_4\) scintillating crystals were carefully prepared for heat and light detection at milli-Kelvin (mK) temperatures. Notably, one crystal was synthesized using archaeological lead, while the other was composed of natural modern lead. The significance of employing two crystals lies in their identical dimensions and proximity, resulting in similar environmental background exposure. Their distinct internal radioactivities, particularly associated with \(^{210}\)Pb, introduce a distinguishing factor between the spectra measured in the two detectors. Our detection method includes achieving clear particle identification through the relative amplitudes of light and heat signals for both crystals. This report compares the electron-induced spectra within energy regions both below and above the endpoint of \(^{210}\)Bi beta decay. This comparative study provides valuable insights into an exact measurement of the \(^{210}\)Bi decay spectrum, forbidden non-unique beta decay.