Background-Limited Silicon Telescope Methodology for Weak Internal Pair Creation Transition in Low-Energy Deuteron-Deuteron Reactions
A background-constrained silicon-telescope methodology has been developed to investigate recently observed internal electron-positron pair creation in low-energy deuteron-deuteron fusion. The decay of the near-threshold $0^+$ resonance in $^4$He produced in DD fusion results in an $e^-e^+$ pair sharing a total energy of 22.84 MeV. These high-energy leptons traverse thin silicon detectors and deposit only part of their kinetic energy. The resulting partial-absorption peak structure overlaps with the natural-radiation background of cosmic-ray secondaries and terrestrial gamma rays. The silicon detector telescope used in the present experiments is characterised against this background through a component-by-component model that combines a GEANT4 cosmic-ray simulation, a large-volume NaI(Tl)-constrained terrestrial-gamma propagation, and a beam-correlated neutron response. Long-duration measurements in multiple orientations and shielding configurations are used to quantify the run-to-run variability of the background and to translate it into an explicit systematic envelope on the extracted signal. The framework is then applied to the beam-on singles spectrum and the two-dimensional coincidence response, yielding a quantitative branching-ratio measurement under background-limited conditions. The methodology is directly transferable to other weak-channel searches in surface laboratories where continuum-like signals overlap with natural-radiation backgrounds.