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Deuteron–deuteron fusion at very low energies is relevant both for nuclear astrophysics and for prospective fusion-energy applications [1]. The reaction cross section decreases sharply with decreasing projectile energy due to the Coulomb barrier; however, in metallic targets, electron screening significantly enhances the barrier penetration probability [2]. Recent studies have suggested that the cross section of the low-energy DD reaction can also be influenced by a narrow threshold resonance in 4He [3,4]. This single-particle-like resonance is expected to decay predominantly through internal pair creation (IPC), producing electron–positron pairs with a total energy of approximately 23 MeV. Earlier experimental studies employed thin single-silicon detectors to identify
the signature of this IPC by the analysis of the partial absorption peak [5,6,7]. However, extending the branching-ratio measurement for deuteron energies below 10 keV remains a challenge due to the rapidly decreasing reaction cross section and contributions from different background components in the relevant detector-response region.
In the present work, a silicon detector telescope operated at the ultra-high-vacuum accelerator facility of the University of Szczecin is employed to reduce background and study the IPC channel. The background response of the detector was characterized using dedicated measurements and Monte-Carlo simulations. The dependence of the background-response function and its time-dependent fluctuations on detector orientation and shielding were investigated. The cosmic-ray component was modelled using the CRY generator coupled to Geant4 simulations [8]. The terrestrial gamma component was mapped independently with a large-volume NaI(Tl) detector and used to model the response function in the Si detectors. In addition, the neutron-induced beam background was evaluated and incorporated into the final analysis. The use of the ΔE–E telescope provided further background suppression and improved the reliability of the IPC signal extraction.
Based on this combined analysis, the electron–proton branching ratio was determined down to Elab =3.5 keV, and its energy dependence was extracted over the measured range. The obtained values support the predicted enhancement of the IPC channel toward very low energies, approaching an electron–proton branching ratio of the order of 10. The IPC channel was also studied in Zr and Pd metallic targets, establishing the material dependence of the electron–proton branching ratio. These results extend the available experimental information on the low-energy DD reaction and provide new constraints on the interpretation of the IPC channel in terms of threshold-resonance excitation. The present work also establishes an experimental and analysis procedure for future measurements at still lower energies, where the branching ratio is expected to increase further.
[1] R. Ouyed et al., Astrophys. Space Sci. 361 (2016) 89.
[2] J. Kasagi et al., J. Phys. Soc. Jpn. 71 (2002) 2881–2885.
[3] K. Czerski et al., Europhys. Lett. 54 (2001) 449–455.
[4] K. Czerski et al., Phys. Rev. C (Letters) L011601 (2022) 106.
[5] K. Czerski et al., Phys. Rev. C (Letters) L021601 (2024) 109.
[6] H. Gokul Das et al., Measurement 114392 (2024) 228
[7] R. Dubey et al., Phys. Rev. X 15 (2025) 041004
[8] C. Hagmannet al., IEEE Nuclear Science Symposium Conference Record 2 (2007) 1143–1146.