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The direct determination of nuclear reaction rates at thermal energies remains a central challenge in nuclear astrophysics and strongly coupled plasma physics, where fusion occuring far below the Coulomb barrier is strongly influenced by electron screening and many-body effects [1]. Deuteron–deuteron (d–d) reactions provide a sensitive probe of these conditions, with relevance for both astrophysical environments and fusion energy research.
In the present work, the $^2$H(d,p)$^3$H reaction taking place in Pd target is studied at the ultra high vacuum accelerator facility of the University of Szczecin using atomic and molecular deuterium beams (D$_1^+$, D$_2^+$ and D$_3^+$) with energies from 20 keV down to 3.5 keV. The measured thick-target yields exhibit a pronounced, nearly energy-independent plateau below 5 keV, as also observed in PdTi and NiBe targets, indicating that protons are emitted from thermalized ion tracks induced by projectile collision cascades [2]. Detailed spectral analysis reveals two well-separated components in the proton, triton, and $^{3}$He spectra: a direct beam–target peak and a nearly zero center-of-mass energy thermal component associated with reactions occurring within the ion track. A very thin Al foil placed in front of the detector improves energy resolution, allowing clearer separation of these peaks, although the extraction of the $^{3}$He contribution remains limited by background. The constant yield component observed at the lowest energies enables a direct, model-independent determination of the d–d reaction rate at meV energies, allowing comparison with theoretical predictions, with the rate governed by the combined effects of electron screening, deuterium diffusion, and threshold resonance contributions.
A key observation of this study is the strong dependence of the plateau yield on the molecular structure of the incident beam. The yield obtained with D$_3^+$ is approximately 1.5 times higher than that for D$_2^+$, indicating that D$_3^+$ behaves as an intact molecular projectile rather than as separated ions. This leads to the conclusion that the Coulomb explosion of deuterium molecules at the target surface can be neglected and the cascade of atomic collisions following the entry of the beam ions into the target results in the formation of a single ion track with a higher central temperature. The weak energy dependence of the reaction yield plateau can be explained by coupling electronic and crystal lattice degrees of freedom excited by the energy absorption process of incident ions within the ion track, using the electron–phonon coupling concept. From the other hand, the absolute value of the plateau yield agrees very well with the theoretical d-d cross section enhanced due to the electron screening effect and the threshold resonance in $^4$He [3].
[1] Ouyed, R., and P. Jaikumar, Astrophys. Space Sci. 361, 89 (2016).
[2] K. Czerski et al., arXiv:2409.02112 [nucl-ex].
[3] K. Czerski, et al., Phys. Rev. C 106 (2022) L011601.