Deuteron-deuteron nuclear reactions at extremely low energies

The theoretical analysis of the ${}^2\mathrm{H}{\left(d,p\right)}^3\mathrm{H}$ reaction taking place in both metallic as well as gaseous targets at deuteron energies of several keV presented here indicates a strong contribution of the single-particle $0^{+}$ threshold resonance. Additional arguments based on the weak coupling between the 2 + 2 and 3 + 1 clustering states of the compound nucleus ${}^4\mathrm{He}$ support this resonance and suggest its large partial width for the internal electron-positron pair formation that overestimates the proton width. A detailed study of the interplay between the resonance transition and the electron screening effect enables estimation of the nuclear reaction rate of the deuteron-deuteron fusion reactions at room temperature.

Figure 1

The DD $0^{+}$ threshold resonance contribution observed in the ${}^2\mathrm{H}{\left(d,p\right)}^3\mathrm{H}$ reaction. (a) Thick-target enhancement factor obtained for the Zr target. (b) $S$ factor obtained for the gaseous target.

Figure 2

Schematic four-nucleon energy surface separating 1 + 3 and 2 + 2 cluster states for the angular momentum $L=1$. The red colored level represents the DD $0^{+}$ threshold resonance.

Figure 3

Nonresonant (dotted lines) and resonant (solid lines) cross sections for $U_e=400\mathrm{eV}$ (upper part) and $U_e=100\mathrm{eV}$ (lower part). Blue lines correspond to the resonance energy of 1 eV and the red one to 10 eV. The resonance width is assumed to be 0.1 eV.