Measurement of the Plasma Astrophysical $S$ Factor for the ${}^3\mathrm{He}(d,p){}^4\mathrm{He}$ Reaction in Exploding Molecular Clusters

The plasma astrophysical $S$ factor for the ${}^3\mathrm{He}(d,p){}^4\mathrm{He}$ fusion reaction was measured for the first time at temperatures of few keV, using the interaction of intense ultrafast laser pulses with molecular deuterium clusters mixed with ${}^3\mathrm{He}$ atoms. Different proportions of ${\mathrm{D}}_2$ and ${}^3\mathrm{He}$ or ${\mathrm{CD}}_4$ and ${}^3\mathrm{He}$ were mixed in the gas target in order to allow the measurement of the cross section for the ${}^3\mathrm{He}(d,p){}^4\mathrm{He}$ reaction. The yield of 14.7 MeV protons from the ${}^3\mathrm{He}(d,p){}^4\mathrm{He}$ reaction was measured in order to extract the astrophysical $S$ factor at low energies. Our result is in agreement with other $S$ factor parametrizations found in the literature.

Figure 1

Experimentally measured $⟨\sigma {⟩}_{kT}$ for the ${}^3\mathrm{He}(d,p){}^4\mathrm{He}$ reaction as a function of the temperature $kT$. The solid line is the result of the fit with Eq. (4). See text for details. The upper scale shows the corresponding Gamow peak energy. The ${\chi }^2$ of the fit is 0.6 with 5 degrees of freedom.

Figure 2

Astrophysical $S$ factor for the ${}^3\mathrm{He}(d,p){}^4\mathrm{He}$ reaction as a function of the energy in the center of mass frame ($E_{\mathrm{cm}}$). The solid black circles show the $S$ factor, calculated from the fit of the experimental $⟨\sigma {⟩}_{kT}$ in Fig. 1. The $S$ factor is extrapolated in the energy range 5–300 keV (dashed red line). The shaded area shows the uncertainty on this evaluation. Our result is compared with other experimental data available in Refs. 5 (open crosses), [3] (open triangles), [4] (open diamonds), and [2] (open squares). The upper scale shows the temperature corresponding to the Gamow peak energy in the lower scale.