Beam-energy dependence and updated test of the Trojan-horse nucleus invariance via a measurement of the ${}^2\mathrm{H}(d,p){}^3\mathrm{H}$ reaction at low energies

The ${}^2\mathrm{H}(d,p){}^3\mathrm{H}$ bare nucleus astrophysical $S\left(E\right)$ factor has been measured indirectly at energies from about 500 keV down to several keV by means of the Trojan-horse method applied to the ${}^2\mathrm{H}({}^6\mathrm{Li},pt){}^4\mathrm{He}$ quasifree reaction induced at 11 MeV. The obtained results are compared with direct data as well as with previous indirect investigation of the same binary reactions. It shows that the precision of $S\left(E\right)$ data in the low-energy range extracted via the same Trojan-horse nucleus [${}^6\mathrm{Li}=(d\oplus \alpha )$] increases while the incident energy of the virtual binary process approaches the zero-quasi-free-energy point. The very good agreement between data extracted from different Trojan-horse nuclei $[{}^6\mathrm{Li}=(d\oplus \alpha )$ vs ${}^3\mathrm{He}=(d\oplus p)]$ gives a strong updated test for the independence of the binary indirect cross section on the chosen Trojan-horse nucleus at low energies.

Figure 1

The schematic representation of Trojan-horse method. (a) Normal, (b) TH: ${}^6\mathrm{Li}$, and (c) TH: ${}^3\mathrm{He}$.

Figure 2

Experiment setup of the ${}^2\mathrm{H}({}^6\mathrm{Li},pt){}^4\mathrm{He}$ reaction measurement.

Figure 3

Experimental $Q_3$ value spectrum for the 11-MeV runs with events from the kinematic locus cuts. The peak around 2.5 MeV is in good agreement with the theoretical value of ${}^2\mathrm{H}({}^6\mathrm{Li},pt){}^4\mathrm{He}$ ($Q=2.558$ MeV).

Figure 4

Calculated mass spectrum of the three outgoing particles. Green: $m_1\simeq 3$ ($t$), blue: $m_2\simeq 1$ ($p$), and red: $m_3\simeq 4$ ($\alpha$).

Figure 5

The $S\left(E\right)$ factor obtained from THM measurements with same TH $[{}^6\mathrm{Li}=(d\oplus \alpha \left)\right]$ and different energy compared with direct data. The $S_{\mathrm{THM}}/S_{\mathrm{Direct}}$ value with $E_{\text{c.m.}}$ is shown below as well.

Figure 6

The $S\left(E\right)$ factor obtained from different THM measurements with different TH (${}^6\mathrm{Li}=(d\oplus \alpha )$ vs ${}^3\mathrm{He}=(d\oplus p)$) compared with direct data to test the Trojan horse nucleus invariance. The $S_{\mathrm{THM}}/S_{\mathrm{Direct}}$ value with $E_{\mathrm{c}.\mathrm{m}.}$ is shown below as well.