Beam energy dependence and updated test of the Trojan horse nucleus invariance via the d(d,p)t measurement at ultra-low energies

The $\mathrm{^2H}(d,p)\mathrm{^3H}$ bare nucleus astrophysical S(E) 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 quasi-free process $\mathrm{^2H({}^6Li},pt)\mathrm{^4He}$ induced at the lithium beam energy of 11 and 9.5 MeV, which makes the virtual binary process incident energy $\mathrm {E}_{dd}^{qf}$ go much closer to the zero-quasi-free-energy point than that in the previous similar experiment. 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(E) data in low energy range extracted via the same Trojan horse nucleus ($\mathrm{^6Li}=(d \oplus \alpha)$ ) becomes better when the incident energy decreases from high value down to the zero-quasi-free-energy point. The very good agreement between data extracted from different Trojan horse nucleus ($\mathrm{^6Li}=(d \oplus \alpha)$ vs. $\mathrm{^3He}=(d \oplus p)$) gives a strong updated test for the independence of the binary indirect cross section on the chosen Trojan horse nucleus at low energies.