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The $\mathrm{^2H}(d,p)\mathrm{^3H}$ bare nucleus astrophysical S(E) factorhas been measured indirectly at energies from about 500 keV down to several keVby 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 11and 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 inthe previous similar experiment. The obtained results are compared with directdata as well as with previous indirect investigation of the same binaryreactions. It shows that the precision of S(E) data in low energy rangeextracted via the same Trojan horse nucleus ($\mathrm{^6Li}=(d \oplus \alpha)$) becomes better when the incident energy decreases from high value down to thezero-quasi-free-energy point. The very good agreement between data extractedfrom different Trojan horse nucleus ($\mathrm{^6Li}=(d \oplus \alpha)$ vs.$\mathrm{^3He}=(d \oplus p)$) gives a strong updated test for the independenceof the binary indirect cross section on the chosen Trojan horse nucleus at lowenergies.

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