  The study of d(d,p)t reaction is very important for the nucleosynthesis in
both standard Big Bang and stellar evolution, as well as for the future fusion
reactors planning of energy production. The d(d,p)t bare nucleus astrophysical
S(E) factor has been measured indirectly at energies from about 400 keV down to
several keV by means of the Trojan horse method applied to the quasi-free
process $\rm {}^2H({}^6Li,pt){}^4He$ induced at a lithium beam energy of 9.5
MeV, which is closer to the zero quasi-free energy point. An accurate analysis
leads to the determination of the $\rm S_{bare}(0)=56.7 \pm 2.0 keV \cdot b$
and of the corresponding electron screening potential $\rm U_e = 13.2 \pm 4.3
eV$. In addition, this work gives an updated test for the Trojan horse nucleus
invariance comparing with previous indirect investigations using $\rm
{}^3He=(d+p)$ breakup.
