Reaction rates of the fusion reaction $^{12}$C+$^{12}$C at E$_{CM}$ = 2.10 to 4.75 MeV for the $^{20}$Ne and $^{23}$Na exit channels

The fusion reaction $^{12}$C + $^{12}$C has been studied at E$_{CM}$ = 2.10 to 4.75 MeV by $\gamma$-ray spectroscopy using a C target of ultra-low hydrogen contamination. The deduced astrophysical \~{S}(E) factor exhibits previously unknown resonances at E $\leq$ 3.0 MeV, in particular a strong narrow resonance at E = 2.14 MeV, which lies at the high-energy tail of the Gamow peak. The resonance increases the present non-resonant reaction rate of the $\alpha$ channel significantly near T = 8 x 10$^{8}$ K. Due to the resonance structure, extrapolation to the Gamow energy E$_{G}$ = 1.5 MeV is quite uncertain.