  Carbon burning is a crucial process for a number of important astrophysical
scenarios. The lowest measured energy is around E$_{\rm c.m.}$=2.1 MeV, only
partially overlapping with the energy range of astrophysical interest. The
currently adopted reaction rates are based on an extrapolation which is highly
uncertain because of potential resonances existing in the unmeasured energy
range and the complication of the effective nuclear potential. By comparing the
cross sections of the three carbon isotope fusion reactions,
${}^{12}$C+${}^{12}$C, ${}^{12}$C+${}^{13}$C and ${}^{13}$C+${}^{13}$C, we have
established an upper limit on the molecular resonance strengths in
${}^{12}$C+${}^{12}$C fusion reaction. The preliminary results are presented
and the impact on nuclear astrophysics is discussed.
