  Triple-$\alpha$ reaction rates have been determined well with the sequential
process via the narrow resonances. However, the direct triple-$\alpha$ process
at off-resonant energies still remains in unsolved problems. In the present
report, the direct triple-$\alpha$ contribution is estimated with a
non-adiabatic method, and it is found to be 10$^{-15}$--10$^{-3}$ pb order in
photodisintegration cross sections of $^{12}$C(2$^+_1 \rightarrow$ 0$^+$) for
$0.15 < E < 0.35$ MeV. This is far below the values predicted by the recent
adiabatic models. In spite of the large difference, the derived rates are found
to be concordant with NACRE at the helium burning temperatures.
