  Starting from the WKB approximation, a new barrier penetration formula is
proposed for potential barriers containing a long-range Coulomb interaction.
This formula is especially proper for the barrier penetration with penetration
energy much lower than the Coulomb barrier. The penetrabilities calculated from
the new formula agree well with the results from the WKB method. As a first
attempt, this new formula is used to evaluate alpha decay half-lives of atomic
nuclei and a good agreement with the experiment is obtained.
