  In this paper we revisit the one-dimensional tunnelling problem. We consider
different approximations for the transmission through the Coulomb barrier in
heavy ion collisions at near-barrier energies. First, we discuss approximations
of the barrier shape by functional forms where the transmission coefficient is
known analytically. Then, we consider Kemble's approximation for the
transmission coefficient. We show how this approximation can be extended to
above-barrier energies by performing the analytical continuation of the radial
coordinate to the complex plane. We investigate the validity of the different
approximations considered in this paper by comparing their predictions for
transmission coefficients and cross sections of three heavy ion systems with
the corresponding quantum mechanical results.
