  Photodetachment of H$^-$ near a potential barrier is studied. A new formula
is presented for the cross sections induced by a barrier. The new formula
describes two quantum effects near barrier tops. For energies near and above
barrier tops, the quantum over-barrier reflection effects are included and the
induced oscillations in the cross sections are still prominent; for energies
near and below barrier tops, the quantum tunneling across barriers is taken
into account and consequently the oscillations are weakened. For energies far
away from the barrier tops, the new formula agrees with the standard
closed-orbit theory. We demonstrate that a potential barrier of various width
and location can be realized by placing a negative ion near a metal surface and
applying an electric field pointing to the surface. The width and location of
the barrier can be systematically changed by varying the electric field
strength and the distance between the negative ion and the surface. Results are
also presented for estimating the sizes and locations of aforementioned quantum
effects in the cross sections.
