Truncated Coulomb potential for planar channeling

It is shown that if the atomic screening function is described in the Thomas-Fermi approximation, the corresponding continuous potential for planar channeling to a good accuracy reduces to a truncated Coulomb potential. The sum of two displaced Coulomb potentials also accurately approximates interplanar static continuous potentials for Si, Ge, W crystals in orientation (110), as well as the thermal potential of a Ge crystal in orientation (111), not too close to atomic planes. Such a possibility can be used to facilitate the description of channeled and quasichanneled particle motions. We illustrate this by calculating classical particle channeling periods, quantum energy levels, and the probability of tunneling of a negatively charged particle through a single atomic plane. Simple scaling laws in dependencies of those quantities on the atomic number Z result this case.