A new approximation for the continuous interaction potentials of atomic planes and strings with channeled electrons and positrons in crystals is proposed. A model in which atomic electron distributions within a certain atomic subshell are assumed to be exponentially decaying is used. Contrary to the Thomas-Fermi (TF) and Thomas-Fermi-Dirac (TFD) models this approach takes into account the shell structure of atoms in reasonably good agreement with the Hartree-Fock method (HF). Simple analytical expressions for the continuous plane (string) potentials are given. Calculations of several planar potentials for positrons channeled in silicon and tungsten are presented. Results are compared with widely known Lindhard and Molière approximations. Some estimates of the Kumakhov spontaneous radiation intensity under positron planar channeling conditions in the classical approximation are also given.