  To study channeling radiation produced by an ultra-relativistic electron beam
channeling through a single crystal, a lattice potential of the crystal is
required for solving the transverse motion of beam electrons under the
influence of the crystal lattice. In this paper, we present a general formalism
for this two-dimensional lattice potential of a crystal with a Lorentz
contraction in the beam channeling direction. With this formalism, the lattice
potential can be calculated without approximation from any given model of
electron-ion interaction for an ultra-relativistic beam channeling in any
crystal direction. The formalism presented should be the standard recipe of the
lattice potential for studying the channeling radiation.
