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

A general formalism of two-dimensional lattice potential on beam transverse plane for studying channeling radiation