The Exact Potential in a Plane Crystal Channel

Abstract

General considerationsWe consider the case of planar channeling. Under planar channeling regime a continuum potential determines the motion of a particle [l]. The expression for the continuum planar potential is [l, 21 where e is the distance of the point we consider from the crystal plane, R is the distance on the plane from the projection of the point, V ( r ) is an atomic screened Coulomb potential, a is the screening length, and n is the areal density of atoms.Two of the most commonly used and most accurate screening functions are those of Moliere [2 to 41 and the "Universal" one [5]. Both The potentialinside a crystal Expression (1) gives the potential for a particle, on a plane from which the particle's distance is e. But inside a crystal the potential is a result of the interaction with all the planes of the crystal lattice. In practice for the potential at a specific point two or at most a few planes were taken into account, by summing their contributions to the total potential. These calculations do not result in simple analytic expressions, easy to handle for further use.We proceed instead along the following way: suppose that a point P is at a distance e from one plane, say plane A, as shown in Fig. 1. We put d = dJ2. For a particle with l ) Panepistimiopolis, Ilissia, GR-15771 Athens, Greece.39 physica (b) 18012