A simple nonbinary scattering model applicable to atomic collisions in crystals at low energies

Hans Henrik Andersen, Peter Sigmund

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Abstract

This paper presents the solution of a special scattering problem which may be important in the theory of slowing-down of atomic particles in crystals . A projectile moves along the center axis of a regular ring of n equal atoms which are free and do not interact with each other. The interaction between the projectile and each ring atom is described by a Born-Mayer potential, and the scattering is assumed to be elastic and governed by the classical equations of motion. Because of symmetry, the problem can be reduced to plane motion of a particle in a potential of elliptic symmetry. The elliptic force field is approximated by a spherical one, which is dependent on the initial conditions of the individual scattering problem . For the spherical symmetrical potential, scattering angles and related quantities have been tabulated, but simple analytical approximations can be used too. As a result, one obtains the asymptotic velocities of the ring atoms as well as the energy loss of the projectile. Furthermore, it can be decided whether the projectile is reflected by the ring. Both the feasibility of assumptions specifying the problem and the validity of different approximations made in the transformation from the elliptic to the spherical potential are investigated. Special attention is paid to proper definitions of collision time and collision length which are important in collisions in crystals. Limitations to classical scattering arising from the uncertainty principle prove to be more serious than assumed previously. Inelastic contributions to the energy loss can easily be included . The oscillator forces binding lattice atoms turn out to influence the scattering process only at very small energies. The validity of the so-called momentum approximation and a related perturbation method are also investigated.
Original languageEnglish
Title of host publicationMatematisk-Fysiske Meddelelser udgivet af Det Kongelige Danske Videnskabernes Selskab
Place of PublicationKøbenhavn
PublisherDet Kongelige Danske Videnskabernes Selskab
Publication date1966
Pages5-50
Publication statusPublished - 1966
Externally publishedYes
SeriesMatematisk-fysiske meddelelser udgivet af Det Kongelige Danske Videnskabernes Selskab
Number15
Volume34

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