Analytical Description of the Resonance Dechanneling Effect in the Case of Axial‐To‐Planar Channeling Transition

Abstract

The theory of resonance dechanneling under axial-to-planar transition conditions is further developed. For describing the structure of the atomic planes a n analytical potential expression is used in the Thomas-Fermi-MoliBre approximation on the basis of Lindhards string of strings model. As a result of the investigation of the nonlinear equation of ion motion along the planar channel an expression is derived to calculate the 'tilt angle amin required for planar channeling to be effective. This angle increases with increasing transversal coordinate in the planar channel.I n this way the angular interval amin < a < amax is obtained which separates the axial channeling from the "pure" planar one. In a linear approximation of increasing transversal oscillation amplitude the initial amplitude is calculated, for particles which take part in the resonance of given order. The theoretical results are in sufficient agreement with numerical calculations and experimental values.Die Theorie der Resonanzdekanalisierung unter den Bedingungen des Axial-Flachen-ubergangs wird weiterentwickelt. Zur Beschreibung der Struktur der Atomflachen wird ein analytischer Ausdruclr in der Thomas-Fermi-MoliL;re-N&herong im Rahmen des Lindhardschen ,,Ketten von Ketten"-Modells verwendet. I m Ergebnis der Untersuchiingen der nichtlinearen Gleichungen der Ionenbewegung im Flachenkanal wird ein Ansdruck fur den Einfallswinkel amin gefunden. von dem a b planare Kanalleitung realisiert ist. Dieser Winkel wachst mit der Transversalkoordinate im Flachenkanal an. Somit wird das Winkelintervall a,in < a < amax erhalten, welches die axiale und die ,,reine" Fliichenkanalleitung trennt. Weiterhin werden allgemeine Resonanzbedingungen und ein Ausdrnck fur die Amplitudenabhiingigkeit der Schwingungsfrequenz der kanalisierten Ionen abgeleitet. In einer linearen Niiherung des Anwachsens der Schwingungsamplitude wird die Anfangsamplitude filr die Teilchen berechnet, die a n der Resonanz der gegebenen Ordnnng teilnehmen. Die theoretischen Ergebnisse stinimen befriedigend mit Computerrechnungen und experimentellen Werten iiberein.

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