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INSTITUTE OF PHYSICS PUBLISHING EUROPEAN JOURNAL OF PHYSICS Eur. J. Phys. 24 (2003) 47–65 PII: S0143-0807(03)38404-1 Screened Coulomb scattering versus Thomson scattering Pascal Monceau 1 , Thomas Szydlo 2 and Galliano Valent 3 1 Laboratoire de Physique Th´eorique de la Mati`ere Condens´ee, Pˆole Mati`ere et Syst`emes Complexes, (FR2438 CNRS) Universit´ ePar is7-Denis Diderot, 2 Place Jussieu, 75251 Paris Cedex 05, France 2 D´epartement de Physique et Mod´elisation, Universit´ ed’Evry Val d’Essonne, Boulevard F Mitterrand, 91025 Evry Cedex, France 3 Laboratoire de Physique Th´eorique et des Hautes Energies, Unit´ eAssoci´ee au CNRS UMR 7589, 2 Place Jussieu, 75251 Paris Cedex 05, France Received 19 June 2002, in final form 18 September 2002 Published 10 December 2002 Online at Abstract We examine a simplified approach to the classical scattering of a particle by a neutral atom, first for a Thomson-like model and then for different screened Coulomb potentials. As an application we discuss in detail why, in the experiments of Geiger and Marsden on the scattering of α particles by matter, screening effects are negligible. On the way we encounter several unusual phenomena in classical scattering theory. 1. Introduction Most of the information on the structure of matter (atoms, molecules, nuclei, etc) comes, roughly speaking, from two sources: (1) Spectroscopic data, from whichwe get thebound-state energies. If one hassome idea about the interactions between the constituents one can compute the corresponding energies and compare the results with experiment. (2) Scattering data, where the measured scattering cross-section data give useful,albeit partial, information about the potentiallaw between the constituents. Historically the first model of atomic structure was Thomson’s model. Only after Geiger and Marsden’s experiments [1] came the proposal by Rutherford [2] (reprinted in the more accessible reference [3]) of the planetary structure of the atom. A more systematic study of the experimental consequences of Rutherford’s model was undertaken later [4]. Recently, Zoli examined [5], according to classical scattering theory, the differences between scattering by a Coulomb potential and by a Thomson-like potential, and concluded that the experimental data favoured the planetary atom model, which we know, today, to be the case. In his work, Zoli compared pure Coulomb scattering with the potential law U ( r ) = g r , r ± 0 , (1) 0143-0807/03/010047+19$30.00 © 2003 IOP Publishing Ltd Printed in the UK 47
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48 PMonceau et al and scattering from a Thomson-like potential U Th ( r ) = g µ 1 r 2 a 2 , 0 6 r 6 a , 0 , r > a . (2) In the latter case a is the atom size and g atypical energy of the atom. Let us observe that, while for the second potential the atomic size is taken into account by the parameter a , in the Frst potential there is no screening linked to the atomic structure. Nevertheless, such a screening is quite obvious. The incoming alpha particle Frst sees a neutral gold atom, but as soon as it
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This note was uploaded on 08/21/2011 for the course PHYS 101 taught by Professor Daniel during the Spring '11 term at Universidad Nacional de Colombia.

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