Summary
In this paper we calculate the first three Born approximations to the differential cross-section for non-relativistic scattering by a Yukawa potential in the limit of zero screening. The result agrees with the exact (Rutherford) cross-section for Coulomb scattering. This supports the suggestion made by Dalitz that the (divergent) higher Born approximations for Coulomb scattering act solely as a phase-factor multiplying the first Born approximation matrix-element.
Riassunto
Nel presente lavoro si calcolano le tre prime approssimazioni alla sezione d’urto differenziale per lo scattering non relativistico da parte di un potenziale di Yukawa al limite di schermatura zero. Il risultato si accorda con la sezione d’urto esatta (di Rutherford) per lo scattering coulombiano. Ciò avvalora l’ipotesi di Dalitz che le superiori (divergenti) approssimazioni di Born per lo scattering coulombiano agiscano soltanto come fattore di fase che moltiplica l’elemento di matrice della prima approssimazione di Born.
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References
W. Gordon:Zeits. f. Phys.,48, 180 (1928).
R. H. Dalitz:Proc. Roy. Soc., A206, 509 (1951).
C. Møller:Zeits. f. Phys.,66, 513 (1930).
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This work forms part of a D. Phil. thesis and was carried out at Oxford under the supervision of Dr.Handel Davies.
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Kacser, C. Higher born approximations in non-relativistic Coulomb scattering. Nuovo Cim 13, 303–318 (1959). https://doi.org/10.1007/BF02732939
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DOI: https://doi.org/10.1007/BF02732939