Summary
The formulae for the amplitudes of Delbrück scattering given in a previous paper are manipulated and much simpler expressions for them are derived having the form of a sum of twofold and threefold integrals. The integrands are rather compact and contain only rational, irrational and logarithmic functions. In this preliminary work we consider only the amplitudea +− for circularly polarized photons and we give numerical results for photon energy equal to 10.83 MeV and scattering angle in the range from 50° to 150°. For what concerns the real part of the amplitudes, these preliminary results allow one to resolve the discrepancy between the numerical results previously obtained by Ehlotzky and Sheppey and those more recently given by Papatzacos. In fact our results agree with those by Papatzacos and this seems to confirm that the fixed-angle dispersion relation used by Ehlotzky and Sheppey for the calculation of the real parts is incorrect.
Riassunto
Le formule per le ampiezze di diffusione elastica di fotoni da nuclei («Delbrück scattering»), ricavate in un precedente lavoro, sono rimaneggiate in modo da ottenere per esse espressioni molto più semplici aventi la forma di somme di integrali doppi e tripli. Gli integrandi sono piuttosto compatti e contengono solamente funzioni razionali, irrazionali e logaritmiche. In questo lavoro preliminare consideriamo solo l’ampiezza per fotoni polarizzati circolarmentea +− e diamo risultati numerici per l’energia del fotone uguale a 10.83 MeV e per l’angolo di diffusione compreso tra 50° e 150°. Per quanto riguarda la parte reale dell’ampiezza, questi risultati preliminari permettono di risolvere la discrepanza fra i risultati numerici ottenuti in precedenza da Ehlotzky e Sheppey e quelli ricavati più recentemente da Papatzacos. Infatti i nostri risultati concordano con quelli di Papatzacos e ciò sembra confermare che la relazione di dispersione ad angolo fissato usata da Ehlotzky e Sheppey per il calcolo delle parti reali non è corretta.
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References
F. Rohrlich andR. L. Gluckstern:Phys. Rev.,86, 1 (1952).
F. Ehlotzky andG. C. Sheppey:Nuovo Cimento,33, 1185 (1964).
P. Kessler:Journ. Phys. Rad.,19, 739 (1958).
P. Papatzacos:Delbrück scattering, University of Trondheim, Norvay (1974) (unpublished).
V. Costantini, B. De Tollis andG. Pistoni:Nuovo Cimento,2 A, 733 (1971) (henceforth referred to as A).
Subroutine RIWIAD (Riemann Integration with Interval Adjustement) D114, CERN (authors:Dutner, Lautrup andSheppey).
Our amplitudea +− is related to the amplitudes for linearly polarized photons as follows:a +− = 1/2 (a 11 −a 22) (see eqs. (52) of A). Therefore it has the opposite sign with respect to that defined byPapatzacos in eq. (VII.6,9) of his work.
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De Tollis, B., Lusignoli, M. & Pistoni, G. On Delbrück scattering. Nuov Cim A 32, 227–235 (1976). https://doi.org/10.1007/BF02730005
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DOI: https://doi.org/10.1007/BF02730005