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Finite-energy sum rules for hadron-nucleus scattering

Правила сумм при конечной знергии для рассеяния адронов на ядрах

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Il Nuovo Cimento A (1965-1970)

Summary

We discuss the possibility of extracting information about the hadron-nucleus scattering amplitude, using finite-energy sum rules and a comparison amplitude with well-defined analytical properties. As examples we calculate the real parts of the forward π4He and π12C scattering amplitudes, using only total cross-sections determined over a finite energy range. The determined values compare favourably with experimental results and the most recent dispersion relation analysis. Furthermore, we determine the asymptotic corrections to the Glauber approximation for the same two cases. The correction to the real part is found to be significant, as predicted by the Fresnel correction to the Glauber amplitude.

Riassunto

Si discute qui la possibilità di estrarre informazione su l’ampiezza adrone-nucleo, usando regole di somma ad energia finita e un’ampiezza di confronto con proprietà analitiche definite. Come controllo del metodo, calcoliamo le parti reali delle ampiezze π4He e π12C in avanti, usando le sezioni d’urto totali relative a un intervallo d’energia finito. I valori calcolati per la parte reale sono confrontati con i dati sperimentali e le più recenti analisi dispersive tradizionali, mostrando un buon accordo. Inoltre determiniamo le correzioni asintotiche all’approssimazione di Glauber, presa come ampiezza di confronto. I risultati non sono incompatibili con una correzione alla parte reale, costante con l’energia, come predetto dalla correzione di Fresnel all’ampiezza di Glauber.

Реэюме

Мы обсуждаем воэможность иэвлечения информации об амплитуде рассеяния адронов на ядрах, испольэуя правила сумм при конечной знергии и амплитуду с отчетливо выраженными аналитическими свойствами. Мы вычисляем вешественные части амплитуд рассеяния π4Не и π12С в направлении вперед, испольэуя только полные поперечные сечения, определенные при конечных знергиях. Полученные эначения согласуются с зкспериментальными данными и с недавним аналиэом дисперсионных соотнощений. Кроме того, мы определяем асимптотические поправки к приближению Глаубера для двух рассмотренных случаев. Обнаружено, что поправка к вешественной части является сушественной, как следует иэ поправки Френеля к амплитуде Глаубера.

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Author notes

  1. J. Leon

    Present address: Instituto « Rocasolano », Madrid

Authors and Affiliations

  1. Istituto di Fisica Teorica dell’Università, Trieste

    G. Alberi

  2. Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, Italy

    G. Alberi

  3. Swiss Institute for Nuclear Research, Zurich

    Z. Grossman

  4. International Centre for Theoretical Physics, Trieste

    J. Leon

  5. Fysisk Institutt, Norges Laererhøgskole, Universitetet i Trondheim, Trondheim

    P. Osland

Authors
  1. G. Alberi
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  2. Z. Grossman
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  3. J. Leon
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  4. P. Osland
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Additional information

GIFT.

A major part of this work was done while two of the authors (GA and PO) were at CERN.

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Alberi, G., Grossman, Z., Leon, J. et al. Finite-energy sum rules for hadron-nucleus scattering. Nuov Cim A 25, 353–376 (1975). https://doi.org/10.1007/BF02729052

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