Summary
The recently introduced dispersion relations for the logarithm of the scattering amplitude are combined with the Glauber formalism for scattering by composite systems. The dispersion relations yield the angular dependence of the phase of the single-particle amplitudes which can be substituted directly into the Glauber expressions. The total and differential cross-sections are then immediately calculable. The method is illustrated by a detailed treatment of πd elastic scattering, but is readily extended to other beam particles and targets.
Riassunto
Si combinano col formalismo di Glauber per lo scattering di sistemi composti le relazioni di dispersione introdotte recentemente per il logaritmo dell'ampiezza di scattering. Le relazioni di dispersione formiscono la dipendenza angolare della fase delle ampiezze delle particelle singole, che può essere sostituita direttamente nelle espressioni di Glauber. Si possono allora immediatamente calcolare le sezioni d'urto totale e differenziale. Si illustra il metodo con un'analisi dettagliata dello scattering elastico πd, e lo si estende con facilità ad altri fasci di particelle e bersagli.
Резюме
Недавно введенные дисперсионные соотношения для логарифма амплитуды рассеяния объединяются с формализмом Глаубера для рассеяния сложных систем. Эти дисперсионные соотношения дают угловую зависимость фазы одно-частичных амплитуд, которая может быть непосредственно подставлена в выражения Глаубера. После этого полное и дифференциальное поперечные сечения могут быть вычислены. Этот метод иллюстрируется подробным рассмотрением упругого πd рассеяния, по может быть без труда обобщен на другие пучки частиц и мишени.
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McClure, J.A., Jorna, S. Use of new dispersion relations in the Glauber formalism with application to πd scattering. Nuovo Cimento A (1965-1970) 67, 667–677 (1970). https://doi.org/10.1007/BF02758871
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DOI: https://doi.org/10.1007/BF02758871