Summary
The scattering at high energy of a relativistic spinless particle by a (complex) potential is studied. It is shown that the phase shift, in the impact-parameter representation, becomes energy independent at high energy. We prove that, consequently, both the elastic and inelastic total cross-sections approach nonzero limits as the energy goes to infinity.
Riassunto
Si studia lo scattering di alta energia di una particella relativistica senza spin su un potenziale (complesso). Si dimostra che lo spostamento di fase, nella rappresentazione del parametro d’impatto, diviene indipendente dall’energia ad alte energie. Si dimostra, in consequenza, che sia la sezione d’urto elastica che quella inelastica si avvicinano a limiti non nulli quando l’energia tende all’infinito.
Резюме
Исследуется рассеяние при высоких энергиях релятивистской бесспиновой частицы на (комплексном) потенциале. Показывается, что фазовыи сдвиг, в представлении прицельного параметра, становится независящим от энергии. Мы доказываем, что и упругое и неупругое полные поперечные сечения стремятся к ненулевым пределам, когда энергия стремится к бесконечности.
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Research supported by the Swiss National Science Foundation.
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Martin, P.A. On the high-energy limit in potential scattering. Nuov Cim A 17, 73–95 (1973). https://doi.org/10.1007/BF02790288
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DOI: https://doi.org/10.1007/BF02790288