Summary
Exact expressions for the lower bounds of the maximum of the scattering amplitude of differential cross-section between two (complementary) constant angles, as well as betweent=const andu const are derived using the Nevanlinna principle, both for finite energies as in the high-energy limit. Computations were performed for two distinct assumptions about the analyticity domain of the scattering amplitude: for the shrinking ellipse of Lehmann and for the Mandelstam cosine cut complex plane.
Riassunto
Per mezzo del principio di Nevanlinna si deducono le espressioni esatte dei limiti inferiori del massimo dell'ampiezza di scattering della sezione d'urto differenziale fra due angoli costanti (complementari), ed anche trat=cost eu=cost, sia per energie finite che nel limite delle alte energie. I calcoli sono stati eseguiti in base a due distinte ipotesi sul dominio di analiticità dell'ampiezza di scattering: in base all'ellisse di contrazione di Lehmann ed in base al piano complesso tagliato del coseno di Mandelstam.
Резюме
Используя принцип Неванлинна и при конечных энергиях и в пределе высоких энергий, выводятся точные выражения для нижних граииц максимума амплитуды рассеяния или дифференциального поперечного сечения между двумя (дополнительными) постоянными углами, а также приt=const иu=const. Вычисления проводятся при двух различных предположениях относительно области аналитичности амплитуды рассеяния; для сужающегося эллипса Лемана и для комплексной плоскости косинуса угла рассеяния с манделстамовским разрезом.
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References
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Exactly the same behaviour is found of the Cerulus-Martin intermediate domain: there is a misprint in the formula in footnote (11) ofKinoshita (3)—an exponent of 1/2 is to be added to the factor (1−y).
The problem of thestability of the extrapolation of the (experimental) scattering amplitude which will be extensively treated in a subsequent paper.
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Ciulli, S. Large-angle and large-momentum-transfer lower bounds for the differential cross-section in the Lehmann ellipse and the Mandelstam cut-plane cases. Nuovo Cimento A (1965-1970) 61, 463–485 (1969). https://doi.org/10.1007/BF02756855
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DOI: https://doi.org/10.1007/BF02756855