Asymptotic bounds on the derivatives of the elastic scattering amplitudes

✍ Scribed by Arvind S. Vengurlekar

• Publisher: Elsevier Science
• Year: 1977
• Tongue: English
• Weight: 975 KB
• Volume: 109
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(77)90168-3

✦ Synopsis

Using unitarity, analyticity in the Lehmann-Martin ellipse, and asymptotic polynomial boundedness, rigorous high energy upper bounds are established on the derivatives of the absorptive parts A@, t) of elastic scattering amplitudes at i = 0. These are used to obtain a number of useful results including bounds on A@, t) and its derivatives for 0 < I < to, s --, m (t,, = 4m,,a for nn and TN). Lower bounds on the derivatives at t < 0 are derived and used to determine the near-forward physical region in which the derivatives can not vanish. We also obtain upper bounds on the derivatives of elastic differential cross sections for t < tJ4, s ---f co.

• Recently, asymptotic lower bounds for 0 < t < t, and unitarity upper and lower bounds for t < 0 have been obtained on d In A(s, t)/dt. See Ref. 23.