Asymptotic properties of scattering amplitudes and their experimental consequences

• Published in: Nuclear physics. B 1971-01, Vol.28 (1), p.253-282
• Main Authors: Eden, R.J., Kaiser, G.D.
• Format: Article
• Language: English
• ISSN: 0550-3213; 1873-1562
• DOI: 10.1016/0550-3213(71)90377-4

Bounds are obtained on the asymptotic behaviour of scattering amplitudes that violate the Pomeranchuk theorem and correspond to asymptotically-constant total cross sections. It is proved that the differential cross sections have forward peaks whose height grows like B ln 2( s) and whose width shrinks line B′ {ln( s)} −2. It is proved that the amplitudes have zeros in the region | t| ∼ B″ {ln( s)} −2, and bounds are obtained on the constants B, B′ and B″. A range of possible experimental consequences is studied and it is found that interference between Coulomb interactions and strong interactions plays a major role in determining whether the new theoretical results can be observed in practice. A narrow strong peak in the Coulomb region cannot be excluded and may invalidate some experimental procedures for obtaining the phases of forward amplitudes and total cross sections.