Behavior of Regge Poles in a Potential at Large Energy

H. A. Bethe and T. Kinoshita
Phys. Rev. 128, 1418 – Published 1 November 1962
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Abstract

Following Mandelstam's suggestion, we consider a potential which can be expanded in a power series in r, beginning with 1r. Then at large energy (positive or negative) there will be Regge poles at all negative integral values of l. If the 1r term is absent in the expansion of the potential, the pole at l=1 will be absent. Generally, if r2n1 is the first nonvanishing odd power term in the potential expansion, the poles at 1, 2, , n are absent. If the potential expansion contains only even non-negative powers of r, there will be no Regge poles at finite negative l in the limit of large energy. If the potential behaves as ar2 at small r, the scattering amplitude has a cut in the l plane from 12a12 to 12+a12, and the Regge poles are no longer located at negative integers at large energy. For finite energy, it is shown that a pole at a positive integer or half-integer l implies another pole at l1 but that the residues at these poles are, in general, different from each other.

  • Received 27 June 1962

DOI:https://doi.org/10.1103/PhysRev.128.1418

©1962 American Physical Society

Authors & Affiliations

H. A. Bethe and T. Kinoshita

  • Laboratory of Nuclear Studies, Cornell University, Ithaca, New York

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Issue

Vol. 128, Iss. 3 — November 1962

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