Summary
The Regge trajectories α(E) associated with the scattering of relativistic particles at a Coulomb potential are considered as analytic functions of the energyE. The trajectories for particle and antiparticle scattering are related by a simple crossing relation. In addition to the branch points atE=±m, the functions α(E) have complex branch points which are related to the possibility of a collapse into the centre. Corresponding singularities are expected for a Yukawa potential resulting from a vector meson interaction. The possible relevance of these results for relativistic dispersion theory is discussed.
Riassunto
Si considerano le traiettorie di Regge α(E) associate allo scattering di particelle relativistiche ad un potenziale Coulombiano come funzioni analitiche dell’energiaE. Le traiettorie per lo scattering particella-antiparticella sono in un rapporto dato da una semplice relazione incrociata. Oltre ai punti di ramificazione adE=±m, le funzioni α(E) hanno punti di ramificazione complessi che si riferiscono alla possibilità di una ricaduta nel centro. Si prevedono singolarità corrispondenti nel potenziale di Yukawa risultante dalla interazione di un mesone vettoriale. Si discute la possibile importanza di questi risultati nella teoria relativistica della dispersione.
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References
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CompareR. Oehme:Nuovo Cimento,4, 1316 (1956).
See, for example,R. Oehme:Phys. Rev. Lett.,4, 246 (1960).
The potentials considered here are not contained in the class discussed byM. Froissart:Complex Angular Momenta in Potential Scattering (1962) (to be published).
R. Oehme:Nuovo Cimento,13, 778 (1959), andThe Compound Structure of Elementary Particles, inWerner Heisenberg und die Physik unserer Zeit (Braunschweig, 1961), p. 240.
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Work supported in part by the U.S. Atomic Energy Commission.
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Oehme, R. Regge poles in relativistic schrödinger theory. Nuovo Cim 25, 183–192 (1962). https://doi.org/10.1007/BF02733323
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DOI: https://doi.org/10.1007/BF02733323