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A perturbative expansion for large angular momenta

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Il Nuovo Cimento (1955-1965)

Summary

A perturbative formalism is presented, in the framework of potential scattering, in which the usual energy denominators are substituted by angular-momentum denominators. The trick is accomplished by expanding the partial wave function over free wave functions of different angular momenta at the same energy. A perturbative expansion is also given for f0(λ,-k)/f.(λ,-k) being f0 and f. the free and the exact Jost functions, respectively. The convergence of the solution improves for high angular momenta.

Riassunto

Nella teoria del Potenziale si presenta un formalismo perturbativo in oui i soliti denominatori di energia sono sostituiti da denominatori di momento angolare. CiÒ si ottiene sviluppando Fonda parziale in oude imperturbate di diverso momento angolare ma di uguale energia. Si dà anche uno sviluppo perturbativo per f.0(λ,-k)/f(λ,-k), ove f.0 ed f. sono le funzioni di Jost rispettivamente libera ed esatta. Si dimostra che la convergenza della soluzione migliora a grandi momenti angolari.

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References

  1. A. Erdelyi, W. Magnus, F. Oberhettinger andF. Tricomi:Tables of Integral Transforms, vol.2 (New York, 1954), ch. XII.

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Authors and Affiliations

  1. Istituto di Fisica dell‘ Università, Torino

    V. De Alfaro, E. Predazzi & C. Rossetti

  2. Sezione di Torino, Istituto Nazionale di Fisica Nucleare, Torino

    V. De Alfaro, E. Predazzi & C. Rossetti

Authors
  1. V. De Alfaro
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  2. E. Predazzi
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  3. C. Rossetti
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De Alfaro, V., Predazzi, E. & Rossetti, C. A perturbative expansion for large angular momenta. Nuovo Cim 30, 522–535 (1963). https://doi.org/10.1007/BF02828830

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  • DOI: https://doi.org/10.1007/BF02828830

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