Summary
The approximate solution to the multichannelN/D equations proposed by Pagels is used to predictS-wave bound states in an attractive Yukawa potential. In the first-order Born approximation the results are reasonable, but large deviations occur when the second-order Born approximation is added to the potential. This raises a serious problem of how to take into account higher-order corrections to the potential.
Riassunto
Si usa la soluzione approssimata delle equazioniN/D di molti canali proposta da Pagels per predire gli stati legati di ondaS in un potenziale di Yukawa attrattivo. Nell’approssimazione di Born del primo ordine si ottengono risultati ragionevoli, ma si hanno grandi deviazioni quando si aggiunge al potenziale l’approssimazione di Born del secondo ordine. Ciò solleva un serio problema sul modo di tener conto di correzioni di ordine maggiore al potenziale.
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References
H. Pagels:Phys. Rev.,140, B 1599 (1965).
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S. C. Frautschi:Regge Poles and S-Matrix Theory (New York, 1964).
L. Lewin:Dilogarithms and Associated Functions (London, 1958).
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Smith, J. On an approximate solution to the multichannelN/D equations. Nuovo Cimento A (1965-1970) 44, 733–739 (1966). https://doi.org/10.1007/BF02911198
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DOI: https://doi.org/10.1007/BF02911198