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TheN/D method and the diffraction picture

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Il Nuovo Cimento (1955-1965)

Summary

Elastic spin 0-spin 0 scattering is considered and it is argued that, in order to have a simple connection between the total amplitude and the partial-wave amplitude in the high-energy region, the latter has to satisfy the boundary condition corresponding to the « diffraction picture ». If the amplitude can be written in the conventionalN l (ν)/D l (ν) form, whereN l (ν) has only a left-hand cut andD l (ν) only a right-hand cut, and where there are no arbitrary subtraction constants, it follows that the imaginary part ofD l (ν) behaves likeν −1/2 forν→∞ (apart from possible logarithmic factors).

Riassunto

Si studia lo scattering elastico spin 0-spin 0 e si argomenta che, per avere una semplice connessione fra l’ampieza totale e l’ampiezza dell’onda parziale nella regione di alta energia, quest’ultima deve soddisfare la condizione ai limiti corrispondente allo « schema di diffrazione ». Se l’ampiezza può essere scritta nella formaN l (ν)/D l (ν) convenzionale, in cuiN l (ν) ha solo un taglio a sinistra eD l (ν) solo un taglio a destra, segue che la parte immaginaria diD l (ν) si comporta comeν −1/2 perν→∞ (a prescindere da possibili fattori logaritmici).

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Literatur

  1. M. Bander andG. L. Shaw:Ann. Phys. (N. Y.),31, 506 (1965).

    Article  MathSciNet  ADS  Google Scholar 

  2. H. Lehmann:Nucl. Phys.,29, 300 (1962);L. Van Hove:Phys. Lett.,5, 252 (1963);7, 76 (1963);N. N. Khuri andT. Kinoshita:Phys. Rev. Lett.,14, 84 (1965);Phys. Rev.,137, B 720 (1965);P. Olesen:Phys. Lett.,13, 175 (1964);14, 66 (1965);Y. S. Jin andS. W. MacDowell:Phys. Rev.,138, B 1279 (1965);A. Białas andE. Białas Nuovo Cimento 37, 1686 (1965);A. Martin:Phys. Lett.,15, 76 (1965);R. Wit:Phys. Lett.,15, 350 (1965).

    Article  Google Scholar 

  3. R. Omnès:Phys. Rev.,133, B 1543 (1964); errata (UCRL 11008) to be published inPhys. Rev.;E. J. Squires:Nuovo Cimento,34, 1277 (1964).

    Article  MathSciNet  ADS  Google Scholar 

  4. E. J. Squires:Nuovo Cimento,34, 1751 (1964).

    Article  MathSciNet  Google Scholar 

  5. L. Lanz andG. M. Prosperi:Nuovo Cimento,33, 201 (1964).

    Article  MathSciNet  Google Scholar 

  6. P. Olesen:Nucl. Phys.,60, 641 (1964);62, 593 (1965);64, 685 (1965). The dynamical model studied in these papers cannot be treated by use of the conventionalN/D method in a self-consistent manner; the reason for this is the incompatibility of the dynamical assumption about ReA l (ν), the conventionalN/D method, and the diffraction picture (this statement is a consequence of the results obtained in the present paper).

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Author information

Authors and Affiliations

  1. Institute for Theoretical Physics, University of Copenhagen, Copenhagen

    P. Olesen

  2. Department of Mathematics, University of Durham, Durham City

    E. J. Squires

Authors
  1. P. Olesen
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  2. E. J. Squires
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Additional information

TheN/D method and the diffraction picture have been discussed previously byJ. Hamilton:Strong Interactions and High-Energy Physics (London, 1964), p. 281 (see in particular the discussion pp. 342–351). Our result clarifies the previous discussion.

He appreciates interesting discussions with Dr.K. Johnson, Dr.D. H. Lyth and Dr.J. Smith.

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Olesen, P., Squires, E.J. TheN/D method and the diffraction picture. Nuovo Cim 39, 956–966 (1965). https://doi.org/10.1007/BF02734629

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  • DOI: https://doi.org/10.1007/BF02734629

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