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Prog. Theor. Phys. Vol. 35 No. 3 (1966) pp. 463-484

[ Full Text PDF : FREE ACCESS (1204K) ]

An Impact Parameter Formalism. II

— High Energy Elastic Scattering —

Toshimi Adachi

The Tokyo Metropolitan Technical College, Shinagawa, Tokyo

(Received November 19, 1965)

Abstract:

The mathematical structure of the impact parameter formalism proposed by Kotani and Adachi is discussed. The formalism is regarded as a counterpart of the partial wave expansion of the scattering amplitude. An impact parameter amplitude is defined as a function of impact parameter and total energy. This amplitude has two characteristic features, corresponding to particle-like and wave-like pictures. The latter nature has not been taken into account in previous impact parameter formalisms.
In order to investigate the character of the impact parameter amplitude, our formalism is applied to high energy elastic scattering. A phenomenological analysis of the diffraction scattering is characterized by two parameters. Various expressions for the impact parameter amplitudes which are connected with the large angle proton-proton scattering are derived. The absorption coefficients for each particle waves are obtained.
The Lommel function of two variables is widely used in the diffraction scattering, just as it has been employed in the diffraction theory of classical light waves.


URL : http://ptp.ipap.jp/link?PTP/35/463/
DOI : 10.1143/PTP.35.463

[ Full Text PDF : FREE ACCESS (1204K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 35 No. 3 (1966) pp. 485-507 :
    An Impact Parameter Formalism. III
    Toshimi Adachi and Tsuneyuki Kotani
  2. Progress of Theoretical Physics Vol. 35 No. 3 (1966) pp. 576-578 :
    Analytic Property of Impact Parameter Amplitude
    Toshimi Adachi and Tsuneyuki Kotani
  3. Progress of Theoretical Physics Vol. 36 No. 2 (1966) pp. 313-336 :
    Scattering Phase Shifts at High Energies
    Yoshio Higuchi and Shigeru Machida
  4. Progress of Theoretical Physics Vol. 36 No. 4 (1966) pp. 745-760 :
    Impact Parameter Formalism. IV
    Toshimi Adachi, Tsuneyuki Kotani and Minoru Takeda
  5. Progress of Theoretical Physics Vol. 37 No. 6 (1967) pp. 1211-1227 :
    Impact-Parameter Representation for Proton-Proton Helicity Amplitudes at High Energies
    Reijiro Kubo
  6. Progress of Theoretical Physics Vol. 39 No. 2 (1968) pp. 430-452 :
    An Impact Parameter Representation of the Scattering Problem*
    Toshimi Adachi and Tsuneyuki Kotani
  7. Progress of Theoretical Physics Vol. 39 No. 3 (1968) pp. 785-816 :
    An Impact Parameter Representation of the Scattering Problem*
    Toshimi Adachi and Tsuneyuki Kotani
  8. Progress of Theoretical Physics Vol. 39 No. 4 (1968) pp. 1006-1019 :
    An Impact-Parameter Representation of Pion-Nucleon Scattering Amplitudes at High Energies
    Reijiro Kubo
  9. Progress of Theoretical Physics Vol. 80 No. 5 (1988) pp. 752-756 :
    Note on a New Form of Impact Parameter Representation
    Toshimi Adachi, Gyo Sakaguchi and Shigeru Sasabe

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