Reflection Model and High-Energy <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow><mi>p</mi></math></span> Backward Peaks

Ming Chiang Li

doi:10.1103/PhysRevD.1.326

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Reflection Model and High-Energy $π^{-} p$ Backward Peaks

Ming Chiang Li

Department of Physics, Virginia Polytechnic Institute, Blacksburg, Virginia 24061

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Phys. Rev. D 1, 326 – Published 1 January, 1970

DOI: https://doi.org/10.1103/PhysRevD.1.326

Abstract

We propose a classical optical model for high-energy elastic scattering. The model predicts that the logarithmic slopes for forward differential cross sections should be either the same or twice as large as the backward ones. The backward peak is due to the contribution from the discontinuity in the boundary of the optical medium. The model has the property that the mechanisms responsible for the forward and backward scatterings are not independent of each other. This is contrasted with conventional models which view the forward and backward scatterings as arising from independent mechanisms. For example, in absorptive and Regge-pole models the main contribution to the forward scattering comes from $t$ -channel exchange, while backward scattering arises from $u$ -channel exchange. A fit is made to the high-energy $π^{-} p$ data in both forward and backward directions, and good results are obtained.

References (14)

G. Wentzel, Z. Physik 38, 518 (1926) H. A. Kramers, ibid. 39, 828 (1926) M. Brillouin, J. Phys. 3, 65 (1922)
J. M. Blatt and V. F. Weisskopf, Theoretical Nuclear Physics (John Wiley & Sons, Inc., New York, 1952)
K. Gottfried and J. D. Jackson, Nuovo Cimento 34, 735 (1964) J. D. Jackson, Rev. Mod. Phys. 37, 484 (1965) L. Durand and Y. T. Chiu, Phys. Rev. Letters 12, 399 (1964) ibid.13, 45(E) (1964)
V. Barger and D. Cline, Phys. Rev. 155, 1792 (1967) ibid.21, 392 (1968) (unpublished)
E. Merzbacher, Quantum Mechanics (John Wiley & Sons, Inc., New York, 1961)
E. MerzbacherHigher Transcendental Functions, edited by A. Erdélyi (McGraw-Hill Book Co., New York, 1953) E. MerzbacherHandbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (U. S. Department of Commerce, National Bureau of Standards, Washington, D. C., 1964)
R. G. Newton, Scattering Theory of Wave and Particles (McGraw-Hill Book Co., New York, 1966), Applied Mathematics Series 55
H. M. Nussenzveig, J. Math. Phys. 10, 82 (1969) ibid.10, 125 (1969) Ann. Phys. (N. Y.) 21, 344 (1963)
K. W. Ford and J. A. Wheeler, Ann. Phys. (N. Y.) 7, 259 (1959)
H. C. Bryant and N. Jarmie, Ann. Phys. (N. Y.) 47, 127 (1968)
R. Serber, Phys. Rev. Letters 10, 357 (1963) Rev. Mod. Phys. 36, 649 (1964)
S. Fernbach, R. Serber, and T. B. Taylor, Phys. Rev. 75, 1352 (1949)
K. J. Foley, S. J. Lindenbaum, W. A. Love, S. Ogaki, J. J. Russell, and L. C. L. Yuan, Phys. Rev. Letters 11, 425 (1963) E. W. Anderson, E. J. Bleser, H. R. Blieden, G. B. Collins, D. Garelick, J. Menes, F. Turkot, D. Birnbaum, R. M. Edelstein, N. C. Hien, T. J. McMahon, J. Mucci, and J. Russ, ibid. 20, 1529 (1968) A. Ashmore, C. J. S. Damerell, W. R. Frisken, R. Rubinstein, J. Orear, D. P. Owen, F. C. Peterson, A. L. Read, D. G. Ryan, and D. H. White, ibid. 21, 387 (1968) J. Orear, D. P. Owen, F. C. Peterson, A. L. Read, D. G. Ryan, D. H. White, A. Ashmore, C. J. S. Damerell, W. R. Frisken, and R. Rubinstein, ibid. 21, 389 (1968)
Omitted endnote

[c1] G. Wentzel, Z. Physik 38, 518 (1926) H. A. Kramers, ibid. 39, 828 (1926) M. Brillouin, J. Phys. 3, 65 (1922)

[c2] J. M. Blatt and V. F. Weisskopf, Theoretical Nuclear Physics (John Wiley & Sons, Inc., New York, 1952)

[c3] K. Gottfried and J. D. Jackson, Nuovo Cimento 34, 735 (1964) J. D. Jackson, Rev. Mod. Phys. 37, 484 (1965) L. Durand and Y. T. Chiu, Phys. Rev. Letters 12, 399 (1964) ibid.13, 45(E) (1964)

[c4] V. Barger and D. Cline, Phys. Rev. 155, 1792 (1967) ibid.21, 392 (1968) (unpublished)

[c5] E. Merzbacher, Quantum Mechanics (John Wiley & Sons, Inc., New York, 1961)

[c6] E. MerzbacherHigher Transcendental Functions, edited by A. Erdélyi (McGraw-Hill Book Co., New York, 1953) E. MerzbacherHandbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (U. S. Department of Commerce, National Bureau of Standards, Washington, D. C., 1964)

[c7] R. G. Newton, Scattering Theory of Wave and Particles (McGraw-Hill Book Co., New York, 1966), Applied Mathematics Series 55

[c8] H. M. Nussenzveig, J. Math. Phys. 10, 82 (1969) ibid.10, 125 (1969) Ann. Phys. (N. Y.) 21, 344 (1963)

[c9] K. W. Ford and J. A. Wheeler, Ann. Phys. (N. Y.) 7, 259 (1959)

[c10] H. C. Bryant and N. Jarmie, Ann. Phys. (N. Y.) 47, 127 (1968)

[c11] R. Serber, Phys. Rev. Letters 10, 357 (1963) Rev. Mod. Phys. 36, 649 (1964)

[c12] S. Fernbach, R. Serber, and T. B. Taylor, Phys. Rev. 75, 1352 (1949)

[c13] K. J. Foley, S. J. Lindenbaum, W. A. Love, S. Ogaki, J. J. Russell, and L. C. L. Yuan, Phys. Rev. Letters 11, 425 (1963) E. W. Anderson, E. J. Bleser, H. R. Blieden, G. B. Collins, D. Garelick, J. Menes, F. Turkot, D. Birnbaum, R. M. Edelstein, N. C. Hien, T. J. McMahon, J. Mucci, and J. Russ, ibid. 20, 1529 (1968) A. Ashmore, C. J. S. Damerell, W. R. Frisken, R. Rubinstein, J. Orear, D. P. Owen, F. C. Peterson, A. L. Read, D. G. Ryan, and D. H. White, ibid. 21, 387 (1968) J. Orear, D. P. Owen, F. C. Peterson, A. L. Read, D. G. Ryan, D. H. White, A. Ashmore, C. J. S. Damerell, W. R. Frisken, and R. Rubinstein, ibid. 21, 389 (1968)

[c14] Omitted endnote

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Reflection Model and High-Energy $π^{-} p$ Backward Peaks