Spectroscopy of N-Δ Excited States and the Quark-Model

  • R. K. Bhaduri
Part of the NATO ASI Series book series (NSSB, volume 142)


My lectures here will expound on the simple quark model of baryons to understand the variety of baryon resonances that are encountered experimentally. We would mainly concentrate on the excited states of the nucleon (N) and the delta (Δ), that are “seen” in πN scattering, and in the pion photoproduction and electroproduction experiments. Resonances are associated with peaks in cross sections, and are manifest, for example, in a plot of the total πN cross section, σT as a function of the pion laboratory momentum or the CM energy squared, s. In Fig. 1, σT+p), which is entirely in the isospin I = 3/2 channel, is plotted. It has a huge bump corresponding to the Δ(1232), and some minor peaks where many other overlapping Δ- resonances contribute. In Fig. 2, σT-р) is plotted, and here both the I = 1/2 and I = 3/2 channels contribute in the ratio 2:1. This plot has more structure, and some of the N-resonances can be identified. It is clear from these plots, however, that other experiments and more careful analysis of the data are necessary to isolate the characteristics of these excited states.


Wave Function Partial Wave Oscillator Model Intrinsic State Partial Wave Amplitude 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. Donnachie, in “Hadronic Interaction of Electrons and Photons”, Proceedings of the eleventh Scottish Universities Summer School in Physics, 1970, edited by J. Cumming and H. Osborn ( Academic Press, New York ) p. 109.Google Scholar
  2. [2]
    R. E. Cutkosky, et al., Phys. Rev. D20, 2804 and 2839 (1979).ADSGoogle Scholar
  3. [3]
    E. Pietarinen, Nucl. Phys. B107, 21 (1976); R. Koch and E. Pietarinen, Nucl. Phys. A336, 331 (1980).ADSCrossRefGoogle Scholar
  4. [4]
    Reviews of Particle Properties, in Rev. Mod Phys. 56, S206 (1984).Google Scholar
  5. [5]
    F. E. Close, “An Introduction to Quarks and Partons”, ( Academic Press, New York, 1979 ).Google Scholar
  6. [6]
    F. Foster, G. Hughes, Rep. Prog. Phys. 46, 1445 (1983).ADSCrossRefGoogle Scholar
  7. [7]
    R. H. Dalitz, in Les Houches Lectures, 1965 ( Gordon and Breach, New York, 1965 ).Google Scholar
  8. [8]
    R. K. Bhaduri, Mira Dey, Phys. Lett. 125B, 513 (1983).ADSGoogle Scholar
  9. [9]
    D. Faiman, A. W. Hendrey, Phys. Rev. 173, 1720 (1968).ADSCrossRefGoogle Scholar
  10. [10]
    N. Isgur, G. Karl, Phys. Rev. D18, 4187 (1978).ADSGoogle Scholar
  11. [11]
    N. Isgur, G. Karl, Phys, Rev. D19, 2653 (1979).ADSGoogle Scholar
  12. [12]
    G. Karl, E. Obryk, Nucl. Phys. B8, 609 (1968).ADSCrossRefGoogle Scholar
  13. [13]
    N. K. Nielsen, Am. J. Phys. 49, 1171 (1981).ADSCrossRefGoogle Scholar
  14. [14]
    A. De Rujula, H. Georgi, S. L. Glashow, Phys. Rev. D12, 147 (1975).Google Scholar
  15. [15]
    For derivation, see, for example, V. Berestetskii, E. M. Lifshitz and L. P. Pitaeveskii, “Relativistic Quantum Theory, Park I” ( Pergamon Press, Oxford 1979 ) p. 280.Google Scholar
  16. [16]
    L. I. Schiff, “Quantum Mechanics” (McGraw-Hill, New York, 1968), p. 482. The sign of the Thomas term depends on whether the potential transforms like a scalar or a vector under Lorentz transformation.Google Scholar
  17. [17]
    D. Gromes, Z. Phys. C18, 249 (1983).Google Scholar
  18. [18]
    M. V. N. Murthy, M. Brack, R. K. Bhaduri, В. K. Jennings, Z. Phys. С (1985) to be published.Google Scholar
  19. [19]
    S. Capstick, N. Isgur, University of Toronto preprint (1985).Google Scholar
  20. [20]
    C. P. Forsyth, R. E. Cutkosky, Z. Phys. C18, 219 (1983).Google Scholar
  21. [21]
    M. V. N. Murthy, R. K. Bhaduri, Phys. Rev. Letter. 54, 745 (1985).ADSCrossRefGoogle Scholar
  22. [22]
    For a review, and references to original papers, see M. A. Preston and R. K. Bhaduri, “Structure of the Nucleus”, (Addison-Wesley, Reading, Mass. 1975 ) p. 463.Google Scholar
  23. [23]
    R. E. Peierls, J. Yoccoz, Proc. Phys. Soc. (London) 70, 381 (1957).MathSciNetADSMATHCrossRefGoogle Scholar
  24. [24]
    R. K. Bhaduri, C. K. Jennings, J. C. Waddington, Phys. Rev. D29, 2051 (1984).ADSGoogle Scholar
  25. [25]
    M. V. N. Murthy, M. Dey, J. Dey, R. K. Bhaduri, Phys. Rev. D30, 152 (1984).ADSGoogle Scholar
  26. [26]
    A. Bohr, B. R. Mottelson, “Nuclear Structure”, Benjamin, Reading, Mass. 1975 ) Vol. II, p. 77.Google Scholar
  27. [27]
    B. R. Mottelson, in “The Many Body Problem”, Les Houches lectures, 1958 ( John Wiley, New York, 1959 ) p. 313.Google Scholar
  28. [28]
    L. J. Reinders, in “Baryon 1980”, edited by N. Isgur (University of Toronto, 1980 ).Google Scholar
  29. [29]
    R. K. Bhaduri, L. E. Cohler, Y. Nogami, Phys. Rev. Lett. 44, 1369 (1980).ADSCrossRefGoogle Scholar
  30. [30]
    R. K. Bhaduri, L. E. Cohler, Y. Nogami, Nuovo Cimento 65, 376 (1981).ADSCrossRefGoogle Scholar
  31. [31]
    G. E. Brown, M. Rho, Phys. Lett. 82B, 177 (1979); S. Théberge, A. W. Thomas and G. A. Miller, Phys. Rev. D22, 2838 (1980); M. Weise, in Fifth Tropical School on Quarks, Mesons and Isobars in Nuclei, Motril, Granada, Spain, 1982.Google Scholar
  32. [32]
    Such an approach was suggested by A. Manohar and H. Georgi, Nucl. Phys. B234, 189 (1984).Google Scholar
  33. [33]
    M. V. N. Murthy, R. K. Bhaduri, E. Tabarah, to be published.Google Scholar
  34. [34]
    B. Silvestre-Brac, C. Gignoux, Phys. Rev. D32, 743 (1985).MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • R. K. Bhaduri
    • 1
  1. 1.Physics DepartmentMcMaster UniversityHamiltonCanada

Personalised recommendations