Il Nuovo Cimento A (1965-1970)

, Volume 86, Issue 1, pp 42–86 | Cite as

A mathematical method for extracting nuclear information from electron-nucleus scattering data

  • T. A. Minelli
  • A. Pascolini
  • C. Villi


The radial distributions of the centre of mass of protons are derived from phenomenological electric-charge densities used in the analyses of electron-nucleus scattering data. The exact method devised for this purpose allows one to reduce the electron-nucleus Fredholm's integral equation to a system of two resolvent differential equations, whose mathematical structure and constant coefficients are bound to a variety of proton models. The forms assumed for the empirical charge densities are critically examined.


21.10 Shape, charge and radius 


25.30 Electron and positron scattering 

Математический метод извлечения ядерной информации из данных по электрон-ядерному рассеянию


Выводятся радиальные распредения центра масс протонов из феноменологических плотностей электрического заряда, которые используются при анализе данных по электрон-ядерному рассеянию. Точный метод, разработанный для этой цели, позволяет свести решение злектрон-ядерного интегрального уравнения Фредгольма к системе двух дифференциальных уравнений, матемацическая структура и постоянные коэффициенты которых связаны для множества моделей прототона. Критически анализируются формы, которые используются для эмпирических плотностей заряда.


Le distribuzioni dei centri di massa dei protoni sono ricavate dalle densità fenomenologiche della carica elettrica usate nell'analisi dei dati sperimentali relativi alla diffusione di elettroni da parte di nuclei. Si sviluppa un metodo esatto in base al quale le densità nucleari sono soluzioni di un'equazione integrade di Fredholm il cui nucleo è definito analiticamente dai modelli di struttura protonica adottati. Le forme analitiche delle densità di carica scelte empiricamente sono esaminate criticamente.


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  1. (1).
    L. R. B. Elton:Nuclear Sizes (Oxford University Press, Oxford, 1961).Google Scholar
  2. (2).
    R. Hofstadter:Annu. Rev. Nucl. Sci.,7, 231 (1957).CrossRefADSGoogle Scholar
  3. (3).
    Recent tabulations may be found inC. W. De Jager, H. de Vries andC. de Vries:At. Data Nucl. Data Tables,14, 479 (1974);R. C. Barrett andD. F. Jackson:Nuclear Sizes and Structure (Clarendon Press, Oxford, 1977).CrossRefADSGoogle Scholar
  4. (4).
    See, for example,I. Sick:Nucl. Phys. A,218, 509 (1974).CrossRefADSGoogle Scholar
  5. (5).
    «Model independent» approaches have been introduced byF. Lenz:Z. Phys.,222, 491 (1969);V. K. Lukyanov, I. Zh. Petkov andYu. S. Pol':Yad. Fiz.,9, 349 (1969) (English translation:Sov. J. Nucl. Phys.,9, 204 (1969);J. L. Friar andJ. W. Negele:Nucl. Phys. A,212, 93 (1973);B. Dreher, J. Friedrich, R. Merle, H. Rothhaas andG. Lürs:Nucl. Phys. A,235, 219 (1974);J. Borysowicz andJ. H. Hetherington:Phys. Rev. C,7, 2293 (1973). See also (4)CrossRefADSGoogle Scholar
  6. (6).
    See, for example, the discussion inC. Ciofi Degli Atti:Electron scattering by nuclei, inProgress in Particle and Nuclear Physics, Vol.3 (Pergamon Press, Oxford, 1980), p. 207.Google Scholar
  7. (7).
    SeeB. Frois:Electron Scattering and Nuclear Structure, inProceedings of the International Conference on Nuclear Physics, Florence, 1983, Vol.2, Invited papers (Compositori, Bologna, 1983), p. 221 and papers therein quoted.Google Scholar
  8. (8).
    Detailed information on models II, III and IV is given in the review book byR. Hofstadter:Electron Scattering and Nuclear and Nucleon Structure (W. A. Benjamin. Inc., New York, N. Y., 1963); see alsoW. T. Toner, T. J. Braunstein, W. L. Lakin, F. Martin, M. L. Perl, T. F. Zipf, H. C. Bryant andB. D. Dieterle:Phys. Lett. B,36, 251 (1971). The form factor (1.9) withb p=0 has been used in a speculative comparison of muon-proton and electron-proton deep inelastic scattering (W. T. Toner, T. J. Braunstein, W. L. Lakin, F. Martin, M. L. Perl, T. F. Zipf, H. C. Bryant, andB. D. Dieterle:Phys. Lett. B,36, 251 (1971)).Google Scholar
  9. (9).
    See, for example,R. P. Feynman:Photon-Hadron Interactions (W. A. Benjamin, New York, N. Y., 1972), lecture 22.Google Scholar
  10. (10).
    C. G. Simon, F. Borkowski, Ch. Schmitt andV. Walther:Nucleon structure and nucleon-nucleon interaction, inFew-Body Systems and Electromagnetic Interactions, edited byC. Ciofi Degli Atti andE. de Santis (Springer-Verlag, Berlin, 1978), p. 27.CrossRefGoogle Scholar
  11. (11).
    R. Herman andR. Hofstadter:High Energy Electron Scattering Tables (Stanford, Cal., 1960).Google Scholar
  12. (12).
    R. Hofstadter andR. Herman:Phys. Rev. Lett.,6, 293 (1961).CrossRefADSGoogle Scholar
  13. (13).
    W. Reuter, G. Fricke, K. Merle andH. Miska:Phys. Rev. C,26, 806 (1982).CrossRefADSMATHGoogle Scholar
  14. (14).
    F. J. Kline, H. Crannell, J. T. O'Brien, J. S. McCarthy andR. R. Whitney:Nucl. Phys. A,209, 381 (1973).CrossRefADSGoogle Scholar
  15. (15).
    W. Schütz: Ph.D. Thesis, T.H. Darmstadt (1973).Google Scholar
  16. (16).
    B. B. P. Sinha, G. A. Peterson, R. R. Whitney, I. Sick andJ. S. McCarthy:Phys. Rev. C,7, 1930 (1973).CrossRefADSGoogle Scholar
  17. (17).
    A. S. Litvinenko, N. G. Shevchenko, N. G. Alfanas'ev, A. Yu. Buki, G. A. Savitskii, V. M. Khavastunov, A. A. Khomich, I. I. Chkalov andV. P. Likhachev:Yad. Fiz.,15, 1104 (1972) (English translation:Soc. J. Nucl. Phys.,15, 611 (1972)).Google Scholar
  18. (18).
    J. Heisenberg, R. Hofstadter, J. S. McCarthy, I. Sick, B. C. Clark, R. Herman andD. G. Ravenhall:Phys. Rev. Lett.,23, 1402 (1969).CrossRefADSGoogle Scholar
  19. (19).
    See, for example,F. Malaguti, A. Uguzzoni, E. Verondini andP. E. Hodgson: Riv. Nuovo Cimento,5, No. 1 (1982).Google Scholar

Copyright information

© Società Italiana di Fisica 1985

Authors and Affiliations

  • T. A. Minelli
    • 1
    • 2
  • A. Pascolini
    • 1
    • 2
  • C. Villi
    • 1
    • 2
  1. 1.Dipartimento di Fisica dell'UniversitàPadova
  2. 2.Istituto Nazionale di Fisica NucleareSezione di PadovaPadovaItalia

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