Acta Physica Hungarica

, Volume 69, Issue 3–4, pp 233–247 | Cite as

Evaluation procedure for nuclear RMS charge radii

  • I. Angeli
Nuclear Physics


Data sources are listed and an evaluation procedure is described that have been used recently to derive the best values of nuclear root-mean-square (RMS) charge radii measured by fast electron scattering and muonic atom X-rays. The evaluation procedure consists of two algorithms. The first one performs a search for discrepant data “outliers” together with an eventual reassignment of their errors; this algorithm is active only for groups containing at leastn=5 data. The second algorithm forms a weighted mean and its error for each data group; it takes into account both external and internal consistencies. An illustrative Table of input data as well as a Table of “1990 best values” of nuclear RMS charge radii are also included.


Root Mean Square Evaluation Procedure Charge Radius Muonic Atom Discrepant Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    I. Angeli and J. Csikai, Nucl. Phys.,A158, 389, 1970.CrossRefGoogle Scholar
  2. 2.
    C. W. de Jager, H. de Vries and C. de Vries, At. Data Nucl. Tables,14, 479, 1974.CrossRefADSGoogle Scholar
  3. 3.
    H. de Vries, C. W. de Jager and C. de Vries, At. Data Nucl. Tables,36, 495, 1987.CrossRefADSGoogle Scholar
  4. 4.
    R. Engfer, H. Schneuwly, J. L. Vuilleumier, H. K. Walter and A. Zehnder, At. Data Nucl. Data Tables,14, 509, 1974.CrossRefADSGoogle Scholar
  5. 5.
    G. A. Beer, M. S. Dixit, A. Fry, J. A. MacDonald, G. R. Mason, A. Olin, R. M. Pearce and P. R. Poffenberger, Abstr. Contr. Papers. 8th Int. Conf. High. En. Phys. Nucl. Structure, Aug. 13–17, Vancouver, Canada, p. 21.Contr. 1B27, 1979.Google Scholar
  6. 6.
    P. Bergem, G. Piller, A. Ruetschi, L. A. Schaller, L. Schellenberg and H. Schneuwly, Phys. Rev.,C37, 2821, 1988.ADSCrossRefGoogle Scholar
  7. 7.
    E. Borie and G. A. Rinker, Phys. Rev.,A18, 324, 1978. I. Beltrami, K. Bos, P. F. A. Goudsmit, U. Kiebele, B. Jeckelmann, H. J. Leisi, W. Ruckstuhl, G. Strassner, A. Vacchi and R. Weber, Nucl. Phys.,A444, 589, 1985.CrossRefADSGoogle Scholar
  8. 8.
    F. N. W. de Boer, B. Aas, P. Baertschi, W. Beer, I. Beltrami, K. Bos, P. F. A. Goudsmit, U. Kiebele, B. Jeckelmann, H. J. Leisi, W. Ruckstuhl G. Strassner, A. Vacchi and R. Weber, Nucl. Phys.,A444, 589, 1985.CrossRefGoogle Scholar
  9. 9.
    A. Brandão and T. von Egidy, Z. Naturf.,31a, 211, 1976.ADSGoogle Scholar
  10. 10.
    D. A. Close, J. J. Malanify and J. P. Davidson, Nuovo Cimento,34A, 301, 1976.ADSGoogle Scholar
  11. 11.
    D. A. Close, J. J. Malanify and J. P. Davidson, Phys. Rev.,C17, 1433, 1978.CrossRefADSGoogle Scholar
  12. 12.
    B. S. Dolbilkin, A. E. Zabridin, R. L. Kondratev, V. P. Lisin and A. L. Polonskii, Yad. spektr. strukt. at. yadra, Tez. dokl. XXXVI. soveshch., (Kharkov, 15–18 April), p. 352, 1986.Google Scholar
  13. 13.
    J. M. Finn, H. Crannel, P. L. Hallowell, J. T. O’Brien and S. Penner, Nucl. Phys.,A274, 28, 1976.CrossRefGoogle Scholar
  14. 14.
    K. Kaeser, T. Dubler, B. Robert-Tissot, L. A. Schaller, L. Schellenberg and H. Schneuwly, Helv. Phys. Acta,52, 238, 1978.Google Scholar
  15. 15.
    D. Kessler, H. Mes, A. C. Thompson, A. L. Anderson, M. S. Dixit and R. J. McKee, Phys. Rev.,C11, 1719, 1975.CrossRefADSGoogle Scholar
  16. 16.
    A. A. Khomich, N. G. Shevchenko, E. O. Babichev, A. Yu. Buki, V. N. Mazan’ko and V. P. Sergienko, Yad. Fiz.,47, 305, 1988.Google Scholar
  17. 17.
    W. Kunold, M. Schneider, L. M. Simons, J. Wust and R. Abele, Z. Physik,A312, 11, 1983.CrossRefADSGoogle Scholar
  18. 18.
    D. B. Laubacher, Y. Tanaka, R. M. Steffen, E. B. Shera and M. V. Hoehn, Phys. Rev.,C27, 1772, 1983.CrossRefADSGoogle Scholar
  19. 19.
    A. Nakada, N. Haik, J. Alster, J. B. Bellicard, S. Cochavi, B. Frois, M. Huet, P. Leconte, P. Ludeau, M. A. Moinester, Phan Xuan Ho and S. Turck, Phys. Rev., Lett.,38, 584, 1977.CrossRefADSGoogle Scholar
  20. 20.
    E. A. J. M. Offermann, Ph. D. Thesis, University of Amsterdam, 1988.Google Scholar
  21. 21.
    A. Olin, P. R. Poffenberger, G. A. Beer, J. A. MacDonald, G. R. Mason and W. C. Sperry, Nucl. Phys.,A360, 426, 1981.CrossRefGoogle Scholar
  22. 22.
    H.-J. Pfeiffer and H. Daniel, Nucl. Phys.,A264, 498, 1976.CrossRefGoogle Scholar
  23. 23.
    T. Q. Phan, P. Bergem, A. Ruetschi, L. A. Schaller and L. Schellenberg, Phys. Rev.,C32, 609, 1985.CrossRefADSGoogle Scholar
  24. 24.
    R. J. Powers, F. Boehm, P. Vogel, A. Zehnder, T. King, A. R. Kunselman, P. Roberson, P. Martin, G. H. Miller, R. E. Welsch and D. A. Jenkins, Nucl. Phys.,A262, 493, 1976.CrossRefGoogle Scholar
  25. 25.
    R. J. Powers, P. Barreau, B. Bihoreau, J. Miller, J. Morgenstern, J. Picard and L. Roussel, Nucl. Phys.,A316, 295, 1979.CrossRefGoogle Scholar
  26. 26.
    W. Ruckstuhl, B. Aas, W. Beer, I. Beltrami, K. Bos, P. F. A. Goudsmit, H. J. Leisi, G. Strassner, A. Vacchi, F. W. N. de Boer, U. Kiebele and R. Weber, Nucl. Phys.,A430, 685, 1984.CrossRefGoogle Scholar
  27. 27.
    L. A. Schaller, T. Dubler, K. Kaeser, G. A. Rinker, B. Robert-Tissot, L. Schellenberg and H. Schneuwly, Nucl. Phys.,A300, 225, 1978.Google Scholar
  28. 28.
    L. A. Schaller, L. Schellenberg, A. Ruetschi and H. Schneuwly, Nucl. Phys.,A343, 333, 1980.Google Scholar
  29. 29.
    L. A. Schaller, L. Schellenberg, T. Q. Phan, G. Piller, A. Ruetschi and H. Schneuwly, Nucl. Phys.,A379, 525, 1982.Google Scholar
  30. 30.
    L. A. Schaller, A. Brandao, P. Bergem, M. Boschung, T. Q. Phan, G. Piller, A. Ruetschi, H. Schneuwly, G. Fricke, G. Mallot and H. G. Sieberling, Phys. Rev.,C31, 1007, 1985.CrossRefADSGoogle Scholar
  31. 31.
    L. Schellenberg, B. Robert-Tissot, K. Kaeser, L. A. Schaller, H. Schneuwly, G. Fricke, S. Glückert, G. Mallot and E. B. Shera, Nucl. Phys.,A333, 333, 1980.CrossRefGoogle Scholar
  32. 32.
    E. B. Shera, E. T. Ritter, R. B. Perkins, G. A. Rinker, L. K. Wagner, H. D. Wohlfahrt, G. Fricke and R. M. Steffen, Phys. Rev.,C14, 731, 1978.Google Scholar
  33. 33.
    E. B. Shera, H. D. Wohlfahrt, M. V. Hoehn and Y. Tanaka, Phys. Letters,112B, 124, 1982.ADSGoogle Scholar
  34. 34.
    D. W. L. Sprung, M. Vallieres, X. Champi and J. Martorell, Nucl. Phys.,A325, 125, 1979.CrossRefGoogle Scholar
  35. 35.
    V. G. Vlasenko, N. G. Afanas’ev, I. M. Arkatov, B. A. Goldstein, E. A. Kuplennikov, V. I. Ogurtsev and V. I. Startsev, Proc. Conf. Leningrad, Vol.2, p. 123. 1970.Google Scholar
  36. 36.
    H. D. Wohlfahrt, E. B. Shera, M. V. Hoehn, Y. Yamazaki and R. M. Steffen, Bull. Am. Phys. Soc.,23 HL4, 1978.Google Scholar
  37. 37.
    H. D. Wohlfahrt, E. B. Shera, M. V. Hoehn, Y. Yamazaki and R. M. Steffen, Phys. Rev.,C23, 533, 1981.CrossRefADSGoogle Scholar
  38. 38.
    Y. Yamazaki, E. B. Shera, M. V. Hoehn and R. M. Steffen, Phys. Rev.,C18, 1474, 1978.CrossRefADSGoogle Scholar
  39. 39.
    J. D. Zumbro, E. B. Shera, Y. Tanaka, C. E. Bemis Jr., M. V. Hoehn, W. Reuter and R. M. Steffen, Phys. Rev. Lett.,53, 1888, 1984.CrossRefADSGoogle Scholar
  40. 40.
    I. Angeli, Z. Physik,A334, 377, 1989.ADSGoogle Scholar
  41. 41.
    B. N. Taylor, Numerical Comparisons of Several Algorithms for Treating Inconsistent Data in a Least-Squares Adjustment of the Fundamental Constants. NBSIR-81-2426 Final Report., U. S. Dept. of Commerce, Washington, 1982.Google Scholar
  42. 43.
    I. Angeli and T. Tari, ATOMKI Közlemények,23, 143, 1981.Google Scholar
  43. 44.
    E. R. Cohen and B. N. Taylor, Rev. Mod. Phys.,59, 1121, 1987.CrossRefADSGoogle Scholar
  44. 45.
    M. Pugh and G. H. Winslow, The Analysis of Physical Measurements, Addison-Wesley, Reading, Mass., 1966.Google Scholar
  45. 46.
    A. G. Worthing and J. Geffner, Treatment of Experimental Data, John Wiley, New York, 1958.Google Scholar
  46. 47.
    B. L. Van der Waerden, Mathematische Statistik, Springer, Berlin, 1965.MATHGoogle Scholar
  47. 48.
    R. T. Birge, Phys. Rev.,40, 207, 1932.MATHCrossRefADSGoogle Scholar
  48. 49.
    P. G. Guest, Numerical Methods of Curve Fitting, University Press, Cambridge, 1961.MATHGoogle Scholar
  49. 50.
    Z. T. Bődy and K. M. Dede, Acta Phys. Hung.,28, 155, 1970.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó 1991

Authors and Affiliations

  • I. Angeli
    • 1
  1. 1.Institute of Experimental PhysicsKossuth Lajos UniversityDebrecenHungary

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