Barrett moments and rms charge radii

  • I. Angeli


An empirical relation is established between Barrett equivalent radii R k,α and rms charge radii < r 2 >1/2 based on the results of model-independent and Fermi model analyses of 2p → 1s transitions in muonic atoms. This relation follows simple Z dependence, and can be usefully applied to derive rms radii < r 2 >1/2 or differences δ AA ′ < r 2 >1/2 in cases where only R k,α data or isotope shifts δ AA R k,α are published. The atomic number dependence of the Barrett parameters k(Z) and α(Z) is also given by empirical formulae. It is shown that the Barrett moment can be expanded in a sum of integer moments < r m > (m ≥ 2) using an effective exponential parameter α eff(Z). The moments < r m > and isotopic differences δ < r m > of the two-parameter Fermi distribution expressed in terms of the parameters c and a are given in the Appendix for m = 1 – 10.


nuclear rms charge radii Barrett moments 


21.10.Ft 36.10.Dr 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R.C. Barrett, Phys. Lett. B33 (1970) 388.ADSGoogle Scholar
  2. 2.
    K.W. Ford and G.A. Rinker, Jr., Phys. Rev. C7 (1973) 1206.ADSGoogle Scholar
  3. 3.
    G. Fricke et al., Atomic Data and Nuclear Data Tables 60 (1995) 177.CrossRefADSGoogle Scholar
  4. 4.
    P. Mazanek, Diploma Thesis, KPH/11, Univ. Mainz, 1989.Google Scholar
  5. 5.
    D. Rychel, Diploma Thesis, Univ. Mainz, 1983.Google Scholar
  6. 6.
    B. Dreher, J. Friedrich, K. Merle, H. Rothaas and G. Lührs, Nucl. Phys. A235 (1974) 219.ADSGoogle Scholar
  7. 7.
    P. Mazanek, Ph.D. Thesis, KPH 5/92, Univ. Mainz, 1992.Google Scholar
  8. 8.
    I. Angeli, J. Phys. G: Nucl. Part. Phys. 17 (1991) 439.CrossRefADSGoogle Scholar
  9. 9.
    I. Angeli, Hyperfine Interactions (2001), to be published.Google Scholar
  10. 10.
    A.J.C. Burghardt, Ph.D. Thesis, Univ. Amsterdam, 1989.Google Scholar
  11. 11.
    J. Herberz, Ph.D. Thesis, Univ. Mainz, KPH/6/89, 1989.Google Scholar
  12. 12.
    K.W. Ford and J.G. Wills, Phys. Rev. 185 (1969) 1429.CrossRefADSGoogle Scholar
  13. 13.
    E.C. Seltzer, Phys. Rev. 188 (1969) 1916.CrossRefADSGoogle Scholar
  14. 14.
    D. Andrae, Phys. Rep. 336 (2000) 414.CrossRefADSGoogle Scholar
  15. 15.
    L.R.B. Elton, Nuclear Sizes, Oxford University Press, 1961, Appendix C.Google Scholar
  16. 16.
    C.W. de Jager, H. de Vries and C. de Vries, Atomic Data and Nuclear Data Tables 14 (1974) 479.CrossRefADSGoogle Scholar
  17. 17.
    M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, Dover Publications, Inc., New York, 1970, p. 807.Google Scholar
  18. 18.
    I. Angeli and T. Tari, ATOMKI Reports, A/5 (1986) 13.Google Scholar

Copyright information

© Akadémiai Kiadó 2002

Authors and Affiliations

  • I. Angeli
    • 1
  1. 1.Institute of Experimental PhysicsUniversity of DebrecenDebrecenHungary

Personalised recommendations