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Some Statistical Problems in the Computation of Nuclidic Mass Formulae

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Nuclidic Masses

Abstract

The volume of the literature on nuclidic mass formulae bears witness to much vexation. There is no agreement on the terms to be used. Simple drop-model terms account for the major portion of each mass (v. Weizsäcker 1935) and thus are a natural zeroth approximation. But how may we improve them into a first or second approximation while we are not quite certain about the structure of the nuclear surface? There are also strong shell model terms (discovered experimentally by Duckworth and collaborators, 1950/51), but again we do not yet know a universally acceptable procedure to refine these in higher orders. Anyway, how do we reconcile the collective and the individual particle effects while basic nuclear theory is still unsettled?

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References

  1. J. Mattauch, L. Waldmann, H. Bieri, and F. Everling, Die Massen der leichten Nuklide. Z. Naturf. b11 a, 525–548 (1956). The Masses of Light Nuclides. Ann. Rev. Nucl. Sci. 6, 179-214 (1956). In both references the factor 101 on top of the columns from 17F to 21Ne should read 10−1.

    ADS  Google Scholar 

  2. W. Feller, An Introduction to Probability Theory and its Applications, 2nd. ed., especially chapter 3. New York: Wiley. 1957.

    MATH  Google Scholar 

  3. P. G. Guest, Numerical Methods of Curve Fitting. Cambridge University Press. 1961.

    Google Scholar 

  4. M. H. Quenouille, Associated Measurements. London: Butterworth. 1952.

    MATH  Google Scholar 

  5. T. N. E. Greville, On Smoothing a Finite Table: A Matrix Approach. J. Soc. Industr. Appl. Math. 5, 137–154 (1957).

    Article  MathSciNet  MATH  Google Scholar 

  6. H. Cramér, Mathematical Methods of Statistics, chapters 22 and 24. Princeton University Press. 1946.

    Google Scholar 

  7. A. C. Aitken, On Fitting Polynomials to Weighted Data by Least Squares. Proc. Roy. Soc. Edinb. 54, 1–11 (1933). On Fitting Polynomials to Data with Weighted and Correlated Errors. Ibid. 54, 12-16 (1933).

    Google Scholar 

  8. W. G. Cochran, The Omission or Addition of an Independent Variate in Multiple Linear Regression. Suppl. J. Roy. Stat. Soc. 5, 171–176 (1938).

    Article  Google Scholar 

  9. R. L. Plackett, Some Theorems in Least Squares. Biometrika 37, 149–157 (1950).

    MathSciNet  MATH  Google Scholar 

  10. D. G. King-Hele, G. E. Cook, and Janice M. Rees, Earth’s Gravitational Potential: Even Zonal Harmonics from the 2nd to the 12th. Nature 197, 785 (1963).

    Article  ADS  Google Scholar 

  11. L. L. Foldy, A Note on Atomic Binding Energies. Phys. Rev. 83, 397–399 (1951).

    Article  ADS  Google Scholar 

  12. A. D. Booth, Numerical Methods. London: Butterworth. 1955.

    MATH  Google Scholar 

  13. P. B. Madić, A Method of Solving Ill-Conditioned Systems of Linear Simultaneous Algebraic Equations. Bull. Inst. Nucl. Sci. “Boris KidriČ” 6, 75–86 (1956). Transformation of Ill-Conditioned Systems into Well-Conditioned. Ibid. 6, 87-91 (1956).

    Google Scholar 

  14. A. S. C. Ehrenberg, The Unbiased Estimation of Heterogeneous Error Variances. Biometrika 37, 347–357 (1950).

    MathSciNet  MATH  Google Scholar 

  15. — E. J. Williams, Applications of Component Analysis to the Study of Properties of Timber. Austral. J. Appl. Sci. 3, 101–118 (1952).

    Google Scholar 

  16. — J. P. Stttcliffe, Error of Measurement and the Sensitivity of a Test of Significance. Psychometrika 23, 9–17 (1958).

    Article  Google Scholar 

  17. G. S. Watson and E. J. Hannan, Serial Correlation in Regression Analysis: II. Biometrika 43, 436–448 (1956). And further references given there.

    MathSciNet  Google Scholar 

  18. J. Mandel, Fitting a Straight Line to Certain Types of Cumulative Data. J. Amer. Stat. Assoc. 52, 552–566 (1957).

    Article  MathSciNet  MATH  Google Scholar 

  19. F. S. Acton, Analysis of Straight-Line Data, chapter 10. New York: Wiley. 1959.

    MATH  Google Scholar 

  20. M. Merrington and C. M. Thompson, Tables of Percentage Points of the Inverted Beta (F) Distribution. Biometrika 33, 73–88 (1943).

    MathSciNet  Google Scholar 

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Author information

Author notes

  1. Ernst Breitenberger

    Present address: Ohio University, Athens, Ohio, USA

Authors and Affiliations

  1. University of South Carolina, USA

    Ernst Breitenberger

Authors
  1. Ernst Breitenberger
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Editor information

Editors and Affiliations

  1. School of Physics, University of Minnesota, Minneapolis, Minnesota, USA

    Walter H. Johnson Jr.

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© 1964 Springer-Verlag/Wien

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Breitenberger, E. (1964). Some Statistical Problems in the Computation of Nuclidic Mass Formulae. In: Johnson, W.H. (eds) Nuclidic Masses. Springer, Vienna. https://doi.org/10.1007/978-3-7091-5556-1_10

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  • DOI: https://doi.org/10.1007/978-3-7091-5556-1_10

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-5558-5

  • Online ISBN: 978-3-7091-5556-1

  • eBook Packages: Springer Book Archive

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