Pairing Effect on the Binding Energy Curve of N = Z Atomic Nuclei


The saw-tooth phenomenon on the binding energy curve of N = Z nuclei is due to the low binding energy between the α-particles. It was suspected by Gamow to be of van der Waals type, found here to be deuteron bonds. The binding energy per nucleon, in absolute value, of an α-particle is larger than any other combination of 4 nucleons. Therefore, the binding energy per nucleon is low for odd-odd N = Z nuclei and maximum for even-even N = Z nuclei. The assumption of N = Z nuclei to be an assembly of α-particles and deuteron bonds predicts the binding energy of the 32 first N = Z nuclei with a rms deviation of 0.25 MeV.

Share and Cite:

B. Schaeffer, "Pairing Effect on the Binding Energy Curve of N = Z Atomic Nuclei," World Journal of Nuclear Science and Technology, Vol. 3 No. 3, 2013, pp. 79-82. doi: 10.4236/wjnst.2013.33013.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] R. D. Evans, “The Atomic Nucleus,” McGraw-Hill, New York, 1969.
[2] G. Audi, et al., “The Ame2003 Atomic Mass Evaluation: (II). Tables, Graphs and References,” Nuclear Physics A, Vol. 729, No. 1, 2003, pp. 337-676. doi:10.1016/j.nuclphysa.2003.11.003
[3] J. L. Basdevant, J. Rich and M. Spiro, “Fundamentals in Nuclear Physics,” Springer, Berlin, 2005.
[4] S. Vermote, “Characteristics of Light Charged Particle Emission in Spontaneous and Neutron Induced Fission of Cm and Cf Isotopes,” Thesis, Gent University, 2009.
[5] G. Gamow, “Zur Quantentheorie des Atomkernes,” Zeitschrift für Physik , Vol. 51, No. 3-4, 1928, pp. 204-212. doi:10.1007/BF01343196
[6] G. Gamow and C. L. Critchfield, “Theory of Atomic Nucleus and Nuclear Energy,” BiblioBazaar, Charleston, 2011.
[7] N. D. Cook, “Models of the Atomic Nucleus: Unification through a Lattice of Nucleons,” Springer, Berlin, 2010.
[8] J. M. Blatt and V. F. Weisskopf, “Theoretical Nuclear Physics,” Courier Dover Publications, New York, 1991.
[9] W. von Oertzen, M. Freer and Y. Kanada-En’yo, “Nuclear clusters and nuclear molecules,” Physics Reports, Vol. 432, No. 2, 2006, pp. 43-113.doi:10.1016/j.physrep.2006.07.001
[10] M. P. Carpenter, “Viewpoint: Do Alpha Particles Cluster inside Heavy Nuclei?” Physics, Vol. 3, 2010, p. 8. doi:10.1103/Physics.3.8
[11] B. Schaeffer, “Ab Initio Calculation of 2H and 4He Binding Energies,” Journal of Modern Physics, Vol. 3, No. 11, 2012, pp. 1709-1715. doi:10.4236/jmp.2012.311210
[12] L.-D. Zhang, J.-Y. Guo and X.-Z. Fang, “With the Alpha-Cluster Model to Explain the Change of Separating Energy,” Chinese Physics C, Vol. 33, No. z1, 2009, pp. 140-141.
[13] B. Schaeffer, “Electromagnetic Theory of the Binding Energy of the Hydrogen Isotopes,” Journal of Fusion Energy, Vol. 30, No. 5, 2011, pp. 377-381. doi:10.1007/s10894-010-9365-0

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.