The present multi-harmonic shell clustering of a nucleus is a direct consequence of the fermionic nature of nucleons and their average sizes. The most probable form and the average size for each proton or neutron shell are here presented by a specific equilibrium polyhedron of definite size. All such polyhedral shells are closely packed leading to a shell clustering of a nucleus. A harmonic oscillator potential is employed for each shell. All magic and semi-magic numbers, g.s. single particle and total binding energies, proton, neutron and mass radii of 40Ca, 48Ca, 54Fe, 90Zr, 108Sn, 114Te, 142Nd, and 208Pb are very successfully predicted.
G. S. Anagnostatos, J. Giapitzakis, A. Kyritsis, “Rotational Invariance of Orbital-Angular-Momentum Quantization of Direction for Degenerate States”, Lettere Al Nuovo Cimento, Vol. 32, No. 11, 1981, pp. 332-335.
L. Ray, G. W. Hoffmann, and W. R. Coker, “Nonrelativistic and Relativistic Descriptions of Proton-Nucleus Scattering,” Physics Reports, Vol. 212, No. 5, 1992, pp. 223-328. doi:10.1016/0370-1573(92)90156-T
S. D. Schery, D. A. Lind and C. D. Zafiratos, “Radius of the Neutron Distribution in 208Pb from (p, n) Quasielastic Scattering,” Physical Review C, Vol. 9, No. 1, 1974, pp. 416-418. doi:10.1103/PhysRevC.9.416
S. Abrahamyan, Z. Ahmed, H. Albataineh, K. Aniol. D. S. Armstrong, et al., “Measurement of the Neutron Radius of 208Pb through Parity-Violation in Electron Scattering”, cited as: arXiv: 1201.2568v2 [nucl-ex], Cornell University Library, 13 Jan. 2012, journal reference: Physical Review Letters, Vol. 108, No. 11, 2012, pp. 112502-112507.
G. S. Anagnostatos, A. N. Antonov, P. Ginis, J. Giapitzakis and M. K. Gaidarov, “Nucleon Μomentum and Density Distributions in 4He Considering Internal Rotation,” Physical Review C, Vol. 58, No. 4, 1998, pp. 2115-2119.
M. K. Gaidarov, A. N. Antonov, G. S. Anagnostatos, S. E. Massen, M. V. Stoitsov and P. E. Hodgson, “Proton Momentum Distribution in Nuclei beyond 4He,” Physical Review C, Vol. 52, No. 6, 1995, pp. 3026-3031.