JMP  Vol.4 No.5 B , May 2013
Quantum Isomorphic Shell Model: Multi-Harmonic Shell Clustering of Nuclei
Abstract: 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.  
Cite this paper: G. S. Anagnostatos, "Quantum Isomorphic Shell Model: Multi-Harmonic Shell Clustering of Nuclei," Journal of Modern Physics, Vol. 4 No. 5, 2013, pp. 54-65. doi: 10.4236/jmp.2013.45B011.

[1]   C. W. Sherwin, “Introduction to Quantum Mechanics,” Holt Rinehart and Winston, New York, 1959, p.205.

[2]   J. Leech, “Equilibrium of Sets of Particles on a Sphere,” Mathematical Gazette, Vol. 41, No. 36, 1957, pp. 81-90. doi:10.2307/3610579

[3]   G. S. Anagnostatos, “Symmetry Description of the Independent Particle Model,” Lettere Al Nuovo Cimento, Vol. 29, No. 6, 1980, pp. 188-192.

[4]   G. S. Anagnostatos, “The Geometry of the Quantization of Angular Momentum (l, s, j) in Fields of Central Symmetry, Lettere Al Nuovo Cimento, Vol. 28, No. 17, 1980, pp. 573- 576.

[5]   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. doi:10.1007/BF02745301

[6]   H. M. Cundy and A. P. Rollett, “Mathematical Models,” 2nd Ed., Oxford University Press, 1961, p.76.

[7]   H. S. M. Coxeter, “Regular Polytopes”, 2nd Ed., The Macmillan Company, New York, 1963.

[8]   G. S. Anagnostatos, “Isomorphic Shell Model for Closed-Shell Nuclei, ” International Journal of Theoretical Physics, Vol. 24, 1985, pp. 579-613. doi:10.1007/BF00670466

[9]   De Jager, C. W. H. de Vries, C. de Vries, “Nuclear Charge and Momentum Distribution,” Atomic Data and Nuclear Data Tables, Vol. 14, No. 5-6, 1974, pp. 479-665. doi:10.1016/S0092-640X(74)80002-1

[10]   W. F. Hornyak, “Nuclear Structure,” Academic, New York, 1975, p 13.

[11]   J. D. Vergados, “Mathematical Methods in Physics,” Akourastos Giannis, Greece, 1970.

[12]   A. H. Wapstra and N. B. Gove, “Atomic Mass Table,” Automic Data and Nuclear Data Tables, Vol. 9, 1971, pp. 267-301. doi:10.1016/S0092-640X(09)80001-6

[13]   E.G.Nadjakov, K.P.Marinova, and Yu.P.Gangrsky, “Systematics of Nuclear Charge Radii”, Automic Data and Nuclear Data Tables, Vol. 56, 1994, pp. 133-167. doi:10.1006/adnd.1994.1004

[14]   I. Angeli, “Recommended Values of R.M.S. Charge Radii”, Heavy Ion Phys., Vol. 8, No. 1-2, 1998, pp. 23-29.

[15]   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

[16]   R. C. Barrett., “Colloques,” Journal de Physique, Vol. 34, 1973, pp. 23-28.

[17]   A. Trzcinska, “Nuclear Periphery Studied with Antiprotonic Atoms”, Hyp. Inter., Vol. 194, No. 1, 2009, pp. 271-276.

[18]   J. Terasaki, J. Engel, “Self-Consistent Description of Multipole Strength: Systematic Calculations,” Physical Review C, Vol. 74, No. 4, 2006, pp. 044301-044319. doi:10.1103/PhysRevC.74.044301

[19]   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

[20]   G. F. Bertsch, P. F. Bortignon, R. A. Broglia, “Damping of Nuclear Excitations,” Reviews of Modern Physics, Vol. 55, 1983, pp. 287-314. doi:10.1103/RevModPhys.55.287

[21]   H. J. Koemer and J. P. Schiffer, “Neutron Radius of 208Pb from Sub-Coulomb Pickup,” Physical Review Letters, Vol. 27, No. 21, 1971, pp. 1457-1460. doi:10.1103/PhysRevLett.27.1457

[22]   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.

[23]   E. Merzbacher, “Quantum Mechanics,” John Wiley and Sons, Inc. New York, 1961, p. 42

[24]   C. Cohen-Tannoudji, B. Diu, F. Laloe, “Quantum Mechanics, ” John Wiley & Sons, New York, 1977, p. 240.

[25]   A. Bohr, B. R. Mottelson, “Nuclear Structure,” W. Α. Benjamin, Inc., Advanced Book Program, Reading, Massachusetts, London, Vol. 2, 1975.

[26]   J. Dabrowski, J. Rozynek and G. S. Anagnostatos, “Σ- Atoms and the ΣΝ Interaction,” Eur. Phys. J. A, Vol. 14, 2002, pp. 125-131.

[27]   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.

[28]   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.

[29]   G. S. Anagnostatos, P. Ginis, J. Giapitzakis, “α-Planar States in 28Si, ” Physical Reviewe C, Vol. 58, No. 6, 1998, pp. 3305-3315 doi:10.1103/PhysRevC.58.3305

[30]   P. K. Kakanis and G. S. Anagnostatos, “Persisting α-Planar Structure in 20Ne,” Physical Review C, Vol. 54, No. 6, 1996, pp. 2996-3013. doi:10.1103/PhysRevC.54.2996

[31]   G. S. Anagnostatos, “Classical Equations-of-Motion Model for High-Energy Heavy-Ion Collisions,” Physical Review C, Vol. 39, No. 3, 1989, pp. 877-883. doi:10.1103/PhysRevC.39.877

[32]   G. S. Anagnostatos and C. N. Panos, “Semiclassical Simulation of Finite Nuclei,” Physical Review C, Vol. 42, No. 3, 1990, pp. 961-965. doi:10.1103/PhysRevC.42.961

[33]   G. S. Anagnostatos, “Towards A Unification of Independent and Collective Models, 20th Conference of the Hellenic Nuclear Physical Society, Athens, May 27-28, 2011 (PDF in: