Quantum Isomorphic Shell Model: Multi-Harmonic Shell Clustering of Nuclei

G. S. Anagnostatos

Institute of Nuclear Physics, National Center for Scientific Research Demokritos, Greece.

DOI: 10.4236/jmp.2013.45B011                

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.

 

Keywords

Cluster Models; ⁴⁰Ca, ⁴⁸Ca, ⁵⁴Fe, ⁹⁰Zr, ¹⁰⁸Sn, ¹¹⁴Te, ¹⁴²Nd, ²⁰⁸Pb, Binding Energies; Coulomb Energies; Proton; Neutron; Mass Radii; Atomic Fermions

Conflicts of Interest

The authors declare no conflicts of interest.

References

[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: www.uoi.gr/HNPS).