Abstract
The classical part of the isomorphic model for closed-shell nuclei is presented based on two physical assumptions, namely (a) the nucleons of a closed shell nucleus, considered at their most probable positions, are in an instantaneous dynamic equilibrium on spherical shells, and (b) the dimensions of the shells are determined by their close packing given that a neutron and a proton are represented by hard spheres of definite sizes. The first assumption leads to the instantaneous angular structure, and the second to the instantaneous radial structure of closed-shell nuclei. Applications of the model coming from this classical part alone and presented here are structural justification of all magic numbers, neutron (proton) and charge rms radii, nuclear densities of closed-shell nuclei, and Coulomb, kinetic, and binding energies. All the predictions are in good agreement with experimental data. A characteristic novelty of the isomphic model is that assumption (a) is related to the independent particle model, and assumption (b) to the liquid-drop model. The isomorphic model may provide a link between these two basic nuclear physics models since it incorporates features of both.
Similar content being viewed by others
References
Alkhazov, G. D., Belostotsky, S. L., Domchenkov, O. A., Dotsenko, Yu. V., Kuropatkin, N. P., Nickulin, V. N., Shuvaev, M. A., and Vorobyov, A. A. (1976). In Proc. Int. Conf. on the Radial Shape of Nuclei, M. Guenin, ed., pp. 47–48.
Anagnostatos, G. S. (1973).Canadian Journal of Physics,51, 998.
Anagnostatos, G. S. (1977).Atomkernenergie,29, 207.
Anagnostatos, G. S. (1978).Lettere al Nuovo Cimento,22, 507.
Anagnostatos, G. S. (1980a).Lettere al Nuovo Cimento,28, 573.
Anagnostatos, G. S. (1980b).Lettere al Nuovo Cimento,29, 188.
Anagnostatos, G. S., and Panos, C. N. (1982).Physical Review C,26, 260.
Anagnostatos, G. S., Touliatos, S., Kyritsis, A., and Yapitzakis, J. (1980).Atomkernenergie,35, 60.
Anagnostatos, G. S., Yapitzakis, J, and Kyritsis, A. (1981).Lettere al Nuovo Cimento,32, 332.
Bernstein, A. M., and Seidler, W. A. (1972).Physics Letters 39B, 583.
Bertozzi, W., Friar, J., Heisenberg, J., and Negele, J. W. (1972).Physics Letters,41B, 408.
Bertsch, G. F. (1983).Scientific American,248, 40.
Brown, B. A., Massen, S. E., and Hodgson, P. E. (1979).Journal of Physics G,5, 1655.
Celenza, L. S., and Shakin, C. M. (1983).Physial Review C,27, 1561.
Cook, N. D. (1976).Atomkernenergie. (1978).28, 195.
Coxeter, H. S. M. (1963).Regular Polytopes, 2nd edition, Macmillan, New York.
de Boer, J., and Mang, H. J., eds. (1973). Proceedings of the International Conference on Nuclear Physics, p. 101.
de Jager, C. W., de Vries, H., and de Vries, C. (1974).Atomic Data and Nuclear Data Tables,14, 479–508.
Engfer, R., Schneuwly, H., Vuilleumier, J. L., Walter, H. K., and Zehnder, A.,Atomic Data and and Nuclear Data Tables,14, 509–597.
Greenless, G. W., Hnizdo, V., Karban, O., Lowe, J., and Makofske, W. (1970).Physical Review C 2, 1063.
Hill, D. L. (1957). InEncyclopedia of Physics, S. Flugge, ed., Springer-Verlag, Berlin, Vol. XXXIX, p. 211.
Hodgson, P. E. (1980). Invited paper presented at the Workshop in Nuclear Physics, Drexell University.
Hodgson, P. E. (1981). Invited paper presented at the IV International Symposium on Nuclear Physics, Oaxtepec, Mexico.
Holden, N. E., and Walker, F. W. (1972).Chart of the Nuclides, 11th edition, General Electric Co., Schenectady, New York.
Hornyak, W. F. (1975).Nuclear Structure, Academic, New York, p. 194.
Inglis, D. R. (1969).Physics Today,22, 29.
Jackson, D. F. (1976). Invited paper presented at the Int. Conf. on the Radial Shape of Nuclei, A. Budzanowski and A. Kapuscik, eds., pp. 141–161.
Kaplan I. (1962).Nuclear Physics, 2nd edition, Addison-Wesley, Reading Massachusetts, p. 222.
Leech, J. (1957).Mathematical Gazette,41, 81.
Margenau, H. (1941).Physical Review,59, 37.
Mariscotti, M. A. J., Scharff-Goldhaber, G., and Buck, B.Physical Review,178, 1864.
Mayer, M. G., and Jensen, J. H. D. (1955).Elementary Theory of Nuclear Shell Structure, Wiley, New York, p. 58.
Moszkowski, S. A. (1957). In “Models of nuclear structure,” inEncyclopedia of Physics, S. Flügge, Springer-Verlag, Berlin, Vol. 39, pp. 411–450.
Negele, J. W. (1976). Invited paper presented at the Int. Conf. on the Radial Shape of Nuclei, A. Budzanowski and A. Kapuscik, eds., pp. 79–102.
Nolen, J. A., and Schiffer, J. P. (1969).Annual Review of Nuclear Science,19, 471.
Panos, C. N., and Anagnostatos, G. S. (1982a). In Proc. Int. Conf. on Nuclear Structure, A. van der Woude and B. J. Verhaar, eds., p. 58.
Panos, C. N., and Anagnostatos, G. S. (1982b).Journal of Physics G,8, 1651.
Paulin, L. (1965a).Science,150, 297.
Pauling, L. (1965b).Nature,206, 174.
Pyle, G. J., and Greenless, G. W. (1969).Physical Review,181, 1444.
Rebel, H. (1976). Invited paper presented at the Int. Conf. on the Radial Shape of Nuclei, A. Budzanowski and A. Kapuscik, eds., pp. 163–210.
Robson, D. (1978).Nuclear Physics,A308, 381.
Stock, H. (1976). Invited paper presented at the Int. Conf. on the Radial Shape of Nuclei, A. Budzanowski and A. Kapuscik, eds., pp. 103–139.
Svenne, J. P. (1980).Journal of Physics G,6, 465.
Théberge, S., and Thomas, A. W.Nuclear Pjysics A,393, 252.
Thomas, A. W. (1983). ref. TH. 3552-CERN, March.
Trainor, L. E. H., and Gupta, R. K. (1971).Canadian Journal of Physics,49, 133.
Wapstra, A. H., and Gove, N. B. (1971).Nuclear Data Tables,9, 267.
Wilkinson, D. H. (1977).Nuclear Instruments and Methods,146, 143.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Anagnostatos, G.S. Isomorphic shell model for closed-shell nuclei. Int J Theor Phys 24, 579–613 (1985). https://doi.org/10.1007/BF00670466
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00670466