Advertisement

Abstract

The shell model, despite a somewhat checkered career, has emerged as a useful approximation to the many-particle description of the atomic nucleus (E57b, S63). In principle it is perhaps the closest of all nuclear models to being unified, i.e., to describing all properties of all states of all nuclei. Unfortunately, even with the restriction to a shell structure, the number of possible states is often very large and there are few nuclei whose properties can be described without a prohibitive amount of computational labor. Thus several submodels of the shell model have been constructed to reduce the number of states and hence also the computational difficulty. These submodels describe more of the physical structure of states in terms of well-defined quantum numbers. It is as a submodel of the shell model that we can classify the “SU 3 model.”

Keywords

Shell Model Orbital Angular Momentum Young Tableau Oscillator Quantum Intrinsic State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. W28.
    Weyl, H., “Group Theory and Quantum Mechanics,” Dover Publications, New York, 1928.Google Scholar
  2. F37.
    Feenberg, E., and M. Phillips, Phys. Rev. 51:597 (1937).ADSMATHCrossRefGoogle Scholar
  3. W37.
    Wigner, E. P., Phys. Rev. 51:106 (1937).ADSMATHCrossRefGoogle Scholar
  4. J40.
    Jauch, J. M., and E. L. Hill, Phys. Rev. 57:641 (1940).MathSciNetADSMATHCrossRefGoogle Scholar
  5. R42.
    Racah, G., Phys. Rev. 62:438 (1942).ADSCrossRefGoogle Scholar
  6. J51a.
    Jahn, H. A., Proc. Roy. Soc. 205:192 (1951).ADSMATHCrossRefGoogle Scholar
  7. J51b.
    Jahn, H. A., and H. van Wieringen, Proc. Roy. Soc. A209:502 (1951).ADSCrossRefGoogle Scholar
  8. R51.
    Racah, G., “Lecture Notes on Group Theory in Spectroscopy,” Princeton University, 1951.Google Scholar
  9. H53.
    Hill, D. L., and J. A. Wheeler, Phys. Rev. 89:1102 (1953).ADSMATHCrossRefGoogle Scholar
  10. E55a.
    Elliott, J. P., and B. H. Flowers, Proc. Roy. Soc. A229:536 (1955).ADSCrossRefGoogle Scholar
  11. E55b.
    Elliott, J. P., and T. H. R. Skyrme, Proc. Roy. Soc. A232:561 (1955).ADSCrossRefGoogle Scholar
  12. N55.
    Nilsson, S. G., Dan. Mat. Fys. Medd. 29:16 (1955).Google Scholar
  13. B56.
    Blin-Stoyle, R. J., Rev. Mod. Phys. 28:75 (1956).ADSCrossRefGoogle Scholar
  14. K56.
    Kurath, D., Phys. Rev. 101:216 (1956).ADSCrossRefGoogle Scholar
  15. E57a.
    Edmonds, A. R., “Angular Momentum in Quantum Mechanics,” Princeton University Press, Princeton, N. J., 1957.MATHGoogle Scholar
  16. E57b.
    Elliott, J. P., and B. H. Flowers, Proc. Roy. Soc. A242:57 (1957).ADSCrossRefGoogle Scholar
  17. E57c.
    Elliott, J. P., and A. M. Lane, in “Encyclopedia of Physics” S. Flügge, ed., Vol. 39. Springer-Verlag, Berlin-Göttingen-Heidelberg, 1957.Google Scholar
  18. H57.
    Hofstadter, R., Ann. Rev. Nucl. Sci. 7:231 (1957).ADSCrossRefGoogle Scholar
  19. M57.
    Moszkowski, S. A., in “Encyclopedia of Physics,” S. Flügge, ed. Springer-Verlag, Berlin-Göttingen-Heidelberg, 1957.Google Scholar
  20. P57.
    Peierls, R. E., and J. Yoccoz, Proc. Phys. Soc. A70:381 (1957).MathSciNetADSCrossRefGoogle Scholar
  21. E58.
    Elliott, J. P., Proc. Roy. Soc. A245:128 and 562 (1958).ADSCrossRefGoogle Scholar
  22. M58.
    Moskowski, S., Phys. Rev. 110:403 (1958).ADSCrossRefGoogle Scholar
  23. E59.
    “Nuclear Reaction 1,” P. M. Endt and M. Demeur, eds. North Holland Publishing Co., Amsterdam, 1959.Google Scholar
  24. R59.
    Rotenberg, M., R. Bivins, N. Metropolis, and J. K. Wooten, Jr., “The 3-j and 6-j Symbols,” The Technology Press, Massachusetts Institute of Technology, Cambridge, Mass, 1959.Google Scholar
  25. B60a.
    Bargman, V., and M. Moshinsky, Nucl. Phys. 18:697 (1960).CrossRefGoogle Scholar
  26. B60b.
    Bayman, B. F., “Groups and Their Application to Spectroscopy,” Lectures delivered in 1957 at NORDITA. Nordisk Institute for Teoretisk Atom Fysik, Copenhagen, 1960.Google Scholar
  27. B60c.
    Bohr, A., and B. R. Mottelson, in “Nuclear Spectroscopy B,” Fay Ajzenberg-Selove, ed. Academic Press, New York-London VI, C, 1960.Google Scholar
  28. G60.
    Gove, H. E., Proc. Internl. Conf. Nuclear Structure, Kingston: D. A. Bromley and E. W. Vogt, eds. University of Toronto Press, p. 438, 1960.Google Scholar
  29. L60.
    Lawson, R. D., in “Nuclear Spectroscopy B,” Fay Ajzenberg-Selove, ed. Academic Press, New York-London VI, A, 1960.Google Scholar
  30. N60.
    Newton, T. D., “Energy Levels of a Completely Anistropic Oscillator,” Chalk River Nucl. Labs. Rept., CRT-886, 1960.Google Scholar
  31. W60.
    Wilkinson, D. H., in “Nuclear Spectroscopy B,” Fay Ajzenberg-Selove, ed. Academic Press, New York-London, V.F., 1960.Google Scholar
  32. B61.
    Bargman, V., and M. Moshinsky, Nucl. Phys. 23:177 (1961).CrossRefGoogle Scholar
  33. H61a.
    Harvey, M., Ph.D. Thesis, Southampton, 1961.Google Scholar
  34. H61b.
    Hellwege, K. H., ed., “Energy Levels in Light Nuclei,” Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961.Google Scholar
  35. K61.
    Koltan, D. S., Phys. Rev. 124:1162 (1961).ADSCrossRefGoogle Scholar
  36. L61.
    Litherland, A. E., J. A. Kuehner, H. E. Gove, M. A. Clarke, and E. Almqvist, Phys. Rev. Letters 7:98 (1961).ADSCrossRefGoogle Scholar
  37. N61.
    Ne’eman, Y., Nucl. Phys. 26:222 (1961).MathSciNetCrossRefGoogle Scholar
  38. E62.
    Elliott, J. P., “Escuela Latino Americana De Fisca.” Universidad de Mexico, 1962.Google Scholar
  39. G62.
    Gell-Mann, M., Phys. Rev. 125:1067 (1962).MathSciNetADSMATHCrossRefGoogle Scholar
  40. M62.
    Moshinsky, M., “Escuela Latino Americana De Fisca.” Universidad de Mexico, 1962.Google Scholar
  41. W62.
    Willey, R. S., Phys. Rev. 126:1127 (1962).ADSMATHCrossRefGoogle Scholar
  42. B63a.
    Bannerjee, M. K., and C. Levinson, Phys. Rev. 130:1036 (1963).ADSCrossRefGoogle Scholar
  43. B63b.
    Bannerjee, M. K., C. Levinson, and S. Meshkov, Phys. Rev. 130:1064 (1963).ADSCrossRefGoogle Scholar
  44. B63c.
    Brink, D. M., Nucl. Phys. 40:593 (1963).MATHCrossRefGoogle Scholar
  45. B63d.
    Brink, D. M., and G. F. Nash, Nucl. Phys. 40:608 (1963).CrossRefGoogle Scholar
  46. E63a.
    Elliott, J. P., “Selected Topics in Nuclear Theory.” International Atomic Energy Agency, Vienna, 1963.Google Scholar
  47. E63b.
    Elliott, J. P., and M. Harvey, Proc. Roy. Soc. A272:557 (1963).ADSCrossRefGoogle Scholar
  48. L63.
    Litherland, A. E., M. A. Clark, and C. Broude, Phys. Rev. Letters 3:204 (1963).CrossRefGoogle Scholar
  49. H63.
    Harvey, M., Phys. Rev. Letters 3:209 (1963).CrossRefGoogle Scholar
  50. N63.
    Nash, G. F., Nuovo Cimento 30:1064 (1963).CrossRefGoogle Scholar
  51. S63.
    de Shalit, A., and I. Talmi, “Nuclear Shell Theory,” Academic Press, New York-London, 1963.Google Scholar
  52. B64.
    Bouten, M. C., J. P. Elliott, and J. A. Pullen, Comptes Rendus du Congrès International de Physique Nucléaire, pré Madame P. Gugenberger, Centre National de la Recherche Scientifique, Paris, 1964, Vol. II, p. 413. Also preprint, 1966.Google Scholar
  53. C64.
    Carter, E. B., G. E. Mitchell, and R. H. Davies, Phys. Rev. 133B:1421 and 1434 (1964).ADSCrossRefGoogle Scholar
  54. E64.
    Engeland, T., and A. Kallio, Nucl. Phys. 59:211 (1964).CrossRefGoogle Scholar
  55. G64.
    Guiasu, I., and M. Micu, Rev. Roum. Physics 9:911 (1964).MATHGoogle Scholar
  56. H64a.
    Hamermesh, M., “Group Theory and its Application to Physical Problems,” Addison-Wesley, Reading, Mass., 1964.Google Scholar
  57. H64b.
    Harvey, M., Nucl. Phys. 52:542 (1964).CrossRefGoogle Scholar
  58. H64c.
    Harvey, M., Symp. Structure of Low-Medium Mass Nuclei, Kansas, 1964.Google Scholar
  59. H64d.
    Hecht, K. T., in “Selected Topics in Nuclear Spectroscopy,” B. J. Verhaar, ed. North-Holland and John Wiley, 1964.Google Scholar
  60. H64e.
    Horie, H., J. Phys. Soc. Japan 19:1783 (1964).MathSciNetADSCrossRefGoogle Scholar
  61. I64.
    Inoue, T., T. Sebe, H. Hagiwara, and A. Arima, Nucl. Phys. 59:1 (1964).CrossRefGoogle Scholar
  62. K64.
    Kuehner, J. A., and J. D. Pearson, Can. J. Phys. 42:477 (1964).ADSCrossRefGoogle Scholar
  63. M64a.
    McKellar, B. H. J., Phys. Rev. 134:B1190 (1964).ADSCrossRefGoogle Scholar
  64. M64b.
    Middleton, R., and D. J. Pullen, Nucl Phys. 51:63 (1964).CrossRefGoogle Scholar
  65. N64.
    Nash, G. F., Nuovo Cimento 32:727 (1964).CrossRefGoogle Scholar
  66. P64.
    Pandya, S. P., and I. M. Green, Nucl. Phys. 57:658 (1964).CrossRefGoogle Scholar
  67. S64.
    Svenne, J. P., and M. Harvey, unpublished.Google Scholar
  68. T64.
    Tinkham, M., “Group Theory and Quantum Mechanics,” McGraw-Hill Book Co., New York, 1964.MATHGoogle Scholar
  69. A65.
    Arima, A., M. Nomura, and H. Kawarada, Phys. Rev. Letters 19:400 (1965).CrossRefGoogle Scholar
  70. B65a.
    Bassichis, W. H., and G. Ripka, Phys. Rev. Letters 15:320 (1965).CrossRefGoogle Scholar
  71. B65b.
    Block, C., and V. Gillet, Phys. Rev. Letters 16:62 (1965) and 18:58 (1965).CrossRefGoogle Scholar
  72. E65a.
    Engeland, T., Nucl. Phys. 72:68 (1965).CrossRefGoogle Scholar
  73. E65b.
    Evans, H. C., M. A. Eswaren, H. E. Gove, A. E. Litherland, and C. Broude, Can. J. Phys. 43:82 (1965).ADSCrossRefGoogle Scholar
  74. F65.
    Flores, J., E. Chacon, P. A. Mello, and M. de Llano, Nucl. Phys. 72:352 (1965).CrossRefGoogle Scholar
  75. H65.
    Hecht, K. T., Nucl. Phys. 62:1 (1965).MathSciNetCrossRefGoogle Scholar
  76. K65.
    Kelson, I., Phys. Rev. Letters 16:143 (1965).CrossRefGoogle Scholar
  77. L65.
    de Llano, M., P. A. Mello, E. Chacon, and J. Flores, Nucl. Phys. 72:379 (1965).CrossRefGoogle Scholar
  78. M65a.
    Margolis, B., and N. de Takacsy, Phys. Rev. Letters 15:329 (1965).CrossRefGoogle Scholar
  79. M65b.
    Muthukrishnan, R., and M. Baranger, Phys. Rev. Letters 18:160 (1965).CrossRefGoogle Scholar
  80. N65a.
    Newton, T. D., NUSTAT—An Apex Program for Fully Mechanized Shell Model Calculations, Chalk River Nucl. Labs., Ontario, Canada, CRT-1213, 1965.Google Scholar
  81. N65b.
    Nordhagen, R., M. Hoffman, F. Ingelretsen, and A. Tveter, Phys. Rev. Letters 16:163 (1965).CrossRefGoogle Scholar
  82. N65c.
    Nathan, O., and S. G. Nilsson, in “Alpha-Beta-and Gamma-Ray Spectroscopy,” Chap. 10, Kai Siegbahn, ed. North-Holland Publishing Co., Amsterdam, 1965.Google Scholar
  83. S65a.
    Siemssen, R. H., L. L. Lee, Jr., and D. Cline, Phys. Rev. 140:B1258 (1965).ADSCrossRefGoogle Scholar
  84. S65b.
    Skorka, S. J., “Compilation of Electromagnetic Transition Strengths in Light Nuclei (A ≤ 40),” II Institute für Experimental physik, der Universität Hamburg, 1965.Google Scholar
  85. W65.
    Wilsdon, C. E., Ph.D. Thesis, 1965, Sussex.Google Scholar
  86. Z65.
    Zeidman, B., and T. H. Braid, Phys. Rev. Letters 16:139 (1965).CrossRefGoogle Scholar
  87. A66a.
    Abulaffio, C., Nucl. Phys. 81:71 (1966).Google Scholar
  88. A66b.
    Adler, C., T. Carocoran, and C. Most, Nucl. Phys. 88:145 (1966).CrossRefGoogle Scholar
  89. A66c.
    Alexander, T. K., C. Broude, A. J. Ferguson, J. A. Kuehner, A. E. Litherland, R. W. Ollerhead, and P. J. M. Smulders, Gatlinburg Conf. Nucl. Phys., 1966.Google Scholar
  90. B66a.
    Barker, F. C., Nucl. Phys. 83:418 (1966).CrossRefGoogle Scholar
  91. B66b.
    Bernier, J.-P., and M. Harvey, unpublished.Google Scholar
  92. B66c.
    Borysowicz, J., Nucl. Phys. 82:321 (1966).CrossRefGoogle Scholar
  93. B66d.
    Brown, G. E., and A. M. Green, Nucl. Phys. 75:401 (1966).CrossRefGoogle Scholar
  94. B66e.
    Brown, G. E., and A. M. Green, Nucl. Phys. 85:87 (1966).CrossRefGoogle Scholar
  95. B66f.
    Bauer, M., and F. Prats, Nucl. Phys. 89:230 (1966).CrossRefGoogle Scholar
  96. B66g.
    Broglia, R. A., and E. E. Maqueda, Nucl. Phys. 86:457.Google Scholar
  97. C66a.
    Celenza, L. S., R. M. Dreizler, A. Klein, and G. J. Dreiss, Phys. Rev. Letters 23:241 (1966).CrossRefGoogle Scholar
  98. C66b.
    Cohen, S., R. D. Lawson, and J. M. Soper, Phys. Rev. Letters 21:306 (1966).CrossRefGoogle Scholar
  99. F66.
    Flores, J., and M. Moshinsky, “Studies on Nuclear Structure in the 2s, 1d Shell, III Group Theory and Particle-Hole States.” Instituto de Fisica, Universidad de Mexico, Preprint, 1966.Google Scholar
  100. G66.
    Glaudemans, P. W. M., B. H. Wildenthal, and J. B. McGrory, Phys. Rev. Letters 21:427 (1966).CrossRefGoogle Scholar
  101. H66.
    Hughes, D. J., and A. B. Volkov, Phys. Rev. Letters 23:113 (1966).CrossRefGoogle Scholar
  102. I66.
    Inoue, T., T. Sebe, H. Hagiwara, and A. Arima, Nucl. Phys. 85:184 (1966).CrossRefGoogle Scholar
  103. K66a.
    Kuehner, J. A., and R. W. Ollerhead, Phys. Rev. Letters 20:301 (1966).CrossRefGoogle Scholar
  104. K66b.
    Kramer, P., and M. Moshinsky, Nucl. Phys. 82:241 (1966).MathSciNetMATHCrossRefGoogle Scholar
  105. L66.
    Lopas, J. S., O. Häusser, R. D. Gill, and H. J. Rose, Nucl. Phys. 89:127 (1966).CrossRefGoogle Scholar
  106. R66a.
    Robson, D., Annual Reviews of Nuclear Science 16:119 (1966).ADSCrossRefGoogle Scholar
  107. R66b.
    Reif, R., Phys. Rev. Letters 23:125 (1966).CrossRefGoogle Scholar
  108. S66.
    Seaborn, J. B., and J. M. Eisenberg, Nucl. Phys. 82:308 (1966).CrossRefGoogle Scholar
  109. T66.
    Trlifaj, L., M. Gmitro, and M. Sotana, Nucl. Phys. 86:681 (1966).CrossRefGoogle Scholar
  110. W66a.
    Wahsweiler, H. G., M. Danos, and W. Greiner, Phys. Rev. Letters 17:395, and 23:257 (1966).ADSCrossRefGoogle Scholar
  111. W66c.
    Wiza, J. L., R. Middleton, and P. V. Hewka, Phys. Rev. 141:975 (1966).ADSCrossRefGoogle Scholar
  112. Z66.
    Zichichi, A., ed., “Recent developments in particle Symmetries,” Academic Press, New York and London, 1966.Google Scholar
  113. A67.
    Akiyamu, Y., Private Communication, Tokyo University, Japan.Google Scholar
  114. B67.
    Bernier, J.-P., and M. Harvey, Nucl. Phys. A94:593 (1967).ADSCrossRefGoogle Scholar
  115. D67.
    Das Gupta, S., and M. Harvey, Nucl. Phys. A94:602 (1967).ADSCrossRefGoogle Scholar
  116. I67.
    Iosifescu, M., and F. Stancu, Nucl. Phys. B8:471 (1967).ADSCrossRefGoogle Scholar
  117. K67.
    Kaiman, C., J.-P. Bernier, and M. Harvey, Can. J. Phys. 45:1297 (1967).ADSCrossRefGoogle Scholar
  118. S67.
    Sebe, T., Preprint, Hosei University, Japan, and Chalk River Nuclear Laboratories, Canada.Google Scholar
  119. V67.
    Vergados, J. D., Preprint, University of Michigan, Ann Arbor.Google Scholar
  120. W67.
    Wathne, C., and T. Engeland, Nucl. Phys. A94:129 (1967).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press 1968

Authors and Affiliations

  • M. Harvey

There are no affiliations available

Personalised recommendations