- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Reviews of Modern Physics

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Funny Hills: The Shell-Correction Approach to Nuclear Shell Effects and Its Applications to the Fission Process

M. BRACK*, JENS DAMGAARD, A. S. JENSEN, H. C. PAULI*, V. M. STRUTINSKY†, and C. Y. WONG‡

M. BRACK*, JENS DAMGAARD, A. S. JENSEN, H. C. PAULI*, V. M. STRUTINSKY†, and C. Y. WONG‡

  • The Niels Bohr Institute, University of Copenhagen, Denmark

  • *Permanent address: University of Basel, Switzerland.
  • †Present address: Institute for Nuclear Research, Kiev, U.S.S.R. (On leave from I. V. Kurchatov Institute for Atomic Energy, Moscow, U.S.S.R.).
  • ‡Permanent address: Oak Ridge National Laboratory, Tennessee, U.S.A.
PDF

Rev. Mod. Phys. 44, 320 – Published 1 April, 1972

DOI: https://doi.org/10.1103/RevModPhys.44.320

Abstract

This paper reviews various results related to the single-particle structure in spherical and deformed nuclei, discussed from the viewpoint of the so-called shell-correction method. This method stresses the importance of large-scale nonuniformities in the energy distribution of the individual particles especially near the Fermi energy. The way in which these nonuniformities affect in an essential way many nuclear properties, such as the shape stiffness, the spatial density distribution, the total mass of the nucleus, the mass and inertia of the nuclear shape variations, etc. is also discussed. Against this background, the behavior of the nuclear deformation energy is described, in particular for larger distortions relevant to the fission process. In this connection, some qualitative singularities of the phenomenological liquid-drop deformation energy at large shape distortions are pointed out, and their possible implications for fission are discussed. As the problems considered cover a wide range of nuclear properties, this paper is not a review in the narrow sense of the word. Comparison with other approaches as well as historic references are given mainly to clarify specific points, because a complete review would be a monumental undertaking.

View figure in article

References (143)

  1. Proceedings of the Second United Nations International Conference on the Peaceful Uses of Atomic Energy, Geneva, 1-13 September, 1958, (United Nations Publications) Vol. 15
  2. Proceedings of the International Conference on Nuclear Structure, Kingston, Canada, 29 August-3 September 1960, edited by D. A. Bromley and E. W. Vogt (North Holland Publ. Co.)
  3. Proceedings of the Second International Conference on Nuclidic Masses, Vienna, Austria, 15-19 July 1963, edited by W. H. Johnston, Jr., (Springer-Verlag)
  4. Proceedings of the Symposium on the Physics and Chemistry of Fission, held by IAEA, Salzburg, Austria, 22-26 March 1965
  5. Proceedings of the International Symposium on, why and how should we investigate Nuclides far off the Stability Line, Lysekil, Sweden, 21-27 August 1966 (Almqvist and Wiksell, Stockholm)
  6. International Nuclear Physics Conference, Gatlinburg, Tennesee, 12-17 September 1966, edited by R. L. Becker, C. D. Goodman, P. H. Stelson, and A. Zucker, (Academic, New York)
  7. Proceedings of a Conference on Nuclear Data—Microscopic Cross-sections and Other Data Basic for Reactors, held by IAEA, Paris, 17-21 October 1966
  8. Proceedings of the Third International Conference on Atomic Masses, Winnipeg, Canada, 28 August-1 September 1967, edited by R. C. Barber, (University of Manitoba Press)
  9. Proceedings of the Second I A EA Symposium on the Physics and Chemistry of Fission, Vienna, 28 July-1 August 1969
  10. Proceedings of the International Conference on Properties of Nuclear States, Montréal, Canada, 25-30 August 1969 (University of Montréal Press)
  11. Abramowitz, M., and I. A. Segun, Eds., 1964, Handbook of Mathematical Functions (Dover, New York)
  12. Albrecht, K., et al., 1970, Phys. Letters 32B, 229
  13. Andersen, B. L., et al., 1970, Nucl. Phys. A159, 337
  14. Androsenko, K. D., et al., 1969, Vienna, p. 419
  15. Balian, R., and C. Bloch, 1970, Ann. Phys. 60, 401
  16. Balian, R.C. Bloch, and C. Bloch, 1971, Ann. Phys. 64, 271
  17. Baranger, M., and K. Kumar, 1968, Nucl. Phys. A122, 241
  18. Bassichis, W. A., et al., 1971, Livermore Preprint UCRL-73044
  19. Bate, G. L., et al., 1963, Phys. Rev. 131, 722
  20. Batty, C. J., 1970, Phys. Letters 31B, 496
  21. Batty, C. J., and G. W. Greenless, 1969, Nucl. Phys. A133, 673
  22. Batty, C. J., and G. W. Greenless, 1969, Nucl. Phys. A133, 673
  23. Belyaev, S. T., 1959, Kgl. Danske Videnskab. Selskab, Mat.-Fys. Medd. 31, No. 11
  24. Belyakov, V. A., 1964, Sovjet Phys.—JETP 19, 1103
  25. Bès, D. R., 1961, Kgl. Danske Videnskab. Selskab, Mat.-Fys. Medd. 33, No. 2
  26. Bès, D. R., and Z. Szymánski, 1961, Nucl. Phys. 28, 42
  27. Bethe, H. A., and R. F. Bacher, 1936, Rev. Mod. Phys. 8, 82
  28. Bethe, H. A.R. F. Bacher, 1968, Phys. Rev. 167, 879
  29. Bjørnholm, S., and V. M. Strutinsky, 1969, Nucl. Phys. A136, 1
  30. Bloch, C., and R. Balian, 1969, private communication
  31. Bohr, Å., 1952, Kgl. Danske Videnskab. Selskab, Mat-Fys. Medd. 26, No. 14
  32. Bohr, Å., and B. Mottelson, 1953, Kgl. Danske Videnskab. Selskab, Mat.-Fys. Medd. 27, No. 16
  33. Bohr, Å.B. Mottelson, and B. Mottelson, 1969, Nuclear Structure, (Benjamin Inc., New York), Vol. 1
  34. Bohr, Å.B. MottelsonB. Mottelson, and B. Mottelson, to be published, Nuclear Structure (W. A. Benjamin Inc., New York), Vols. 2, 3
  35. Bohr, N., and F. Kalckar, 1937, Kgl. Danske Videnskab. Selskab, Mat.-Fys. Medd. 14, No. 10
  36. Bohr, N.F. Kalckar, and J. A. Wheeler, 1939, Phys. Rev. 56, 426
  37. Bolsterli, M., et al., 1971, Los Alamos Preprint LA-DC-12817
  38. Brack, M., and H.-C. Pauli, 1971, Preprint, Basel University
  39. Bromley, D. A., and J. Weneser, 1968, Comments Nucl. Part. Phys., 2, 151
  40. Brown, G. E., 1969, Comments Nucl. Part. Phys., 3, 136
  41. Bunatyan, G. G., V. M. Kolomietz, and V. M. Strutinsky, 1972, to be published
  42. Cohen, S., and W. J. Swiatecki, 1962, Ann. Phys. 19, 67
  43. Cohen, S.W. J. Swiatecki, and W. J. Swiatecki, 1963, Ann. Phys. 22, 406
  44. Damgaard, J., et al., 1969a, Nucl. Phys. A135, 432
  45. Damgaard, J. et al., 1969b, Vienna, p. 213
  46. Decowsky, P., et al., 1968, Nucl. Phys. A110, 129
  47. Feenberg, E., 1955, Shell Theory of the Nucleus (Princeton U. P.)
  48. Fong, P., 1969, Statistical Theory of Nuclear Fission (Gordon and Breach, New York)
  49. Ford, G. P., et al., 1970, Los Alamos Report, LA-4329
  50. Frenkel, J., 1939, Soviet Phys.—JETP, 9, 641
  51. Frenkel, J., 1939, Phys. Rev. 55, 987
  52. Gareev, F. A., et al., 1970, Sov. J. Nucl. Phys. 11, 667
  53. Geilikman, B. T., 1960, Kingston, p. 874
  54. Geilikman, B. T., 1965, Salzburg, 1, 121
  55. Geilikman, B. T., and G. N. Khlebnikov, 1968, Yad. Fiz. 7, 215
  56. Ghiorso, A., et al., 1954, Phys. Rev. 95, 293
  57. Goeppert-Mayer, M., and J. H. D. Jensen, 1955, Nuclear Shell Structure (Wiley, New York)
  58. Grin, T., 1963, Soviet Phys.—JETP 16, 1327
  59. Gustafson, C., et al., 1966, Lysekil, p. 613
  60. Hahn, O., and F. Strassman, 1939, Naturwissenschaften 27, 11
  61. Halpern, I., and V. M. Strutinsky, 1958, Geneva, p. 408
  62. Hasse, R. W., 1969, Vienna, p. 33
  63. Haxel, O., et al., 1949, Phys. Rev. 75, 1766
  64. Heisenberg, J., et al., 1969, Phys. Rev. Letters 23, 1402
  65. Hendrie, D. L., et al., 1968, Phys. Letters 26B, 127
  66. Hill, D. L., and J. A. Wheeler, 1953, Phys. Rev. 89, 1102
  67. Hyde, E. K., et al., 1964, The Nuclear Properties of the Heavy Elements, 3 (Prentice Hall, Englewood Cliffs, New Jersey)
  68. Inglis, D., 1954, Phys. Rev. 96, 1059
  69. Johansson, S. A. E., 1962, Nucl. Phys. 22, 529
  70. Kirzhnits, D. A., 1967, Field Theoretical Methods in Many-Body Systems (Pergamon, New York)
  71. Kolomietz, V. M., et al., 1971, Preprint ITF-71-93-R, Kiev
  72. Kramers, H. A., 1940, Physica 7, 284
  73. Kumar, K., and M. Baranger, 1968, Nucl. Phys. A110, 529
  74. Landau, L. D., and E. M. Lifshitz, 1959, Quantum Mechanics (Pergamon, New York)
  75. Landau, L. D.E. M. Lifshitz, and E. M. Lifshitz, 1960, Mechanics (Pergamon, New York)
  76. Lawrence, J. N. P., 1965, Phys. Rev. 139, 1227
  77. Lynn, E., 1966, Paris, 2, 89
  78. Lynn, E., and S. Bjørnholm, 1970, private communication
  79. Malov, L. A., S. M. Polikanov, and V. G. Soloviev, 1966, Gatlinburg, p. 786
  80. Mayer, M. G., 1949, Phys. Rev. 75, 1969
  81. Meitner, L., and O. R. Frisch, 1939, Nature 143, 239
  82. Meitner, L.O. R. Frisch, 1950, Nature 165, 561
  83. Meitner, L.O. R. Frisch, 1952, Arkiv Fysik 4, 383
  84. Meldner, H., 1969, Phys. Rev. 178, 1815
  85. Migdal, A. B., 1959, JETP 37, 249 Soviet Phys.—JETP 10 (1960), 176
  86. Migdal, A. B., 1968, Nuclear Theory, The Quasiparticle Method (Benjamin, New York)
  87. Mosel, U., et al., 1971, Phys. Letters 34B, 587
  88. Moskowski, S. A., 1970, Phys. Rev. C 2, 402
  89. Mottelson, B., and S. G. Nilsson, 1955, Phys. Rev. 99, 1615
  90. Mottelson, B.S. G. Nilsson, and S. G. Nilsson, 1959, Kgl. Danske Videnskab. Selskab, Mat. Fys. Skr. 1, No. 8
  91. Muzycka, Ya. A., et al., 1968, Yad. Fiz. 6, 306
  92. Muzycka, Ya. A. et al., 1970, Yad. Fiz. 11, 105 Sov. J. Nucl. Phys. 11, 57
  93. Myers, W. D., and W. J. Swiatecki, 1966a, Nucl. Phys. 81, 1
  94. Myers, W. D.W. J. Swiatecki, and W. J. Swiatecki, 1966b, Lysekil, p. 343
  95. Myers, W. D.W. J. SwiateckiW. J. Swiatecki, 1968, Ph. D. Thesis, Lawrence Radiation Laboratory Report UCRL-18214
  96. Myers, W. D.W. J. SwiateckiW. J. Swiatecki, 1969, Nucl. Phys. A145, 387
  97. Myers, W. D.W. J. SwiateckiW. J. Swiatecki, and W. J. Swiatecki, 1969, Ann. Phys. 55, 395
  98. Möller, P., and S. G. Nilsson, 1970, Phys. Letters 31B, 283
  99. Negele, J. W., 1970, Phys. Rev. C1, 1260
  100. Nemirovsky, P. E., and V. A. Chepurnov, 1966, Sov. J. Nucl. Phys. 3, 730
  101. Nilsson, S. G., 1955, Kgl. Danske Videnskab. Selskab, Mat.-Fys. Medd. 29, No. 16
  102. Nilsson, S. G., and O. Prior, 1961, Kgl. Danske Videnskab Selskab, Mat.-Fys. Medd. 32, No. 16
  103. Nilsson, S. G.O. Prior, et al., 1969, Nucl. Phys. A131, 1
  104. Nilsson, S. G.O. Prior et al., S. G. Thompson, and C. F. Tsang, 1969, Phys. Letters 28B, 458
  105. Nix, J. R., 1969, Nucl. Phys. A130, 241
  106. Oganessian, Yu. T., 1968, preprint JINR E7-3942, Dubna
  107. Pashkevich, V. V., 1969, Nucl. Phys. A133, 400
  108. Pashkevich, V. V., 1969, 1970, private communications Nucl. Phys. A169, 275 (1971)
  109. Pashkevich, V. V., and V. M. Strutinsky, 1969, Yad. Fiz. 9, 56 Sov. J. Nucl. Phys. 9, 35
  110. Pauli, H. C., et al., 1971, Phys. Letters 34B, 264
  111. Pauli, H. C. et al., and T. Ledergerber, 1971, Nucl. Phys. A175, 545
  112. Pavlinchuk, V. A., 1967, private communication
  113. Polikanov, S. M., et al., 1962, Zhur. Eksp. i Teoret. Fiz. 42, 1464 Soviet Phys.—JETP 15, 1016
  114. Quentin, P., and R. Babinet, 1970, Nucl. Phys. A156, 365
  115. Rainwater, J., 1950, Phys. Rev. 79, 432
  116. Rost, E., 1968, Phys. Letters 26B, 184
  117. Seeger, P., 1967, Winnipeg, p. 85
  118. Seeger, P., and R. C. Perisho, 1967, Los Alamos Rept LA-3751
  119. Siemens, P., 1970, Phys. Rev. C1, 98
  120. Smirnov, V. I., 1964, A Course of Higher Mathematics (Pergamon, New York) Vol. 4, Chap. 2
  121. Stein, N., 1969, Montréal, p. 337
  122. Strutinsky, V. M., and A. S. Tyapin, 1963, Zhur. Eksp. i Teoret. Fiz. 45, 960 Soviet Phys.—JETP 18, 664
  123. Strutinsky, V. M.A. S. Tyapin, et al., 1963, Nucl. Phys. 46, 639
  124. Strutinsky, V. M.A. S. Tyapin et al., 1966, Yad. Fiz. 3, 614 Sov. J. Nucl. Phys. 3, 449
  125. Strutinsky, V. M.A. S. Tyapin et al., 1966, Lysekil, p. 629
  126. Strutinsky, V. M.A. S. Tyapin et al., 1967, Nucl. Phys. A95, 420
  127. Strutinsky, V. M.A. S. Tyapin et al., 1968, Nucl. Phys. A122, 1
  128. Strutinsky, V. M.A. S. Tyapin et al., and H.-C. Pauli, 1969, Vienna, p. 155
  129. Swiatecki, W. J., 1963, Vienna, p. 58
  130. Swiatecki, W. J., 1970, in Nuclear Reactions Induced by Heavy Ions, edited by R. Bock and W. R. Hering (North Holland Publ. Co., Amsterdam) p. 729
  131. Swiatecki, W. J., and W. D. Myers, 1970, private communication
  132. Szymánski, Z., 1961, Nucl. Phys. 28, 63
  133. Terrell, J., 1959, Phys. Rev. 113, 527
  134. Tsang, C. F., 1969, Berkeley Report UCRL-18899
  135. Vandenbosch, R., 1963, Nucl. Phys. 46, 129
  136. Vandenbosch, R., and J. R. Huizenga, 1958, Geneva, p. 284
  137. Vautherin, D., and D. M. Brink, 1970, Phys. Letters 32B, 149
  138. Vogel, P., 1968, Nucl. Phys. A112, 583
  139. von Weizsäcker, C. F., 1935, Z. Physik 96, 431
  140. Vorotnikov, P. E., et al., 1967, Sov. J. Nucl. Phys. 5, 210
  141. Wilets, L., 1959, Phys. Rev. 116, 372
  142. Wilets, L., 1964, Theories of Fission (Clarendon Press, Oxford)
  143. Zeldes, N., et al., 1967, Kgl. Danske Videnskab. Selskab, Mat. Fys. Skr. 3, No. 5

Outline

Information

Rev. Mod. Phys. 44, 320– Published 1 April, 1972

    © 1972 American Physical Society

    Sign In to Your Journals Account

    Filter

    Filter

    Article Lookup

    Enter a citation