Advertisement

Zeitschrift für Physik A Atomic Nuclei

, Volume 324, Issue 3, pp 331–345 | Cite as

Comparison of semiclassical and quantum mechanical angular distributions for nuclear fission and evaporation

  • L. C. Vaz
  • J. M. Alexander
  • N. Carjan
Nuclei

Abstract

There is quite a variety of statistical-model equations in the literature that have been derived with different assumptions and for various classes of nuclear reactions. Some have been obtained by consideration of the quantum mechanics and some by semiclassical approximations thereto. Often it is not clear whether or not the results of certain analyses are clouded by these semiclassical approximations. We consider three statistical models that have been heavily employed in recent years: (1) fission decay from a rigid rotor (2) particle evaporation from a spherical system and (3) fission decay from two uncoupled spheres. Comparisons are made of numerical results from semiclassical and from quantum mechanical equations for certain specific reactions. In addition, some general features are displayed and discussed for the differences between these formalisms. For average spins that are often encountered in heavy ion reactions, the results are very similar. We conclude that major differences in current analyses are not due to the methodology; instead they must center on assumptions concerning the physical nature of the transition-state (or decision-point) configurations and their associated level densities.

PACS

25.85 24.10 24.60 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bohr, A.: Proceedings of the International Conference on Peaceful Uses of Atomic Energy. Vol. 2, p. 151. New York: 1956Google Scholar
  2. 2.
    Strutinsky, V.M.: Z. Eksp. Teor. Fiz.30, 606 (1956); Atomnaya Energi2, 508 (1967) (Sov. J. At. Energy2, 621 (1957)Google Scholar
  3. 3.
    Halpern, I., Strutinski, V.M.: Proceedings of the 2nd International Conference on Peaceful Uses of Atomic Energy, Geneva, Switzerland. Vol. 15, p. 408, United Nations, New York: 1958Google Scholar
  4. 4.
    Griffin, J.J.: Phys. Rev.116, 107 (1959)Google Scholar
  5. 5.
    Wheeler, J.A.: In: Fast neutron physics. Marion, J.G., Fowler, J.L. (eds.), Vol. II. New York: Wiley Interscience 1963Google Scholar
  6. 6.
    Vandenbosch, R., Huizenga, J.R.: Nuclear fission. New York: Academic Press 1973Google Scholar
  7. 7.
    Prakash, M., Ramamurthy, V.S., Kapoor, S.S., Alexander, J.M.: Phys. Rev. Lett.52, 990 (1984)Google Scholar
  8. 8.
    Vaz, L.C., Alexander, J.M.: Phys. Rep.97, 1 (1983); Freifelder, R., Prakash, M., Alexander, J.M.: Phys. Rep.133, 315 (1986)Google Scholar
  9. 9.
    Wolfenstein, L.: Phys. Rev.82, 690 (1951)Google Scholar
  10. 10.
    Blatt, J.M., Biedenharn, L.C.: Rev. Mod. Phys.24, 258 (1952)Google Scholar
  11. 11.
    Hauser, W., Feshbach, H.: Phys. Rev.87, 366 (1952)Google Scholar
  12. 12.
    Lane, A.M., Thomas, R.G.: Rev. Mod. Phys.30, 257 (1958)Google Scholar
  13. 13.
    Ericson, T., Strutinski, V.: Nucl. Phys.8, 284 (1958); ibid9, 689 (1959)Google Scholar
  14. 14.
    Douglas, A.C., MacDonald, N.: Nucl. Phys.13, 382 (1959)Google Scholar
  15. 15.
    Ericson, T.: Adv. Phys.9, 425 (1960)Google Scholar
  16. 16.
    Dossing, T.: Licentiat Thesis, University of Copenhagen (1979)Google Scholar
  17. 17.
    Bond, P.D.: Phys. Rev. Lett.52, 414 (1984); Bond, P.D.: Phys. Rev. C.32, 471 and 483 (1985)Google Scholar
  18. 18.
    See for example Vaz, L.C., Alexander, J.M.: Z. Phys. A — Atoms and Nuclei318, 231 (1984)Google Scholar
  19. 19.
    Gradshteyn, I.S., Ryzhik, I.M.: Table of integrals, series, and products. (See Eqs. 8.406-1 and 8.447-1.) New York: Academic Press 1980Google Scholar
  20. 20.
    Cohen, S., Plasil, F., Swiatecki, W.J.: Ann. Phys. (NY)82, 557 (1974)Google Scholar
  21. 21.
    Ajitanand, N.N., La Rana, G., Lacey, R., Moses, D.J., Vaz, L.C., Peaslee, G.F., Castro Rizzo, D.M. de, Kaplan, M., Alexander, J.M.: Phys. Rev. C (submitted for publication)Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • L. C. Vaz
    • 1
  • J. M. Alexander
    • 1
  • N. Carjan
    • 1
    • 2
  1. 1.Department of ChemistryState University of New York at Stony BrookStony BrookUSA
  2. 2.CEN de Bordeaux-GradignanGradignanFrance

Personalised recommendations