On the Semiclassical Description of Nuclear Fermi Liquid Drops

  • Peter Schuck
Part of the NATO ASI Series book series (volume 123)

Abstract

Recent years have seen quite some developments in the understanding and application of semiclassical methods to gross properties of nuclei1–4. Talking about gross properties we mean in fact properties of the nucleus where in a systematic and well defined way the influence of individual shells has been averaged out. One typical quantity to be considered is the single particle level density where the average part of say a fully quantal distribution (corresponding e.g. to some sort of Wood-Saxon or H.F. potential) is easily conceivable. The average part of nuclear groundstate masses is another such quantity and in fact represented by the well known Bethe Weizsäcker mass formula. These are two very well known examples where the average nuclear properties have been studied since long and in very great detail. There are however many more quantities and properties whose average behavior could be investigated in the same way and what in fact is interesting to do. Among those we want to cite e.g. the moment of inertia of rotating nuclei, average nuclear pairing properties, average m-particle-n-hole level densities, average behavior of collective nuclear vibrations, average current distributions in rotating and vibrating nuclei, and many things more. In short, we would like to describe semiclassically all nuclear properties which survived could we artificially blow up nuclei to quasi macroscopic dimensions — like e.g. droplets of liquid He3 — where it is clear that the continuum limit is reached, i.e. no shell effect present any more, but still all quantities depending on the size parameters like e.g. volume, surface, curvature,and deformation of the nuclear droplets. In this region we would like to establish the laws the different quantities obey as a function of these parameters which in most cases can be resumed in a per law dependence on the cubic root of the nucleon number A. These laws should then be taken and extrapolated back to the sizes of real nuclei which at the same time then also define their behavior on the average. We know by now that the well known Strutinsky averaging procedure 5 for nuclei of realistic sizes is exactly equivalent to this point of view for the purely theoretical approaches to the nucleus; but also on the experimental side a specific quantity measured as a function of a large number of nuclei allows to extract exactly the corresponding experimentally determined average of the same quantity. Agreement of average experimental and theoretical numbers then allows us to conclude about our understanding of the nucleus. A whole realm of nuclear properties is thus open to our semiclassical investigations.

Keywords

Level Density Local Density Approximation Wigner Function Giant Resonance Shell Effect 
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. 1.
    R.K. Bhaduri, C.K. Ross, Phys. Rev. Lett.27:606 (1971), J. Treiner, H. Krivine, Nuc. Phys.A371’:253 (1981), M. Brack, Contribution workshop on “Semiclassical Methods in Nuclear Physics”, Proceedings Institute Laue Langevin, March 1980.Google Scholar
  2. 2.
    R. Bengtsson, P. Schuck, Phys. Lett. 89B: 321 (1980).Google Scholar
  3. 3.
    G. Ghosh, R.W. Hasse, P. Schuck, J. Winter, Phys. Rev. Lett. 50: 1250 (1983).ADSCrossRefGoogle Scholar
  4. 4.
    M. Durand, V.S. Ramamurthy,.P. Schuck, Phys. Lett. 113B: 116 (1982)CrossRefGoogle Scholar
  5. 5.
    V.M. Strutinsky, F.A. Ivanjuk, Nucl.Phys. A255: 405 (1975).CrossRefGoogle Scholar
  6. 6.
    J. Bartel, M. Vallières, Phys. Lett. 114B: 303 (1982).Google Scholar
  7. 7.
    G. Holzwarth, Lecture Notes to this conference.Google Scholar
  8. 8.
    J. Blocki, J. Randrup, W.J. Swiatecki, C.F. Tsang, Ann. Phys. 105: 427 (1977).ADSCrossRefGoogle Scholar
  9. 9.
    M. Prakash, S. Shlomo, V.M. Kolomietz, Nucl. Phys. A370: 30 (1981).CrossRefGoogle Scholar
  10. 10.
    N. Rowley, P. Prakash, J. Phys. A: Math. Gen. 16: 3219 (1983).ADSCrossRefGoogle Scholar
  11. 11.
    S. Chandrasekhar, An introduction to the study of stellar structure (Dover, N.Y. 1967) 2nd Edit. (1st Edit. 1939 ).Google Scholar
  12. 12.
    D.A. Kirzhnits: Field Theoretical Methods in Many Body Systems, Pergamon, Oxford 1967Google Scholar
  13. 13.
    P. Ring, P. Schuck, The Nuclear Many Body Problem, Springer-Verlag, 1980.Google Scholar
  14. 14.
    V.S. Ramamurthy, M. Ashgar, S.K. Kataria, Nucl.Phys. A398: 544 (1983).CrossRefGoogle Scholar
  15. 15.
    B.K.Jennings, Ph. D. Thesis, Mc Master University (1976).Google Scholar
  16. 16.
    S.E. Koonin, Ph. D. Thesis, MIT 1975.Google Scholar
  17. 17.
    M. Durand, M. Brack, P. Schuck, Z. Phys. A286: 381 (1978).ADSGoogle Scholar
  18. 18.
    M. Durand, V.S. Ramamurthy, P. Schuck, to be published.Google Scholar
  19. 19.
    J.Treiner, P. Schuck, to be published J. Treiner, These d’Etat, Orsay 1981.Google Scholar
  20. 20.
    C. Guet, H.B. Hakansson, M. Brack, Phys. Lett.97B:7 (1980), J. Bartel, P. Quentin, M. Brack, C. Guet, H.B. Hakansson, Nucl. Phys. A385: 79 (1982).Google Scholar
  21. 21.
    J. Treiner, R.W. Hasse, P. Schuck, J. Physique Lettres 44: L733 (1983).CrossRefGoogle Scholar
  22. 22.
    P. Schuck, R. Bengtsson, M. Durand, J. Kunz, V.S. Ramamurthy, Proc. “Workshop on Nuclear Fission ” (Bad Honnef, October 1981), Lecture Notes in Physics, Vol. 158 ( Springer-Verlag, New York, 1982 ) p. 183.Google Scholar
  23. 23.
    C. Guet, M. Brack, Z. Physik A297: 247 (1980).ADSCrossRefGoogle Scholar
  24. 24.
    B. Grammaticos, A. Voros, Ann. Phys.(NY) 123: 359 (1979).MathSciNetADSCrossRefGoogle Scholar
  25. 25.
    J. Treiner, private communication and J. Treiner, P. Schuck, to be published.Google Scholar
  26. 26.
    Proceedings of “ International Workshop on Gross Properties of Nuclei and Nuclear Excitations VIII”, p. 152, Institut für Kernphysik, Techn. Hochschule, Darmstadt, 1980.Google Scholar
  27. 27.
    M. Girod, D. Gogny, private communication.Google Scholar
  28. 28.
    D. Gogny, P. Schuck, to be published.Google Scholar
  29. 29.
    M. Brack, B.K. Jennings, Nucl. Phys. A258: 264 (1976).CrossRefGoogle Scholar
  30. 30.
    A.A. Lastney, B. Jancovici, Physica 102A: 327 (1980).CrossRefGoogle Scholar
  31. 31.
    M. Durand, J. Kunz, P. Schuck, to be published in Nucl. Phys.Google Scholar
  32. 32.
    A.B. Migdal, Nucl. Phys. 13: 655 (1959).MathSciNetMATHCrossRefGoogle Scholar
  33. 33.
    R.M. Diamond, F.S. Stephenens, W.J. Swiatecki, Phys. Lett. 11: 315 (1964).ADSCrossRefGoogle Scholar
  34. 34.
    R.W. Hasse, P. Schuck, contribution Ill, Proceedings of the International Conference on Nuclears Physics, Florence 1983, Vol. 1.Google Scholar
  35. 35.
    P. Schuck, Z. Physik A279:31,(eq. (8)) (1976) P. Schuck, Journal of Low Temperature Phys. 7:459 (eq.(19))(1972).Google Scholar
  36. 36.
    C. Yannouleas, M. Dworzecka, J.J. Griffin, Nucl. Phys. A397: 239 (1983).CrossRefGoogle Scholar
  37. 37.
    P. Schuck, G. Ghosh, R.W. Hasse, Phys. Lett. 118B: 237 (1982).Google Scholar
  38. 38.
    R. Rosenfelder, Ann. Phys. (NY) 128: 188 (1979).ADSCrossRefGoogle Scholar
  39. 39.
    R.W. Hasse, P. Schuck, U. Stroth, to be published.Google Scholar
  40. 40.
    K. Bedell, C. Pethick, J. Low Temp. Phys 49: 213 (1982).ADSCrossRefGoogle Scholar
  41. 41.
    M.J. Davis, E.J. Heller, J. Chem. Phys. 71 (8): 3383 (1979).ADSCrossRefGoogle Scholar
  42. 42.
    P. Schuck, W. Brenig, Z. Phys. B - Condensed Matter 46: 137 (1972).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1985

Authors and Affiliations

  • Peter Schuck
    • 1
  1. 1.Institut des Sciences NucléairesGrenoble-CédexFrance

Personalised recommendations