Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T01:33:47.380Z Has data issue: false hasContentIssue false
  • English
  • Français

A group theoretical approach to the many nucleon problem

Published online by Cambridge University Press:  24 October 2008

J. A. de Wet
J. A. de Wet
Affiliation:
Department of Applied Mathematics, University of South Africa, Pretoria†
Get access Rights & Permissions [Opens in a new window]

Extract

Representations of the four-dimensional unitary group U4 were considered long ago by Wigner(1)as a model for nuclear isobaric multiplets. However, the Hamiltonian did not include the components of isospin which together with the spin coordinates are known to label the nuclear states. In this paper we shall find representations characterized by the eigenvalues of angular momentum J, isospin T and parity π, and will find mass relations which give good agreement with the experimental energy levels of Li6 and Be8 labelled by the same quantum numbers. The representations found by Wigner give good results for the ground state energies, or masses, of all the nuclei up to a mass number of A = 110(2), and we shall derive Wigner's representations as a special case. In fact, unless these are satisfied it is impossible for particle-like representations of U4 to exist!

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 70 , Issue 3 , November 1971 , pp. 485 - 496
Copyright
Copyright © Cambridge Philosophical Society 1971

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Wigner, E.Phys. Rev. 51 (1937), 106.CrossRefGoogle Scholar
(2)Franzini, P. and Radicati, L. A.Phys. Lett. 6 (1963), 322.CrossRefGoogle Scholar
(3)Eddington, A. S.Fundamental theory (Cambridge, 1948).Google Scholar
(4)Boerner, H.Representations of groups (North-Holland, 1963).Google Scholar
(5)Kahan, T.Theory of groups in classical and quantum physics 1 (Oliver and Boyd, 1965).Google Scholar
(6)Bargmann, V. and Wigner, E. P.Proc. Nat. Acad. Sci. U.S.A. 34 (1946), 211.CrossRefGoogle Scholar
(7)Roman, P.Theory of elementary particles (North-Holland, 1964).Google Scholar
(8)Hamermesh, M.Group theory (Addison Wesley, 1962).Google Scholar
(9)Eddington, A. S.Relativity theory of protons and neutrons (Cambridge, 1936).Google Scholar
(10)De Broglie, L.Act. Scient. et Ind. (1934), 181.Google Scholar
(11)Kemmer, N.Proc. Cambridge Philos. Soc. 39 (1943), 189.CrossRefGoogle Scholar
(12)De Swart, J. J.Rev. Modern Phys. 35 (1963), 916.CrossRefGoogle Scholar
(13)Moshinsky, M. and Syamala Devi, V.J. Mathematical Phya. 10 (1969), 455.CrossRefGoogle Scholar
(14)Azenberg-Selove, F. and Lauritsen, T.Nuclear Phys. 11 (1959), 1.CrossRefGoogle Scholar