FIVE DIMENSIONAL QUASISPIN CLASSIFICATION OF SHELL MODEL STATES IN THE SENIORITY SCHEME.
MICHIGAN UNIV ANN ARBOR DEPT OF PHYSICS
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States of configurations jsuperscript N of the nuclear shell model are classified using the properties of a five dimensional rotation group. A basis is used in which states of a given irreducible representation specified by seniority and reduced isospin are labeled with the physical quantum numbers N nucleon number and T, M sub T isospin quantum numbers. A fourth quantum number is needed for a complete classification. Although there appears to be no fourth commuting operator which is either simple or of clear physical relevance, for all problems of practical importance this fourth number takes no more than two distinct values for fixed N,T and M sub T. It is shown how a complete classification can be made for these cases with results which are tractable and symmetrical under particle-hole conjugation. For the special case of seniority 2 and reduced isospin 1 the complete N,T dependence of matrix elements of the most general two-body interaction is found for an arbitrary j-shell or mixed configuration. This is carried out using a generalized Wigner-Eckart theorem. Author
- Nuclear Physics and Elementary Particle Physics