Abstract
Knowledge of the Racah algebra for the higher unitary groups is exploited to give a general formula for the partial widths for the direct product subgroup U( N k )× U(k) of the full unitary group U( N) of a given shell model vector space. This formula makes it possible to separate the second moments of dynamical operators into the internal and external parts which are needed for detailed applications of the spectral distribution technique. Specific applications are made for k = 2 (isospin) and k = 4 (Wigner supermultiplet symmetry). Explicit expressions are given for the isospin breaking contributions to the spectral widths which make it possible to estimate the intensities of isospin impurities in an average state of a given isospin. The goodness of Wigner supermultiplet symmetry is examined for the 2s-ld shell with a detailed example, the A = 25 nuclei, for which partial widths have been calculated for various modifications of the Kuo-Brown interaction to give a simple measure of the amount of mixing to be expected between states of different space symmetry.
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