SUM-RULES FOR B(M1,0(1)(+)-]1(+)) STRENGTH IN IBM-3 AND IBM-4

Sum rules for B(M1,0(1)(+) --> 1(i)(+)) strength are derived for even-even nuclei in the isospin-invariant forms of the IBM, IBM-3 and IBM-4, in the cases where the respective natural internal symmetries, isospin U(3) and U(6) superset of SU(4), are conserved. Subsequently, the total strength is resolved into its component partial sums to the allowed isospins (and SU(4) representations in IBM-4). In cases where the usual IBM dynamical symmetries are also valid, a complete description of all B(M1, 0(1)(+) --> 1(i)(+)) follows. In contrast to IBM-2, there is fragmentation of the strength even in the dynamical symmetry cases, for T not equal 0, over two stares in IBM-3, and over three states in IBM-4. An application to the first half of the sd-shell reveals differences in strength between IBM-4 and the shell model which may also indicate areas for further study in IBM-2 analyses of heavier nuclei.