# Sum rules for $B(M1,0^+_1\rightarrow1^+_i)$ strength in IBM-3 and IBM-4

Abstract : Sum rules for $B(M1,0^+_1\rightarrow1^+_i)$ 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 $U(6)\supset SU$(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 $B(M1,0^+_1\rightarrow1^+_i)$ is given. In contrast to IBM-2, there is fragmentation of the strength even in the dynamical symmetry cases, for $T\neq 0$, over two states in IBM-3, and over three states in IBM-4. The presence of $pn$ bosons in the ground state of the extended versions reduces the expected strength from that for IBM-2, allowing in principle the possibility of using $B(M1)$ data for a given nucleus to infer which version is the most appropriate.
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Submitted on : Friday, July 7, 2006 - 4:42:18 PM
Last modification on : Tuesday, May 10, 2022 - 3:44:45 PM

### Citation

P. Halse, P. van Isacker, B. R. Barrett. Sum rules for $B(M1,0^+_1\rightarrow1^+_i)$ strength in IBM-3 and IBM-4. Physics Letters B, Elsevier, 1995, 363, pp.145-150. ⟨10.1016/0370-2693(95)01213-A⟩. ⟨in2p3-00084588⟩

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