Abstract
The coupling between the rotational and shape degrees of freedom in soft nuclei is studied using a constrained time-dependent Hartree-Fock approach. The dynamical equations are derived using the time-dependent variational principle on a restricted trial manifold consisting of cranked squeezed states. This procedure is applied to describe the low-lying isovector magnetic excitations observed recently in the $\ensuremath{\gamma}$-soft nucleus ${}^{134}$Ba. The role of shape softness in the fragmentation mechanism of the low-lying $M1$ strength is emphasized.
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