A schematic microscopic method is developed to calculate the $M1$ transition probabilities between the mixed-symmetry and the fully symmetric states in $\gamma$-soft nuclei. The method is based on the random-phase approximation–interacting boson model (RPA-IBM) boson mapping of the most collective isoscalar boson. All other boson modes with higher excitation energies, including the mixed-symmetry boson, are described in the framework of RPA. As an example the $M1$ transition probabilities are calculated for the ${}^{124-134}$Xe isotopes and compared with the experimental data. The results agree well with the data for the ratio $B(M1;1_{ms}^{+}\to 2_2^{+})$/$B(M1;1_{ms}^{+}\to 0_1^{+})$. However, the calculated ratio $B(M1;2_{ms}^{+}\to 2_1^{+})$/$B(M1;1_{ms}^{+}\to 0_1^{+})$ shows a significantly weaker dependence on the mass number than the experimental data.

• Received 9 March 2011

DOI:https://doi.org/10.1103/PhysRevC.84.014315