Excitation energy of the collectiveM1mode in the classical limit of the neutron-proton interacting boson model

Using the classical limit of the neutron-proton interacting boson model, a simple expression is derived for the excitation energy of the collective M1 mode. It is shown that in the SU(3) and SO(6) limits this result is identical to the exact value. For ${}_{}{}^{156}{}_{}{}^{}\mathrm{Gd}$ it agrees to within 2% of the exact value, to be compared with a 12% discrepancy reported by Balantekin and Barrett.