Deformation dependence of magnetic dipole strength below 4 MeV in doubly even rare earth nuclei

We show: (1) In the presence of the pair correlation the M1 transition strength calculated in the deformed oscillator model has a dependence on the quadrupole deformation parameter δ which is considerably stronger than linear and, in fact, it varies quadratically with δ in the limit of small deformation; (2) The deformation dependence in samarium isotopes calculated using the quasiparticle random phase approximation (QRPA) reproduces the qualitative behaviour of the recent experimental data of Ziegler, Rangacharyulu, Richter and Spieler.