Low-energy dipole γ-ray transition rates in even-even deformed nuclei

A study of low-lying magnetic and electric dipole excitations is carried out in ${}^{166,168}\mathrm{Er},$ ${}^{172,174}\mathrm{Yb},$ and ${}^{178}\mathrm{Hf}$ within the quasiparticle-phonon nuclear model with the wave functions consisting of one- and two-phonon terms. It is shown that computed $M1\mathrm{}$ strength below 4 MeV in these nuclei is much stronger fragmented than in Gd and Dy isotopes in agreement with the relevant experimental observation. The scissors state is strongly fragmented and the overlapping between the scissors state and any $1^{+}$ state is less than 0.1. The fragmentation of the one-phonon $1^{+}$ states, as a rule, is stronger than the fragmentation of the one-phonon states with $K^{\pi }{=0\mathrm{}}^{-}$ and $1^{-}.$ The resulting $M1\mathrm{}$ and $E1\mathrm{}$ spectra are compared with available experimental data. The calculated $M1\mathrm{}$ and $E1\mathrm{}$ strengths summed in the energy range 2–4 MeV are in agreement with the relevant experimental data.