Nuclear orientation of ${}^{160}{\mathrm{Ho}}^{g+m}\mathrm{Gd}:$ Sign change of $E2/M1\mathrm{}$ mixing ratios in $\Delta K=2\mathrm{}$ transitions of ${}^{160}\mathrm{Dy}$

Directional distribution of γ rays following the decay of ${}^{160}{\mathrm{Ho}}^{g+m}$ oriented in a gadolinium host at low temperature has been studied. The γ-ray anisotropies of transitions from the levels below 3 MeV in ${}^{160}\mathrm{Dy}$ were measured and multipole mixing ratios δ were determined. The variations in both sign and magnitude of δ for the $M1+E2\mathrm{}$ transitions between the γ-vibrational ${(K}^{\pi }{=2\mathrm{}}^{+})$ and ground-state ${(K}^{\pi }{=0\mathrm{}}^{+})$ bands were observed. The $E2/M1\mathrm{}$ mixing ratios for the $\overrightarrow{2}2$ and $\overrightarrow{4}4$ transitions from the β-vibrational ${(K}^{\pi }{=0\mathrm{}}^{+})$ band to the ground-state band were determined, and the $E0/E2\mathrm{}$ probability ratios obtained are consistent with the values for the β-vibrational bands. The $E2/M1\mathrm{}$ mixing ratios of the $\overrightarrow{\gamma }g$ transitions in ${}^{160}\mathrm{Dy}$ obtained previously by the nuclear orientation of ${}^{160}\mathrm{Tb}$ are compared with the present results. The dynamic deformation model is employed to calculate the collective bands, electromagnetic moments, transition probabilities, and mixing ratios in ${}^{160}\mathrm{Dy}.$ A sign change of the $E2/M1\mathrm{}$ mixing ratio is predicted for the ${10}_{\gamma }\to {10}_g$ transition. Our experimental results give such a sign change for the $4_{\gamma }\to 4_g$ and $6_{\gamma }\to 6_g$ transitions. Comparison with the presently determined experimental values of $X(E0/E2\mathrm{})\mathrm{}$ for $\overrightarrow{\gamma }g$ and $\overrightarrow{\beta }g$ transitions is also given.