Island of Rare Earth Nuclei with Tetrahedral and Octahedral Symmetries: Possible Experimental Evidence

Calculations using realistic mean-field methods suggest the existence of nuclear shapes with tetrahedral $T_d$ and/or octahedral $O_h$ symmetries sometimes at only a few hundreds of keV above the ground states in some rare earth nuclei around ${}^{156}\mathrm{Gd}$ and ${}^{160}\mathrm{Yb}$. The underlying single-particle spectra manifest exotic fourfold rather than Kramers’s twofold degeneracies. The associated shell gaps are very strong, leading to a new form of shape coexistence in many rare earth nuclei. We present possible experimental evidence of the new symmetries based on the published experimental results—although an unambiguous confirmation will require dedicated experiments.

Figure 1

The total Strutinsky energy of ${}^{156}\mathrm{Gd}$ nucleus in function of the lowest-order ($t_3\equiv {\alpha }_{32}$) and octahedral ($o_4$) deformations shown at ${\alpha }_{20}=0$ (top) and in function of the quadrupole (${\alpha }_{20}$) and tetrahedral ($t_3$) deformations, with each point of the plane minimized with respect to $o_4$ (bottom).

Figure 2

Energy differences between the spherical and tetrahedral (left) and tetrahedral and prolate (right) shapes. Each brick in the stack represents 500 keV (left) and 1 MeV (right).

Figure 3

Barriers between tetrahedral and quadrupole minima (cf. Fig. 1 bottom). Each brick in the stack represents 100 keV.

Figure 4

Partial decay scheme of ${}^{156}\mathrm{Gd}$ nucleus showing the negative-parity band connected to the yrast band through $E1$ transitions. The low-spin $E2$ transitions from $9^{-}$ to $1^{-}$ were never observed although numerous and very different population methods have been used; in fact the letters next to the levels refer to the experimental papers according to the code of Ref. 10, where the original references can be found. Energy wise the state $I^{\pi }=1^{-}$ does not belong to the parabolic $I(I+1)$ sequence, lying 77 keV above the otherwise regular parabola, neither it is expected to belong to the tetrahedral (thus $K^{\pi }=2^{\pi }$) band.

Figure 5

Nuclear spin in function of rotational frequency, full dots give experimental results of Ref. 10. Dashed line: octahedral deformation $o_4\leftrightarrow {\alpha }_{40}=0.08$ superposed with $o_3\equiv {\alpha }_{32}=0.10$ tetrahedral deformation from the energy minimization.