Restored symmetries for the observed excited alternating-parity band in even-even nuclei

Abstract

Both the ground [denoted ${G}_{+}$ (${G}_{\ensuremath{-}}$) for a positive-parity (negative-parity) sequence] and excited ($E{x}_{+}$ and $E{x}_{\ensuremath{-}}$) alternating-parity bands have been observed in a few octupole-deformed even-even nuclei. Taking $^{148}\mathrm{Ce}$ as an example, the restored symmetries for the observed bands are investigated by constructing a symmetry group ${E,\phantom{\rule{4pt}{0ex}}{\mathcal{R}}_{1},{\mathcal{R}}_{2},{\mathcal{R}}_{3},\phantom{\rule{4pt}{0ex}}{\mathcal{S}}_{1},{\mathcal{S}}_{2},{\mathcal{S}}_{3},\mathcal{P}}$. All possible wave functions belonging to eight group representations have been analyzed. It is found that, to agree with the observed transitions in $^{148}\mathrm{Ce}, {G}_{+}$ and $E{x}_{+}$ should belong to the same group representation $(+1,\phantom{\rule{4pt}{0ex}}+1,+1,+1,\phantom{\rule{4pt}{0ex}}+1,+1,+1,\phantom{\rule{4pt}{0ex}}+1)$, while ${G}_{\ensuremath{-}}$ and $E{x}_{\ensuremath{-}}$ should belong to the representation $(+1,\phantom{\rule{4pt}{0ex}}\ensuremath{-}1,\ensuremath{-}1,+1,\phantom{\rule{4pt}{0ex}}+1,+1,\ensuremath{-}1,\phantom{\rule{4pt}{0ex}}\ensuremath{-}1)$. A new understanding of the symmetries for the observed excited band is provided, and a different value of simplex quantum number is proposed. From another perspective, the wave functions of the observed ground and excited bands should be symmetrical and antisymmetrical, respectively, which exactly correspond to two modes of symmetry restoration.