Background: Low-energy dipole states have been popular topics in studies of stable and unstable nuclei. In ${}^{24}\mathrm{Mg}$, two low-energy dipole modes, the toroidal and compressional states have been theoretically proposed recently. The former state has been associated with cluster structure, but there is no explicit analysis of the cluster structure.

Purpose: Our purpose is to investigate low-lying $1^{-}$ states in ${}^{24}\mathrm{Mg}$ and clarify their properties such as the dipole transition strengths, nuclear vorticity, and cluster features.

Method: Wave functions of $1^{-}$ states of ${}^{24}\mathrm{Mg}$ are described within the antisymmetrized molecular dynamics framework combined with the generator coordinate method. Excitation energies and dipole transition strengths are calculated. Cluster wave functions are explicitly taken into account to reveal the role of cluster correlations in $1^{-}$ states. Intrinsic matter density and transition current density are analyzed.

Results: Two low-lying dipole states, the $1_{K=1}^{-}$ and $1_{K=0}^{-}$, are obtained. The $1_{K=1}^{-}$ state has the strongest isoscalar toroidal dipole strength and shows two-vortex structure in the intrinsic transition current density. The $1_{K=0}^{-}$ state features the isoscalar compressional dipole strength and exhibits the ${}^{16}\mathrm{O}+{}^8\mathrm{Be}$ cluster correlation.

Conclusions: The toroidal and compressional dipole modes separately appear as $K=1$ and $K=0$ states in the deformed ${}^{24}\mathrm{Mg}$ system. The $1_{K=1}^{-}$ state is the toroidal dipole state with the strong nuclear vorticity but no prominent cluster structure, and the $1_{K=0}^{-}$ state is the compressional dipole state having enhanced cluster structure but weaker vorticity.

• Received 3 October 2019
• Revised 1 May 2020
• Accepted 30 June 2020

DOI:https://doi.org/10.1103/PhysRevC.103.064311