Probing negative-parity states of ${}^{24}$Mg probed via proton and alpha inelastic scattering

Abstract

[Background:] The band structure of the negative-parity states of ${}^{24}$Mg has not yet been clarified. The $K^{\pi }=0^{-}$, $K^{\pi }=1^{-}$, and $K^{\pi }=3^{-}$ bands have been suggested, but the assignments have been inconsistent between experiments and theories. [Purpose:] Negative-parity states of ${}^{24}$Mg are investigated by microscopic structure and reaction calculations via proton and alpha inelastic scattering to clarify the band assignment for the observed negative-parity spectra. [Method:] The structure of ${}^{24}$Mg was calculated using the antisymmetrized molecular dynamics~(AMD). Proton and alpha inelastic reactions were calculated using microscopic coupled-channel (MCC) calculations by folding the Melbourne $g$-matrix $NN$ interaction with the AMD densities of ${}^{24}$Mg. [Results:] The member states of the $K^{\pi }=0^{+}$, $K^{\pi }=2^{+}$, $K^{\pi }=0^{-}$, $K^{\pi }=1^{-}$, and $K^{\pi }=3^{-}$ bands of ${}^{24}$Mg were obtained through the AMD result. In the MCC+AMD results for proton and alpha elastic and inelastic cross sections, reasonable agreements were obtained with existing data, except in the case of the $4_1^{+}$ state. [Conclusions:] The $3^{-}$ state of the $K^{\pi }=3^{-}$ band and the $1^{-}$ and $3^{-}$ states of the $K^{\pi }=0^{-}$ bands were assigned to the $3_1^{-}$(7.62 MeV), $1_1^{-}$(7.56 MeV), and $3_2^{-}$(8.36 MeV) states, respectively. The present AMD calculation is the first microscopic structure calculation to reproduce the energy ordering of the $K^{\pi }=0^{-}$, $K^{\pi }=1^{-}$, and $K^{\pi }=3^{-}$ bands of ${}^{24}$Mg.

14 pages, 9 figures

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