Nonlocalized motion in two-dimensional container of $\alpha$ particles in $3^{-}$ and $4^{-}$ states of ${}^{12}$C

Abstract

The first $3^{-}$ and $4^{-}$ states of ${}^{12}$C are studied in the present container model, in which the shift parameter is introduced to break the parity symmetry for projecting out the negative-parity states. Taking the limit as the shift parameter approaches zero and by variational calculations for one-deformed size parameter, the local energy minima are obtained for the $3^{-}$ and $4^{-}$ states. It is found that the obtained single THSR (Tohsaki-Horiuchi-Schuck-Röpke) wave functions for $3^{-}$ and $4^{-}$ states are 96% and 92% equivalent to the corresponding GCM wave functions, respectively. The calculated intrinsic densities further show that these negative-parity states of three clusters, different with the traditional understanding of rigid triangle structure, are found to have nonlocalized clustering structure in the two-dimensional container picture.

Comments: 7 pages, 5 figures