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The first $3^-$ and $4^-$ states of $^{12}$C are studied in the presentcontainer model, in which the shift parameter is introduced to break the paritysymmetry for projecting out the negative-parity states. Taking the limit as theshift parameter approaches zero and by variational calculations forone-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-R\"{o}pke) wave functions for $3^-$ and $4^-$ statesare 96% and 92% equivalent to the corresponding GCM wave functions,respectively. The calculated intrinsic densities further show that thesenegative-parity states of three clusters, different with the traditionalunderstanding of rigid triangle structure, are found to have nonlocalizedclustering structure in the two-dimensional container picture.

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