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We investigate the $\alpha$+\oo\ cluster structure in the inversion-doubletband ($K^\pi=0_{1}^\pm$) states of \nene\ with an angular-momentum-projectedversion of the Tohsaki-Horiuchi-Schuck-R\"{o}pke (THSR) wave function, whichwas successful "in its original form" for the description of, e.g., the famousHoyle state. In contrast with the traditional view on clusters as localizedobjects, especially in inversion doublets, we find that these {\it single} THSRwave functions, which are based on the concept of nonlocalized clustering, canwell describe the $K^{\pi}=0_1^-$ band and the $K^{\pi}=0_1^+$ band. Forinstance, they have 99.98% and 99.87% squared overlaps for $1^-$ and $3^- $states (99.29%, 98.79% and 97.75% for $0^+, 2^+$ and $4^+$ states),respectively, with the corresponding exact solution of the $\alpha$+\oo\resonating group method. These astounding results shed a completely new lighton the physics of low energy nuclear cluster states in nuclei: The clusters arenonlocalized and move around in the whole nuclear volume, only avoiding mutualoverlap due to the Pauli blocking effect.

Nonlocalized Clustering: A New Concept in Nuclear Cluster Structure Physics