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We investigate the $alpha$+oo cluster structure in the inversion-doublet band ($K^pi=0_{1}^pm$) states of ene with an angular-momentum-projected version of the Tohsaki-Horiuchi-Schuck-R{o}pke (THSR) wave function, which was successful in its original form for the description of, e.g., the famous Hoyle state. In contrast with the traditional view on clusters as localized objects, especially in inversion doublets, we find that these {it single} THSR wave functions, which are based on the concept of nonlocalized clustering, can well describe the $K^{pi}=0_1^-$ band and the $K^{pi}=0_1^+$ band. For instance, 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 light on the physics of low energy nuclear cluster states in nuclei: The clusters are nonlocalized and move around in the whole nuclear volume, only avoiding mutual overlap due to the Pauli blocking effect.
We explain various facets of the THSR (Tohsaki-Horiuchi-Schuck-Ropke) wave function. We first discuss the THSR wave function as a wave function of cluster-gas state, since the THSR wave function was originally introduced to elucidate the 3$alpha$-con
We present a very brief description of the Hartree-Fock method in nuclear structure physics, discuss the numerical methods used to solve the self-consistent equations, and analyze the precision and convergence properties of solutions. As an applicati
Using many-body perturbation theory and coupled-cluster theory, we calculate the ground-state energy of He-4 and O-16. We perform these calculations using a no-core G-matrix interaction derived from a realistic nucleon-nucleon potential. Our calculat
The prospects of extracting new physics signals in a coherent elastic neutrino-nucleus scattering (CE$ u$NS) process are limited by the precision with which the underlying nuclear structure physics, embedded in the weak nuclear form factor, is known.
This contribution gives a short review of recent theoretical advances in most topics of nuclear cluster physics concentrating, however, around {$alpha$} particle clustering. Along the route, the point of view will be critical mentioning not only progress but also failures and open problems.