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We investigate $\alpha$-like correlations in $^{20}$Ne. A quartet of nucleons(different spin/isospin) is moving in a mean field produced by the $^{16}$Ocore nucleus. Improving the Thomas-Fermi model (local density approach), ashell model is considered for the core nucleus. The effective potential of the$\alpha$-like quartet and the wave function for the center-of-mass (c.o.m.)motion are calculated and compared with other approaches.

Quartetting Wave Function Approach to $^{20}$Ne: Shell Model and Local Density Approximation