Quartetting Wave Function Approach to ²⁰Ne: Shell Model and Local Density Approximation

We investigate $\alpha$-like correlations in $^{20}$Ne. A quartet of nucleons (different spin/isospin) is moving in a mean field produced by the $^{16}$O core nucleus. Improving the Thomas-Fermi model (local density approach), a shell 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.