Radii of weakly bound three-body systems: halo nuclei and molecules

A renormalized three-body model with zero-range potential is used to estimate the mean-square radii of three-body halo nuclei and molecular systems. The halo nuclei (${}^6$He, ${}^{11}$Li, ${}^{14}$Be and ${}^{20}$C) are described as point-like inert cores and two neutrons. The molecular systems, with two helium atoms, are of the type ${}^4$He${}_2-$X, where X${=}^4$He, ${}^6$Li, ${}^7$Li, or ${}^{23}$Na. The estimations are compared with experimental data and realistic results.