Abstract
Three-body bound systems are investigated in the limit of very weak binding by use of hyperspherical harmonics. The short-range two-body potentials are assumed to be unable to bind the binary subsystems. Then the mean square radius always converges for vanishing binding except for the most spherical wave function, where all angular momenta involved are zero, which diverges logarithmically. Universal scaling properties are suggested. Any additional long-range repulsive potential, like, for example, the Coulomb potential, leads to finite radial moments even for vanishing binding. Spatially extended charged halos are only possible for very low charges. The spatial extension of three-body systems is in the asymptotic region more confined than for corresponding two-body systems, where the divergences are stronger and more abundant. Numerical examples and transitions to the asymptotic region are shown for square well and Gaussian two-body potentials. The results are applied to several drip-line nuclei.
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