Mean-square radii of two-component three-body systems in two spatial dimensions

We calculate root-mean-square radii for a three-body system confined to two spatial dimensions and consisting of two identical bosons (A) and one distinguishable particle (B). We use zero-range two-body interactions between each of the pairs, and focus thereby directly on universal properties. We solve the Faddeev equations in momentum space and express the mean-square radii in terms of first-order derivatives of the Fourier transforms of densities. The strengths of the interactions are adjusted for each set of masses to produce equal two-body bound-state energies between different pairs. The mass ratio, A=mB/mA, between particles B and A are varied from 0.01 to 100, providing a number of bound states decreasing from 8 to 2. Energies and mean-square radii of these states are analyzed for small A by use of the Born-Oppenheimer potential between the two heavy A particles. For large A the radii of the two bound states are consistent with a slightly asymmetric three-body structure. When A approaches thresholds for binding of the three-body excited states, the corresponding mean-square radii diverge inversely proportional to the deviation of the three-body energy from the two-body thresholds. The structures at these three-body thresholds correspond to bound AB dimers and one loosely bound A particle.