Mean-square radii in mixed-species systems in two dimensions

TL;DR

This paper computes the mean-square radii of a three-body two-dimensional system with mixed species, revealing universal properties and structural insights across different mass ratios using Faddeev equations.

Contribution

It provides a detailed analysis of three-body mean-square radii in 2D for mixed bosonic systems with zero-range interactions, including universal behavior near binding thresholds.

Findings

Mean-square radii diverge near three-body binding thresholds.

System structures vary from symmetric to asymmetric with changing mass ratios.

Universal properties are identified in the behavior of radii and energies.

Abstract

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, ${\cal A}=m_B/m_A$, 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 ${\cal A}$ by use of the Born-Oppenheimer potential between the two heavy $A$-particles. For large ${\cal A}$ the radii of the two bound states are consistent with a slightly asymmetric three-body structure. When ${\cal A}$ 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.