Two-component boson systems with hyperspherical coordinates

TL;DR

This paper analyzes the stability and normal modes of two-boson systems in a trap using hyperspherical coordinates, revealing stable configurations and detailed vibrational modes with more restrictive stability conditions than mean-field approaches.

Contribution

It introduces a hyperspherical coordinate framework to study two-boson systems, providing new insights into their stability and vibrational modes with zero-range interactions.

Findings

Stable structures exist at finite inter-center distances for strong repulsion.

Normal modes include center of mass motion, breathing, and isovector vibrations.

Stability conditions are more restrictive than mean-field predictions.

Abstract

The effective potential is computed for two boson systems in one trap as a function of their two individual hyperadii and the distance between their centers. Zero-range interactions are used and only relative s-states are included. Existence and properties of minima are investigated as a function of these three collective coordinates. For sufficiently strong repulsion stable structures are found at a finite distance between the centers. The relative center of masses motion corresponds to the lowest normal mode. The highest normal mode is essentially the breathing mode where the subsystems vibrate by scaling their radii in phase. The intermediate normal mode corresponds to isovector motion where the subsystems vibrate by scaling their radii in opposite phase. Stability conditions are established as substantially more restrictive than in mean-field computations.