Two-component boson systems with hyperspherical coordinates

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 centres. 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 centres. The relative centre-of-mass 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.