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Communications in Theoretical Physics

A Positronium Molecule Confined in a Two-Dimensional Space Under a Magnetic Field

Xie Wen-Fang

Published Aug 15, 2004• 1 citation
Publisher

Abstract

Making use of hyperspherical coordinates, we investigate the qualitative features of the ground and low-lying states of a positronium molecule confined in a two-dimensional (2D) space under a magnetic field. We find that a positronium molecule has more bound states in 2D than in 3D. With the increase of the magnetic field, the second bound state experiences a transition in angular momentum. The result shows that symmetry plays an essential role in the energy spectrum of low-lying states.

DOI
10.1088/0253-6102/42/2/257

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We examine a system of three-bosons confined to two dimensions in the presence of a perpendicular magnetic field within the framework of the adiabatic hyperspherical method. For the case of zero-range, regularized pseudopotential interactions, we find that the system is nearly separable in hyperspherical coordinates and that, away from a set of narrow avoided crossings, the full energy eigenspectrum as a function of the two-dimensional (2D) sss-wave scattering length is well described by ignoring coupling between adiabatic hyperradial potentials. In the case of weak attractive or repulsive interactions, we find the lowest three-body energy states exhibit even-odd parity oscillations as a function of total internal 2D angular momentum and that for weak repulsive interactions, the universal lowest energy interacting state has an internal angular momentum of M=3M=3M=3. With the inclusion of repulsive higher angular momentum we surmise that the origin of a set of ``magic number'' states (states with anomalously low energy) might emerge as the result of a combination of even-odd parity oscillations and the pattern of degeneracy in the noninteracting lowest Landau level states.