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理论物理通讯：英文版

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

Xie, Wen-Fang

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

Making use of hyperspherical coordinates, we investigate the qualitative features of the ground and lowlying 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.

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

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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.

理论物理通讯：英文版•Jan 1, 2004•0 citations

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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.

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An Adiabatic Study of the Positronium Negative Ion and Other Three-Particle Systems.

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In an effort to unravel the dependence of the dynamics of three-bound-particle systems on the relative masses of the particles, an adiabatic treatment in hyperspherical coordinates is used to study the ground state and some doubly excited states of Ps('-) (positronium negative ion) and other three-particle systems, including H('-) and M('-) (muonium negative ion). Two different methods for the solution of the adiabatic eigenvalue equation are presented; one uses a "prediagonalized" basis of hyperspherical harmonics, and the other uses an asymptotic basis which consists of hydrogenic functions for the positronium. Potential curves for Ps('-) and M('-) in the ('1)S('e), ('1)P('o), ('3)P('e), ('3)P('o) and ('1)D('e) states and for H('-) in the ('1)P('o) states are presented. A method for calculating the probability density as a function of the hyperspherical coordinates (R,(alpha),(theta)(,12)) is introduced and used for the P states of Ps('-). This helps to understand the different symmetries and to distinguish among them. A remarkable linear dependence of the binding energy of the ground state and of the doubly excited states on the reduced mass of the atom, discovered in this study, is presented and discussed.

Civil War Book Review•Jan 1, 1986•0 citations
Making use of hyperspherical coordinates, we investigate the qualitative features of the ground and lowlying 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.
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.
In an effort to unravel the dependence of the dynamics of three-bound-particle systems on the relative masses of the particles, an adiabatic treatment in hyperspherical coordinates is used to study the ground state and some doubly excited states of Ps('-) (positronium negative ion) and other three-particle systems, including H('-) and M('-) (muonium negative ion). Two different methods for the solution of the adiabatic eigenvalue equation are presented; one uses a "prediagonalized" basis of hyperspherical harmonics, and the other uses an asymptotic basis which consists of hydrogenic functions for the positronium. Potential curves for Ps('-) and M('-) in the ('1)S('e), ('1)P('o), ('3)P('e), ('3)P('o) and ('1)D('e) states and for H('-) in the ('1)P('o) states are presented. A method for calculating the probability density as a function of the hyperspherical coordinates (R,(alpha),(theta)(,12)) is introduced and used for the P states of Ps('-). This helps to understand the different symmetries and to distinguish among them. A remarkable linear dependence of the binding energy of the ground state and of the doubly excited states on the reduced mass of the atom, discovered in this study, is presented and discussed.