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arXiv:cond-mat/0108250 · Physics Letters A

Positronium–positronium interaction: resonance, scattering length, and Bose–Einstein condensation

Sadhan K. Adhikari

Published Mar 1, 2002• 27 citations
arXivHTMLPDF
DOI
10.1016/s0375-9601(02)00128-7

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Abstract The production of a Bose–Einstein condensate made of positronium may be feasible in the near future. Below the condensation temperature, the positronium collision process is modified by the presence of the condensate. This makes the theoretical description of the positronium kinetics at low temperature challenging. Based on the quasi-particle Bogoliubov theory, we describe the many-body particle–particle collision in a simple manner. We find that, in a good approximation, the full positronium–positronium interaction can be described by an effective scattering length. Our results are general and apply to different species of bosons. The correction to the bare scattering length is expressed in terms of a single dimensionless parameter that completely characterizes the condensate.

arXiv:1602.05910•Journal of Physics B Atomic Molecular and Optical Physics•Apr 4, 2016•7 citations
The s-wave scattering length for the Positronium-Positronium interaction is estimated semi-phenomenologically with the long-range van der Waals force and the short-range repulsive potential that represents the hard core between two positronium. The obtained value of the scattering length is a∼0.44nma \sim 0.44{\rm nm}a∼0.44nm, and its stability is also checked for different parametrizations. Using this value, the Gross-Pitaevskii equation can be fixed for the Positronium Bose-Einstein condensates (Ps BEC). The static properties of Ps BEC are studied from the solutions of that equation. The phase-transition temperature shift of the Ps BEC due to the Ps-Ps interaction is also evaluated with the mean-field approximation.
The s-wave scattering parameters for the Positronium–Positronium (Ps–Ps) interaction are estimated semi-phenomenologically with the long-range van der Waals force and the short-range repulsive potential. The obtained values of the scattering length and the effective range are a ∼0.44 nm, and r 0 ∼0.2 nm for the symmetric channel. Stability of them is also checked with two kinds of potential with different parametrizations. Spin coupling schemes for the Ps–Ps system are discussed and the formulae of scattering length for each spin channel are derived. Using this value of the scattering length, the Gross-Pitaevskii equation can be fixed for the Positronium Bose-Einstein condensates (Ps BEC). The static properties of Ps BEC are discussed using the solutions of that equation. The critical temperature shift of the phase-transition due to the Ps–Ps interaction is also evaluated in the mean-field approximation.
Abstract The production of a Bose–Einstein condensate made of positronium may be feasible in the near future. Below the condensation temperature, the positronium collision process is modified by the presence of the condensate. This makes the theoretical description of the positronium kinetics at low temperature challenging. Based on the quasi-particle Bogoliubov theory, we describe the many-body particle–particle collision in a simple manner. We find that, in a good approximation, the full positronium–positronium interaction can be described by an effective scattering length. Our results are general and apply to different species of bosons. The correction to the bare scattering length is expressed in terms of a single dimensionless parameter that completely characterizes the condensate.