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arXiv:cond-mat/9911456

S-wave Scattering Length from Effective Positronium-Positronium Interaction for Bose-Einstein Condensates

Kin-ya Oda, Miyakawa, T., Hiroyuki Yabu, T. Suzuki

Published Nov 29, 1999• 0 citations
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Abstract

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 $a \sim 0.44{\rm nm}$, 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.

DOI
10.48550/arxiv.cond-mat/9911456

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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.
The stochastic variational method is used in conjunction with stabilization ideas to compute the low-energy s-wave phase shifts and scattering lengths for Ps-Ps scattering. The scattering lengths obtained were 8.44a0{8.44a}_{0}8.44a0​ for the singlet-singlet and 3.00a0{3.00a}_{0}3.00a0​ for the triplet-triplet states (the spin state refers to the coupling of the two electrons and the coupling of the two positrons in the system). The positive scattering length in the triplet-triplet channel means a stable Bose-Einstein condensate of triplet Ps atoms is physically possible. The large value of the ${}^{3}{\mathrm{Ps}}^{3}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{Ps}}}^{1}{\mathrm{Ps}}^{1}\mathrm{Ps}$ cross section, $7.41\ensuremath{\pi}{a}_{0}^{2}$ suggests the use of spin-polarized positrons as advanced by Platzmann and Mills [Phys. Rev. B 49 454 (1994)].
The stochastic variational method is used in conjunction with stabilization ideas to compute the low energy phase shifts and scattering lengths for positronium-atom scattering. Results are obtained for the Ps-H, Ps- Li+, Ps-He, and Ps-Ps systems. The Ps-H scattering lengths are probably accurate to better than 5% and are the most accurate so far computed. The results for Ps- Li+ and Ps-Ps scattering represent the first published scattering lengths for these systems. The positive scattering length for completely spin-aligned 3Ps-3Ps scattering, namely 2.95a(0), is particularly significant since it demonstrates the feasibility of forming a stable Bose-Einstein condensate of 3Ps atoms.
Bose-Einstein condensates (BECs) of positronium (Ps) have been of experimental and theoretical interest due to their potential application as the gain medium of a $\ensuremath{\gamma}$-ray laser. Ps BECs are intrinsically spinor due to the presence of ortho-positronium (ooo-Ps) and para-positronium (ppp-Ps), whose annihilation lifetimes differ by three orders of magnitude. In this paper, we study the spinor dynamics and annihilation processes in the ppp-Ps/ooo-Ps system using both solutions of the time-dependent Gross-Pitaevskii equations and a semiclassical rate-equation approach. The spinor interactions have an O(4) symmetry which is broken to SO(3) by an internal energy difference between ooo-Ps and ppp-Ps. For an initially unpolarized condensate, there is a threshold density of $\ensuremath{\approx}{10}^{19}$ cm${}^{\ensuremath{-}3}$ at which spin mixing between ooo-Ps and ppp-Ps occurs. Beyond this threshold, there are unstable spatial modes accompanied by spin mixing. To ensure a high production yield above the critical density, a careful choice of external field must be made to avoid the spin mixing instability.
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.
We study the stabilization properties of dipolar Bose-Einstein condensate by temporal modulation of short-range two-body interaction. Through both analytical and numerical methods, we analyze the mean-field Gross-Pitaevskii equation with short-range two-body and long-range, nonlocal, dipolar interaction terms. We derive the equation of motion and effective potential of the dipolar condensate by variational method. We show that there is an enhancement of the condensate stability due to the inclusion of dipolar interaction in addition to the two-body contact interaction. We also show that the stability of the dipolar condensate increases in the presence of time varying two-body contact interaction; the temporal modification of the contact interaction prevents the collapse of dipolar Bose-Einstein condensate. Finally we confirm the semi-analytical prediction through the direct numerical simulations of the governing equation.