Physical Review A

Positronium-positronium scattering using the stochastic variational method

Igor A. Ivanov, Jim Mitroy, Kálmán Varga

Published Jan 4, 2002• 47 citations

Abstract

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 ${8.44a}_{0}$ for the singlet-singlet and ${3.00a}_{0}$ 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)].

DOI: 10.1103/physreva.65.022704

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Physical Review A

Positronium-positronium scattering using the stochastic variational method

Igor A. Ivanov, Jim Mitroy, Kálmán Varga

Published Jan 4, 2002• 47 citations

Publisher

Abstract

{8.44a}_{0}

for the singlet-singlet and

{3.00a}_{0}

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)].

DOI: 10.1103/physreva.65.022704

Related papers

Elastic Positronium-Atom Scattering Using the Stochastic Variational Method

Igor A. Ivanov, Jim Mitroy, Kálmán Varga

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.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.

Physical Review LettersJul 24, 200175 citations

Positronium-hydrogen scattering using the stochastic variational method

Igor A. Ivanov, J. Mitroy, Kálmán Varga

The stochastic variational method (SVM) is used in conjunction with stabilization ideas in order to compute low-energy phase shifts. The method is tested by applying it to a simple model problem, and to s-wave positron-hydrogen scattering. The SVM is then applied to the calculation of the s- and p-wave phase shifts for Ps-H scattering. The scattering lengths obtained were ${4.34a}_{0}$ for the electronic-spin-singlet state and ${2.22a}_{0}$ for the triplet state. The present scattering lengths are probably accurate to $\ifmmode\pm\else\textpm\fi{}3%$ and are the most accurate that have so far been computed for the Ps-H systems.The stochastic variational method (SVM) is used in conjunction with stabilization ideas in order to compute low-energy phase shifts. The method is tested by applying it to a simple model problem, and to s-wave positron-hydrogen scattering. The SVM is then applied to the calculation of the s- and p-wave phase shifts for Ps-H scattering. The scattering lengths obtained were ${4.34a}_{0}$ for the electronic-spin-singlet state and ${2.22a}_{0}$ for the triplet state. The present scattering lengths are probably accurate to $\ifmmode\pm\else\textpm\fi{}3%$ and are the most accurate that have so far been computed for the Ps-H systems.

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Low-energy scattering properties of ground-state and excited-state positronium collisions

Michael D. Higgins, K. M. Daily, Chris H. Greene

Low-energy elastic and inelastic scattering in the Ps( $1s$ )-Ps( $2s$ ) channel is treated in a four-body hyperspherical coordinate calculation. Adiabatic potentials are calculated for triplet-triplet, singlet-singlet, and singlet-triplet spin symmetries in the spin representation of coupled electrons and coupled positrons, with total angular momentum $L=0$ and parity equal to $+1$ . The $s$ -wave scattering lengths for the asymptotic Ps( $1s$ )-Ps( $2s$ ) channel are calculated for each spin configuration. Results obtained for the $s$ -wave scattering lengths are ${a}_{\mathrm{TT}}=7.3(2){a}_{0}\ensuremath{-}i0.02(1){a}_{0}, {a}_{\mathrm{SS}}=13.2(2){a}_{0}\ensuremath{-}i0.9(2){a}_{0}$, and ${a}_{\mathrm{ST}}=9.7(2){a}_{0}$ for each spin configuration. Spin recoupling is implemented to extract the scattering lengths for collisions of Ps in different spin configurations through properly symmetrized unitary transformations. Calculations of experimentally relevant scattering lengths and cross sections are carried out for Ps atoms initially prepared in different uncoupled spin states.Low-energy elastic and inelastic scattering in the Ps($1s$)-Ps($2s$) channel is treated in a four-body hyperspherical coordinate calculation. Adiabatic potentials are calculated for triplet-triplet, singlet-singlet, and singlet-triplet spin symmetries in the spin representation of coupled electrons and coupled positrons, with total angular momentum $L=0$ and parity equal to $+1$. The $s$-wave scattering lengths for the asymptotic Ps($1s$)-Ps($2s$) channel are calculated for each spin configuration. Results obtained for the $s$-wave scattering lengths are ${a}_{\mathrm{TT}}=7.3(2){a}_{0}\ensuremath{-}i0.02(1){a}_{0}, {a}_{\mathrm{SS}}=13.2(2){a}_{0}\ensuremath{-}i0.9(2){a}_{0}$, and ${a}_{\mathrm{ST}}=9.7(2){a}_{0}$ for each spin configuration. Spin recoupling is implemented to extract the scattering lengths for collisions of Ps in different spin configurations through properly symmetrized unitary transformations. Calculations of experimentally relevant scattering lengths and cross sections are carried out for Ps atoms initially prepared in different uncoupled spin states.

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Kenji Oda, Takahiko Miyakawa, Hiroyuki Yabu +1 more

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 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.

Journal of the Physical Society of JapanJun 15, 200123 citations

Possibility of forming a stable Bose-Einstein condensate of $2\,^{3}\!S_1$ positronium atomsPossibility of forming a stable Bose-Einstein condensate of $2\,^{3}\!S_1$ positronium atoms

Y. Zhang, M.-S. Wu, J.-Y. Zhang +3 more

The confined variational method in conjunction with the orthogonalizing pseudo-potential method and the stabilization method is used to study the low energy elastic scattering between two spin-polarized metastable positronium Ps(2\, $^{3}\!S_1$ ) atoms. Explicitly correlated Gaussian basis functions are adopted to properly describe the complicated Coulomb interaction among the four charged particles. The calculated $s$ -wave scattering length ( $\approx8.5\,a_0$ ) is positive, indicating the possibility of forming a stable Bose-Einstein condensate of fully spin-polarized $\text{Ps}(2\,^{3}\!S_1)$ atoms. Our results will open a new way of experimental realization of Ps condensate and development of $γ$ -ray and $\text{Ps}(2\,^{3}\!S_1)$ atom lasers.The confined variational method in conjunction with the orthogonalizing pseudo-potential method and the stabilization method is used to study the low energy elastic scattering between two spin-polarized metastable positronium Ps(2\,$^{3}\!S_1$) atoms. Explicitly correlated Gaussian basis functions are adopted to properly describe the complicated Coulomb interaction among the four charged particles. The calculated $s$-wave scattering length ($\approx8.5\,a_0$) is positive, indicating the possibility of forming a stable Bose-Einstein condensate of fully spin-polarized $\text{Ps}(2\,^{3}\!S_1)$ atoms. Our results will open a new way of experimental realization of Ps condensate and development of $γ$-ray and $\text{Ps}(2\,^{3}\!S_1)$ atom lasers.

arXiv:1903.08353Mar 20, 20192 citations

Positronium scattering from Kr and Xe at low energies

Jim Mitroy, M. W. J. Bromley

The scattering of orthopositronium from Kr and Xe is investigated with the fixed core stochastic variational method. The scattering lengths for Ps-Kr and Ps-Xe scattering in the fixed core approximation are ${3.18a}_{0}$ and ${3.82a}_{0},$ respectively. Inclusion of core-polarization potentials leads to a significant reduction in the scattering lengths. The Ps-Kr and Ps-Xe scattering lengths were ${1.98a}_{0}$ and ${2.29a}_{0}$ for polarization potentials that were tuned to an average of the model electron-atom and positron-atom scattering lengths for the respective atoms. Other choices of the polarization potential resulted in scattering lengths that could be larger by ${0.3a}_{0}$ or smaller by ${0.8a}_{0}.$ The pick-off annihilation parameter ${}_{1}{Z}_{\mathrm{eff}}$ has also been computed as part of the analysis. The present values of ${}_{1}{Z}_{\mathrm{eff}}$ are about 3 to 10 times smaller than the accepted experimental values since short-range electron-positron correlations were ignored when the annihilation matrix element was evaluated.The scattering of orthopositronium from Kr and Xe is investigated with the fixed core stochastic variational method. The scattering lengths for Ps-Kr and Ps-Xe scattering in the fixed core approximation are ${3.18a}_{0}$ and ${3.82a}_{0},$ respectively. Inclusion of core-polarization potentials leads to a significant reduction in the scattering lengths. The Ps-Kr and Ps-Xe scattering lengths were ${1.98a}_{0}$ and ${2.29a}_{0}$ for polarization potentials that were tuned to an average of the model electron-atom and positron-atom scattering lengths for the respective atoms. Other choices of the polarization potential resulted in scattering lengths that could be larger by ${0.3a}_{0}$ or smaller by ${0.8a}_{0}.$ The pick-off annihilation parameter ${}_{1}{Z}_{\mathrm{eff}}$ has also been computed as part of the analysis. The present values of ${}_{1}{Z}_{\mathrm{eff}}$ are about 3 to 10 times smaller than the accepted experimental values since short-range electron-positron correlations were ignored when the annihilation matrix element was evaluated.

Physical Review AMar 17, 200324 citations

{8.44a}_{0}

for the singlet-singlet and

{3.00a}_{0}

{}^{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)].

{4.34a}_{0}

for the electronic-spin-singlet state and

{2.22a}_{0}

for the triplet state. The present scattering lengths are probably accurate to $\ifmmode\pm\else\textpm\fi{}3%$ and are the most accurate that have so far been computed for the Ps-H systems.

Low-energy elastic and inelastic scattering in the Ps(

1s

)-Ps(

2s

) channel is treated in a four-body hyperspherical coordinate calculation. Adiabatic potentials are calculated for triplet-triplet, singlet-singlet, and singlet-triplet spin symmetries in the spin representation of coupled electrons and coupled positrons, with total angular momentum

L=0

and parity equal to

+1

. The

s

-wave scattering lengths for the asymptotic Ps(

1s

)-Ps(

2s

) channel are calculated for each spin configuration. Results obtained for the

s

-wave scattering lengths are ${a}_{\mathrm{TT}}=7.3(2){a}_{0}\ensuremath{-}i0.02(1){a}_{0}, {a}_{\mathrm{SS}}=13.2(2){a}_{0}\ensuremath{-}i0.9(2){a}_{0}$, and

{a}_{\mathrm{ST}}=9.7(2){a}_{0}

for each spin configuration. Spin recoupling is implemented to extract the scattering lengths for collisions of Ps in different spin configurations through properly symmetrized unitary transformations. Calculations of experimentally relevant scattering lengths and cross sections are carried out for Ps atoms initially prepared in different uncoupled spin states.

Possibility of forming a stable Bose-Einstein condensate of

2\,^{3}\!S_1

positronium atoms

^{3}\!S_1

) atoms. Explicitly correlated Gaussian basis functions are adopted to properly describe the complicated Coulomb interaction among the four charged particles. The calculated

s

-wave scattering length (

\approx8.5\,a_0

) is positive, indicating the possibility of forming a stable Bose-Einstein condensate of fully spin-polarized

\text{Ps}(2\,^{3}\!S_1)

atoms. Our results will open a new way of experimental realization of Ps condensate and development of

γ

-ray and

\text{Ps}(2\,^{3}\!S_1)

atom lasers.

{3.18a}_{0}

and

{3.82a}_{0},

respectively. Inclusion of core-polarization potentials leads to a significant reduction in the scattering lengths. The Ps-Kr and Ps-Xe scattering lengths were

{1.98a}_{0}

and

{2.29a}_{0}

for polarization potentials that were tuned to an average of the model electron-atom and positron-atom scattering lengths for the respective atoms. Other choices of the polarization potential resulted in scattering lengths that could be larger by

{0.3a}_{0}

or smaller by

{0.8a}_{0}.

The pick-off annihilation parameter

{}_{1}{Z}_{\mathrm{eff}}

has also been computed as part of the analysis. The present values of

{}_{1}{Z}_{\mathrm{eff}}

are about 3 to 10 times smaller than the accepted experimental values since short-range electron-positron correlations were ignored when the annihilation matrix element was evaluated.