arXiv:1409.3371

The collision between two ortho-Positronium (Ps) atoms: a four-body Coulomb problem

Hasi Ray

Published Sep 11, 2014• 1 citation

Abstract

The elastic collision between two ortho-positronium (e.g. S=1) atoms is studied using an ab-initio static-exchange model (SEM) in the center of mass (CM) frame considering the system as a four-body Coulomb problem where all the Coulomb interaction terms in the direct and exchange channels are treated exactly. A coupled-channel methodology in momentum space is used to solve Lippman-Schwinger equation following the integral approach. A new SEM code is developed in which the Born-Oppenheimer (BO) scattering amplitude acts as input to derive the SEM amplitude adapting the partial wave analysis. The s-, p- and d- wave elastic phase shifts and the corresponding partial cross sections for the spin alignment S=0, i.e. singlet (+) and S=2, i.e. triplet (-) states are studied. An augmented-Born approximation is used to include the contribution of higher partial waves more accurately to determine the total/integrated elastic cross section ( ), the quenching cross section ( ) and ortho to para conversion ratio ( ). The effective range theory is used to determine the scattering lengths and effective ranges in the s-wave elastic scattering. The theory includes the non-adiabatic short-range effects due to exchange.

DOI: 10.48550/arxiv.1409.3371

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arXiv:1409.3371

The collision between two ortho-Positronium (Ps) atoms: a four-body Coulomb problem

Hasi Ray

Published Sep 11, 2014• 1 citation

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.1409.3371

Related papers

The collision between two positronium (Ps) atoms: the exact evaluation of a four-body Coulomb problem

Hasi Ray

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The electron-electron correlation term in two-atomic collision is the most important, most difficult term to obtain the effective interatomic potential. Generally the H and H collision is a four center problem. It is extremely difficult to compute the electron-electron correlation term to include the effect of exchange or antisymmetry between two system electrons exactly. All the two-atomic collision related theoretical data differ from each other due to its difference in approximating the electron-electron correlation term. I invent a trick to evaluate the term exactly. Earlier the positronium (Ps) and H system was easily approximated as a three center problem due to the light mass of Ps. My new code for H-H collision using the ab-initio and exact static-exchange model (SEM) can reproduce exactly the same data of Ps and H system just by using the appropriate atomic parameters. The success of the present trick makes the foundation of a big monument in cold and low energy atomic collision physics. The Feshbach resonances are observed in H(1s)-H(1s) elastic scattering in both the singlet and triplet channels. One can use the trick to solve any four center problem including excitation and ionization processes. Again one can use the idea in larger systems too.The electron-electron correlation term in two-atomic collision is the most important, most difficult term to obtain the effective interatomic potential. Generally the H and H collision is a four center problem. It is extremely difficult to compute the electron-electron correlation term to include the effect of exchange or antisymmetry between two system electrons exactly. All the two-atomic collision related theoretical data differ from each other due to its difference in approximating the electron-electron correlation term. I invent a trick to evaluate the term exactly. Earlier the positronium (Ps) and H system was easily approximated as a three center problem due to the light mass of Ps. My new code for H-H collision using the ab-initio and exact static-exchange model (SEM) can reproduce exactly the same data of Ps and H system just by using the appropriate atomic parameters. The success of the present trick makes the foundation of a big monument in cold and low energy atomic collision physics. The Feshbach resonances are observed in H(1s)-H(1s) elastic scattering in both the singlet and triplet channels. One can use the trick to solve any four center problem including excitation and ionization processes. Again one can use the idea in larger systems too.

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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.

arXiv:1904.04295Journal of Physics Conference SeriesJul 29, 20194 citations

S

-wave phase shifts from normalizable trial functions by examining the spatial behavior of the center-of-mass wave functions. An effective-range expansion linear in the positronium energy fits the results very well and leads to a scattering length ${a}^{(\ensuremath{-})}\ensuremath{\simeq}2.36{a}_{0}$, compared with the static result ${a}^{(\ensuremath{-})}=2.476{a}_{0}$ of Hara and Fraser. The

S

-wave total and ortho-para conversion cross sections are calculated by making use of both

^{1}S

and

^{3}S

results. In the

^{3}S

case, we see no indication of any resonances below the excitation threshold at 5.1 eV.

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.