arXiv:2606.29253 · Physical Review A

Low-energy positron scattering from metastable helium

Anonymous, Hui-Li Han, Ting-Yun Shi, Li-Yan Tang

Published Sep 17, 2026• 0 citations

Abstract

Low-energy positron scattering from singlet and triplet metastable He($1s2s$) is investigated using the $R$-matrix propagation method in hyperspherical coordinates. Elastic and positronium-formation cross sections are reported, and near-threshold resonance structures are analyzed in terms of eigenphase sums and the time-delay matrix. For the triplet target, the calculated cross sections are in agreement with available convergent-close-coupling results and display the expected threshold behavior. Beyond the known $S$-wave features, Feshbach resonance series in higher partial waves extending up to highly excited atomic thresholds are systematically identified. The time-delay matrix further uncovers hidden resonances that produce obvious structures in the positronium-formation cross sections.

DOI: 10.1103/6m7n-md66

Related papers

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

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

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

Nonradiative formation of the positron-helium triplet bound state

Joseph Di Rienzi, Richard J. Drachman

Physical Review AFeb 20, 20074 citations

Near-threshold behavior of positronium-antiproton scattering

I. I. Fabrikant, Alexander Bray, Alisher S. Kadyrov +1 more

Physical Review AJul 5, 201623 citations

Positronium-hydrogen elastic scattering: The electronic S=1 state

Richard J. Drachman, S. K. Houston

Physical Review AAug 1, 197661 citations

Scattering of H¯(1s) off metastable helium atom at thermal energies

Prabal K. Sinha, Arnab Ghosh

Physical Review AJun 12, 20062 citations

Positronium formation and threshold behavior in positron-sodium collisions at low energies

Ning-Ning Gao, Hui-Li Han, Ting-Yun Shi

arXiv:2503.19400Physical Review AJun 26, 20251 citation

arXiv:2606.29253 · Physical Review A

Low-energy positron scattering from metastable helium

Anonymous, Hui-Li Han, Ting-Yun Shi, Li-Yan Tang

Published Sep 17, 2026• 0 citations

arXiv HTML PDF

Abstract

Low-energy positron scattering from singlet and triplet metastable He(

1s2s

) is investigated using the

R

-matrix propagation method in hyperspherical coordinates. Elastic and positronium-formation cross sections are reported, and near-threshold resonance structures are analyzed in terms of eigenphase sums and the time-delay matrix. For the triplet target, the calculated cross sections are in agreement with available convergent-close-coupling results and display the expected threshold behavior. Beyond the known

S

-wave features, Feshbach resonance series in higher partial waves extending up to highly excited atomic thresholds are systematically identified. The time-delay matrix further uncovers hidden resonances that produce obvious structures in the positronium-formation cross sections.

DOI: 10.1103/6m7n-md66

Related papers

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.

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

Nonradiative formation of the positron-helium triplet bound state

Joseph Di Rienzi, Richard J. Drachman

We have previously calculated the cross section for radiative formation of the interesting bound state consisting of a positron bound to helium, where the atomic electrons are in the triplet spin state. That process uses the metastable triplet helium system as target, and, as expected, it has a very small cross section. In this paper we examine a more probable process in which the state of interest is produced in an exchange rearrangement collision between a positronium atom and the singlet helium ground state: $\mathrm{Ps}+\mathrm{He}(^{1}S^{\mathrm{e}})\ensuremath{\rightarrow}\mathrm{Ps}{\mathrm{He}}^{+}(^{3}S^{\mathrm{e}})+{e}^{\ensuremath{-}}$. The present calculation is done in the plane-wave Born approximation, using simple initial and final wave functions and compares post and prior forms.We have previously calculated the cross section for radiative formation of the interesting bound state consisting of a positron bound to helium, where the atomic electrons are in the triplet spin state. That process uses the metastable triplet helium system as target, and, as expected, it has a very small cross section. In this paper we examine a more probable process in which the state of interest is produced in an exchange rearrangement collision between a positronium atom and the singlet helium ground state: $\mathrm{Ps}+\mathrm{He}(^{1}S^{\mathrm{e}})\ensuremath{\rightarrow}\mathrm{Ps}{\mathrm{He}}^{+}(^{3}S^{\mathrm{e}})+{e}^{\ensuremath{-}}$. The present calculation is done in the plane-wave Born approximation, using simple initial and final wave functions and compares post and prior forms.

Physical Review AFeb 20, 20074 citations

Near-threshold behavior of positronium-antiproton scattering

I. I. Fabrikant, Alexander Bray, Alisher S. Kadyrov +1 more

Using the convergent close-coupling theory we study the threshold behavior of cross sections for positronium (Ps) of energy $E$ scattering on antiprotons. In the case of $\mathrm{Ps}(1s$ ) elastic scattering, simple power laws are observed for all partial waves studied. The partial-wave summed cross section is nearly constant, and dominates the antihydrogen formation cross section at all considered energies, even though the latter is exothermic and behaves as $1/{E}^{1/2}$ . For $\mathrm{Ps}(2s$ ), oscillations spanning orders of magnitude on top of the $1/E$ behavior are found in the elastic and quasielastic cross sections. The antihydrogen formation is influenced by dipole-supported resonances below the threshold of inelastic processes. Resonance energies form a geometric progression relative to the threshold. The exothermic antihydrogen formation cross sections behave as $1/E$ at low energies, but are oscillation free. We demonstrate that all these rich features are reproduced by the threshold theory developed by Gailitis [J. Phys. B: At. Mol. Phys. 15, 3423 (1982)].Using the convergent close-coupling theory we study the threshold behavior of cross sections for positronium (Ps) of energy $E$ scattering on antiprotons. In the case of $\mathrm{Ps}(1s$) elastic scattering, simple power laws are observed for all partial waves studied. The partial-wave summed cross section is nearly constant, and dominates the antihydrogen formation cross section at all considered energies, even though the latter is exothermic and behaves as $1/{E}^{1/2}$. For $\mathrm{Ps}(2s$), oscillations spanning orders of magnitude on top of the $1/E$ behavior are found in the elastic and quasielastic cross sections. The antihydrogen formation is influenced by dipole-supported resonances below the threshold of inelastic processes. Resonance energies form a geometric progression relative to the threshold. The exothermic antihydrogen formation cross sections behave as $1/E$ at low energies, but are oscillation free. We demonstrate that all these rich features are reproduced by the threshold theory developed by Gailitis [J. Phys. B: At. Mol. Phys. 15, 3423 (1982)].

Physical Review AJul 5, 201623 citations

Positronium-hydrogen elastic scattering: The electronic S=1 state

Richard J. Drachman, S. K. Houston

We have continued our investigation into the elastic scattering of positronium atoms by hydrogen atoms, extending the work to include the spin-one (triplet) state of the two electrons. Once again we have extracted the $S$ -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.We have continued our investigation into the elastic scattering of positronium atoms by hydrogen atoms, extending the work to include the spin-one (triplet) state of the two electrons. Once again we have extracted the $S$-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.

Physical Review AAug 1, 197661 citations

Scattering of H¯(1s) off metastable helium atom at thermal energies

Prabal K. Sinha, Arnab Ghosh

Quantal calculations for scattering of ground-state antihydrogen by metastable $(n=2S)$ helium atoms have been performed using the nonadiabatic, atomic orbital expansion technique at thermal energies. The zero-energy elastic cross sections of the present systems are much greater than the corresponding value for the ground-state helium target. The low-energy elastic cross section for the singlet metastable helium $[\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{1}S)]$ target is higher than the corresponding value when the target is in the metastable triplet state $[\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}S)]$ .Quantal calculations for scattering of ground-state antihydrogen by metastable $(n=2S)$ helium atoms have been performed using the nonadiabatic, atomic orbital expansion technique at thermal energies. The zero-energy elastic cross sections of the present systems are much greater than the corresponding value for the ground-state helium target. The low-energy elastic cross section for the singlet metastable helium $[\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{1}S)]$ target is higher than the corresponding value when the target is in the metastable triplet state $[\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}S)]$.

Physical Review AJun 12, 20062 citations

Positronium formation and threshold behavior in positron-sodium collisions at low energies

Ning-Ning Gao, Hui-Li Han, Ting-Yun Shi

We investigate the elastic and inelastic scattering of positrons by sodium atoms in both the ground state, Na( $3s$ ), and excited states, Na*( $3p$ , $4s$ , $3d$ ), using the hyperspherical coordinate method with a model potential to represent the atomic core. The threshold behavior of positronium (Ps) formation cross sections is analyzed as the positron impact energy $E$ approaches zero. Within this framework, we derive a generalized expression for partial-wave Ps-formation cross sections at low positron energies, which applies to both ground-state and excited-state sodium targets. Our results confirm that the total threshold behavior follows the expected power-law dependence: $σ_{\text{Ps}} \propto E^{-1/2}$ for exothermic reactions and $σ_{\text{Ps}} \propto E^{a}$ for endothermic reactions, where $a > 0$ . Furthermore, we find that Ps-formation cross sections for positron scattering from excited Na states are significantly larger than those from the ground state in the low-energy region. A notable enhancement of Gailitis-Damburg oscillations is observed above the Ps( $n=2$ ) threshold, which may account for the increase observed in experimental data. Incorporating contributions from excited sodium targets improves agreement with experimental results and may help resolve discrepancies between theoretical predictions and measurements.We investigate the elastic and inelastic scattering of positrons by sodium atoms in both the ground state, Na($3s$), and excited states, Na*($3p$, $4s$, $3d$), using the hyperspherical coordinate method with a model potential to represent the atomic core. The threshold behavior of positronium (Ps) formation cross sections is analyzed as the positron impact energy $E$ approaches zero. Within this framework, we derive a generalized expression for partial-wave Ps-formation cross sections at low positron energies, which applies to both ground-state and excited-state sodium targets. Our results confirm that the total threshold behavior follows the expected power-law dependence: $ σ_{\text{Ps}} \propto E^{-1/2} $ for exothermic reactions and $ σ_{\text{Ps}} \propto E^{a} $ for endothermic reactions, where $ a > 0 $. Furthermore, we find that Ps-formation cross sections for positron scattering from excited Na states are significantly larger than those from the ground state in the low-energy region. A notable enhancement of Gailitis-Damburg oscillations is observed above the Ps($n=2$) threshold, which may account for the increase observed in experimental data. Incorporating contributions from excited sodium targets improves agreement with experimental results and may help resolve discrepancies between theoretical predictions and measurements.

arXiv:2503.19400Physical Review AJun 26, 20251 citation

Low-energy positron scattering from singlet and triplet metastable He(

1s2s

) is investigated using the

R

S

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.

Using the convergent close-coupling theory we study the threshold behavior of cross sections for positronium (Ps) of energy

E

scattering on antiprotons. In the case of

\mathrm{Ps}(1s

) elastic scattering, simple power laws are observed for all partial waves studied. The partial-wave summed cross section is nearly constant, and dominates the antihydrogen formation cross section at all considered energies, even though the latter is exothermic and behaves as

1/{E}^{1/2}

. For

\mathrm{Ps}(2s

), oscillations spanning orders of magnitude on top of the

1/E

behavior are found in the elastic and quasielastic cross sections. The antihydrogen formation is influenced by dipole-supported resonances below the threshold of inelastic processes. Resonance energies form a geometric progression relative to the threshold. The exothermic antihydrogen formation cross sections behave as

1/E

at low energies, but are oscillation free. We demonstrate that all these rich features are reproduced by the threshold theory developed by Gailitis [J. Phys. B: At. Mol. Phys. 15, 3423 (1982)].

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.

Quantal calculations for scattering of ground-state antihydrogen by metastable

(n=2S)

helium atoms have been performed using the nonadiabatic, atomic orbital expansion technique at thermal energies. The zero-energy elastic cross sections of the present systems are much greater than the corresponding value for the ground-state helium target. The low-energy elastic cross section for the singlet metastable helium

[\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{1}S)]

target is higher than the corresponding value when the target is in the metastable triplet state

[\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}S)]

We investigate the elastic and inelastic scattering of positrons by sodium atoms in both the ground state, Na(

3s

), and excited states, Na*(

3p

4s

3d

), using the hyperspherical coordinate method with a model potential to represent the atomic core. The threshold behavior of positronium (Ps) formation cross sections is analyzed as the positron impact energy

E

approaches zero. Within this framework, we derive a generalized expression for partial-wave Ps-formation cross sections at low positron energies, which applies to both ground-state and excited-state sodium targets. Our results confirm that the total threshold behavior follows the expected power-law dependence:

σ_{\text{Ps}} \propto E^{-1/2}

for exothermic reactions and

σ_{\text{Ps}} \propto E^{a}

for endothermic reactions, where

a > 0

. Furthermore, we find that Ps-formation cross sections for positron scattering from excited Na states are significantly larger than those from the ground state in the low-energy region. A notable enhancement of Gailitis-Damburg oscillations is observed above the Ps(

n=2

) threshold, which may account for the increase observed in experimental data. Incorporating contributions from excited sodium targets improves agreement with experimental results and may help resolve discrepancies between theoretical predictions and measurements.