Physical Review A

Elastic positron-cadmium scattering at low energies

M. W. J. Bromley, Jim Mitroy

Published May 25, 2010• 12 citations

Abstract

The elastic and annihilation cross sections for positron-cadmium scattering are reported up to the positronium-formation threshold (at $2.2$ eV). The low-energy phase shifts for the elastic scattering of positrons from cadmium were derived from the bound and pseudostate energies of a very large basis configuration-interaction calculation of the ${e}^{+}$-Cd system. The $s$-wave binding energy is estimated to be $126\ifmmode\pm\else\textpm\fi{}42$ meV, with a scattering length of ${A}_{\mathrm{scat}}=(14.2\ifmmode\pm\else\textpm\fi{}2.1)$${a}_{0}$, while the threshold annihilation parameter, ${Z}_{\mathrm{eff}}$, was $93.9\ifmmode\pm\else\textpm\fi{}26.5$. The $p$-wave phase shift exhibits a weak shape resonance that results in a peak ${Z}_{\mathrm{eff}}$ of $91\ifmmode\pm\else\textpm\fi{}17$ at a collision energy of about $490\ifmmode\pm\else\textpm\fi{}50$ meV.

DOI: 10.1103/physreva.81.052708

Related papers

Configuration-interaction calculations of positron binding to zinc and cadmium

M. W. J. Bromley, Jim Mitroy

Physical Review AJun 13, 200230 citations

Interaction Of Low-Energy Positrons With Mg Atoms: Elastic Scattering, Bound States, And Annihilation

Mahasen. M. Abdel-Mageed, Hala Saad Zaghloul

World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer EngineeringOct 1, 20150 citations

S -wave Ps-Li and Ps-Na scattering

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Physical Review AMay 17, 20045 citations

Positronium-hydrogen elastic scattering

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Physical Review ASep 1, 197591 citations

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

Richard J. Drachman, S. K. Houston

Physical Review AAug 1, 197661 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

Physical Review A

Elastic positron-cadmium scattering at low energies

M. W. J. Bromley, Jim Mitroy

Published May 25, 2010• 12 citations

Publisher

Abstract

The elastic and annihilation cross sections for positron-cadmium scattering are reported up to the positronium-formation threshold (at

2.2

eV). The low-energy phase shifts for the elastic scattering of positrons from cadmium were derived from the bound and pseudostate energies of a very large basis configuration-interaction calculation of the

{e}^{+}

-Cd system. The

s

-wave binding energy is estimated to be

126\ifmmode\pm\else\textpm\fi{}42

meV, with a scattering length of

{A}_{\mathrm{scat}}=(14.2\ifmmode\pm\else\textpm\fi{}2.1)$${a}_{0}

, while the threshold annihilation parameter,

{Z}_{\mathrm{eff}}

, was

93.9\ifmmode\pm\else\textpm\fi{}26.5

. The

p

-wave phase shift exhibits a weak shape resonance that results in a peak

{Z}_{\mathrm{eff}}

91\ifmmode\pm\else\textpm\fi{}17

at a collision energy of about

490\ifmmode\pm\else\textpm\fi{}50

meV.

DOI: 10.1103/physreva.81.052708

Related papers

Configuration-interaction calculations of positron binding to zinc and cadmium

M. W. J. Bromley, Jim Mitroy

The configuration-interaction method is applied to the study of positronic zinc ${(e}^{+}\mathrm{Zn})$ and positronic cadmium ${(e}^{+}\mathrm{Cd}).$ The estimated binding energies and annihilation rates were 0.003 73 hartree and $0.42\ifmmode\times\else\texttimes\fi{}{10}^{9} {\mathrm{sec}}^{\ensuremath{-}1}$ for ${e}^{+}\mathrm{Zn}$ and 0.006 10 hartree and $0.56\ifmmode\times\else\texttimes\fi{}{10}^{9} {\mathrm{sec}}^{\ensuremath{-}1}$ for ${e}^{+}\mathrm{Cd}.$ The low-energy elastic cross section and ${Z}_{\mathrm{eff}}$ were estimated from a model potential that was tuned to the binding energies and annihilation rates. Since the scattering lengths were positive ${(14.5a}_{0}$ for Zn and ${11.6a}_{0}$ for Cd) the differential cross sections are larger at backward angles than at forward angles just above threshold. The possibilities of measuring differential cross sections to confirm positron binding to these atoms is discussed.The configuration-interaction method is applied to the study of positronic zinc ${(e}^{+}\mathrm{Zn})$ and positronic cadmium ${(e}^{+}\mathrm{Cd}).$ The estimated binding energies and annihilation rates were 0.003 73 hartree and $0.42\ifmmode\times\else\texttimes\fi{}{10}^{9} {\mathrm{sec}}^{\ensuremath{-}1}$ for ${e}^{+}\mathrm{Zn}$ and 0.006 10 hartree and $0.56\ifmmode\times\else\texttimes\fi{}{10}^{9} {\mathrm{sec}}^{\ensuremath{-}1}$ for ${e}^{+}\mathrm{Cd}.$ The low-energy elastic cross section and ${Z}_{\mathrm{eff}}$ were estimated from a model potential that was tuned to the binding energies and annihilation rates. Since the scattering lengths were positive ${(14.5a}_{0}$ for Zn and ${11.6a}_{0}$ for Cd) the differential cross sections are larger at backward angles than at forward angles just above threshold. The possibilities of measuring differential cross sections to confirm positron binding to these atoms is discussed.

Physical Review AJun 13, 200230 citations

Interaction Of Low-Energy Positrons With Mg Atoms: Elastic Scattering, Bound States, And Annihilation

Mahasen. M. Abdel-Mageed, Hala Saad Zaghloul

Annihilations, phase shifts, scattering lengths and elastic cross sections of low energy positrons scattering from magnesium atoms were studied using the least-squares variational method (LSVM). The possibility of positron binding to the magnesium atoms is investigated. A trial wave function is suggested to represent e+-Mg elastic scattering and scattering parameters were derived to estimate the binding energy and annihilation rates. The trial function is taken to depend on several adjustable parameters, and is improved iteratively by increasing the number of terms. The present results have the same behavior as reported semi-empirical, theoretical and experimental results. Especially, the estimated positive scattering length supports the possibility of positronmagnesium bound state system that was confirmed in previous experimental and theoretical work.Annihilations, phase shifts, scattering lengths and elastic cross sections of low energy positrons scattering from magnesium atoms were studied using the least-squares variational method (LSVM). The possibility of positron binding to the magnesium atoms is investigated. A trial wave function is suggested to represent e+-Mg elastic scattering and scattering parameters were derived to estimate the binding energy and annihilation rates. The trial function is taken to depend on several adjustable parameters, and is improved iteratively by increasing the number of terms. The present results have the same behavior as reported semi-empirical, theoretical and experimental results. Especially, the estimated positive scattering length supports the possibility of positronmagnesium bound state system that was confirmed in previous experimental and theoretical work.

World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer EngineeringOct 1, 20150 citations

S -wave Ps-Li and Ps-Na scattering

Sumana Chakraborty, Prabal K. Sinha, Arnab Ghosh

Projectile-elastic, target-elastic, and full close-coupling approximation models have been employed to investigate scattering of ortho-positronium off Li and Na atoms at low energies. Nine different basis sets for each system have been used to find the relative importance of atomic (target and projectile) states on the elastic scattering parameters and the convergence of the predicted results with added eigen- and pseudostates. The $s$ -wave elastic phase shifts, scattering lengths and cross sections of both the systems are reported upto the incident energy $k=0.5\phantom{\rule{0.3em}{0ex}}\text{a.u.}$ and compared with the corresponding existing theoretical predictions. It has been found that the van der Waals and higher order long-range interactions play a crucial role in predicting $s$ -wave elastic parameters for Ps--alkali-metal-atom systems at low energies.Projectile-elastic, target-elastic, and full close-coupling approximation models have been employed to investigate scattering of ortho-positronium off Li and Na atoms at low energies. Nine different basis sets for each system have been used to find the relative importance of atomic (target and projectile) states on the elastic scattering parameters and the convergence of the predicted results with added eigen- and pseudostates. The $s$-wave elastic phase shifts, scattering lengths and cross sections of both the systems are reported upto the incident energy $k=0.5\phantom{\rule{0.3em}{0ex}}\text{a.u.}$ and compared with the corresponding existing theoretical predictions. It has been found that the van der Waals and higher order long-range interactions play a crucial role in predicting $s$-wave elastic parameters for Ps--alkali-metal-atom systems at low energies.

Physical Review AMay 17, 20045 citations

Positronium-hydrogen elastic scattering

Richard J. Drachman, S. K. Houston

We have investigated the elastic scattering of positronium atoms by hydrogen atoms below the excitation threshold at 5.1 eV, limiting the investigation to the spin-zero (singlet) state of the two electrons. Nonresonant $S$ -wave phase shifts have been obtained from normalizable trial functions by extracting the center-of-mass wave function and examining its spatial behavior. An effective-range expansion is fitted to the phase shifts and the previously obtained positronium-hydride bound-state energy to yield a scattering length $a\ensuremath{\cong}5.3{a}_{0}$ compared with Fraser's corrected exchange result, $a=7.28{a}_{0}$ ( ${a}_{0}$ is the Bohr radius). The stabilization method suggests that a resonance occurs at a scattering energy of 4.5 eV, about 0.6 eV below the excitation threshold. Using the complex rotation method, we have obtained evidence confirming the existence of the resonance and an estimate of its width of about 6 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}2}$ eV.We have investigated the elastic scattering of positronium atoms by hydrogen atoms below the excitation threshold at 5.1 eV, limiting the investigation to the spin-zero (singlet) state of the two electrons. Nonresonant $S$-wave phase shifts have been obtained from normalizable trial functions by extracting the center-of-mass wave function and examining its spatial behavior. An effective-range expansion is fitted to the phase shifts and the previously obtained positronium-hydride bound-state energy to yield a scattering length $a\ensuremath{\cong}5.3{a}_{0}$ compared with Fraser's corrected exchange result, $a=7.28{a}_{0}$ (${a}_{0}$ is the Bohr radius). The stabilization method suggests that a resonance occurs at a scattering energy of 4.5 eV, about 0.6 eV below the excitation threshold. Using the complex rotation method, we have obtained evidence confirming the existence of the resonance and an estimate of its width of about 6 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}2}$ eV.

Physical Review ASep 1, 197591 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

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

The elastic and annihilation cross sections for positron-cadmium scattering are reported up to the positronium-formation threshold (at

2.2

{e}^{+}

-Cd system. The

s

-wave binding energy is estimated to be

126\ifmmode\pm\else\textpm\fi{}42

meV, with a scattering length of

{A}_{\mathrm{scat}}=(14.2\ifmmode\pm\else\textpm\fi{}2.1)$${a}_{0}

, while the threshold annihilation parameter,

{Z}_{\mathrm{eff}}

, was

93.9\ifmmode\pm\else\textpm\fi{}26.5

. The

p

-wave phase shift exhibits a weak shape resonance that results in a peak

{Z}_{\mathrm{eff}}

91\ifmmode\pm\else\textpm\fi{}17

at a collision energy of about

490\ifmmode\pm\else\textpm\fi{}50

meV.

The configuration-interaction method is applied to the study of positronic zinc

{(e}^{+}\mathrm{Zn})

and positronic cadmium

{(e}^{+}\mathrm{Cd}).

The estimated binding energies and annihilation rates were 0.003 73 hartree and $0.42\ifmmode\times\else\texttimes\fi{}{10}^{9} {\mathrm{sec}}^{\ensuremath{-}1}$ for

{e}^{+}\mathrm{Zn}

and 0.006 10 hartree and $0.56\ifmmode\times\else\texttimes\fi{}{10}^{9} {\mathrm{sec}}^{\ensuremath{-}1}$ for

{e}^{+}\mathrm{Cd}.

The low-energy elastic cross section and

{Z}_{\mathrm{eff}}

were estimated from a model potential that was tuned to the binding energies and annihilation rates. Since the scattering lengths were positive

{(14.5a}_{0}

for Zn and

{11.6a}_{0}

for Cd) the differential cross sections are larger at backward angles than at forward angles just above threshold. The possibilities of measuring differential cross sections to confirm positron binding to these atoms is discussed.

s

-wave elastic phase shifts, scattering lengths and cross sections of both the systems are reported upto the incident energy

k=0.5\phantom{\rule{0.3em}{0ex}}\text{a.u.}

and compared with the corresponding existing theoretical predictions. It has been found that the van der Waals and higher order long-range interactions play a crucial role in predicting

s

-wave elastic parameters for Ps--alkali-metal-atom systems at low energies.

S

-wave phase shifts have been obtained from normalizable trial functions by extracting the center-of-mass wave function and examining its spatial behavior. An effective-range expansion is fitted to the phase shifts and the previously obtained positronium-hydride bound-state energy to yield a scattering length $a\ensuremath{\cong}5.3{a}_{0}$ compared with Fraser's corrected exchange result,

a=7.28{a}_{0}

(

{a}_{0}

is the Bohr radius). The stabilization method suggests that a resonance occurs at a scattering energy of 4.5 eV, about 0.6 eV below the excitation threshold. Using the complex rotation method, we have obtained evidence confirming the existence of the resonance and an estimate of its width of about 6 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}2}$ eV.

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 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.