Physical Review A

Positron annihilation in the positron-helium ion e+[He(2S3)]

Alexei M. Frolov

Published Mar 21, 2005• 15 citations

Abstract

The $({e}^{\ensuremath{-}},{e}^{+})$-pair annihilation is considered in the positron-helium ${e}^{+}[\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}S)]$ four-body ion, in which the positron forms a bound state with the helium atom in its lowest triplet state [i.e., in the $2\phantom{\rule{0.2em}{0ex}}^{3}S\phantom{\rule{0.3em}{0ex}}(L=0)$ state]. A number of bound-state properties of this system have been determined for the ${e}^{+}[\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}S)]$ ions, where the $^{\ensuremath{\infty}}\mathrm{He}$, $^{4}\mathrm{He}$, and $^{3}\mathrm{He}$ helium nuclei are considered. Some applications related to the positron annihilation in the ${e}^{+}[\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}S)]$ ion are also discussed.

DOI: 10.1103/physreva.71.032506

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Bound state properties, positron annihilation and hyperfine structure splittings in the four-body positron-helium $$e^{+} [^{3}$$He($$2^{3}S_e$$)] and $$e^{+} [^{4}$$He($$2^{3}S_e$$)] ions

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Hyperfine structure splitting of the positron-helium ions e +[3He(23 S)] and e +[4He(23 S)]

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The hyperfine structure splittings are determined for the lowest bound state in the positron-helium ion e +[3He(23 S)] and e +[4He(23 S)]. In particular, it has been found that the three hyperfine structure splittings—5824.3986, 76 466.5308, and 5824.4019 MHz—can be observed for the e +[3He(23 S)] ion. In the e +[4He(23 S)] ion, only one hyperfine structure splitting 82963.0427 MHz can be observed. All these values can be measured in modern experiments.

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Physical Review A

Positron annihilation in the positron-helium ion e+[He(2S3)]

Alexei M. Frolov

Published Mar 21, 2005• 15 citations

Publisher

Abstract

The

({e}^{\ensuremath{-}},{e}^{+})

-pair annihilation is considered in the positron-helium

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

four-body ion, in which the positron forms a bound state with the helium atom in its lowest triplet state [i.e., in the

2\phantom{\rule{0.2em}{0ex}}^{3}S\phantom{\rule{0.3em}{0ex}}(L=0)

state]. A number of bound-state properties of this system have been determined for the

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

ions, where the

^{\ensuremath{\infty}}\mathrm{He}

^{4}\mathrm{He}

, and

^{3}\mathrm{He}

helium nuclei are considered. Some applications related to the positron annihilation in the

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

ion are also discussed.

DOI: 10.1103/physreva.71.032506

Related papers

Bound state properties, positron annihilation and hyperfine structure splittings in the four-body positron-helium $e^{+} [^{3}$ He( $2^{3}S_e$ )] and $e^{+} [^{4}$ He( $2^{3}S_e$ )] ionsBound state properties, positron annihilation and hyperfine structure splittings in the four-body positron-helium $$e^{+} [^{3}$$He($$2^{3}S_e$$)] and $$e^{+} [^{4}$$He($$2^{3}S_e$$)] ions

Alexei M. Frolov

The European Physical Journal DApr 1, 20251 citation

Hyperfine structure splitting of the positron-helium ions $e^{+}[$ He $(2^3S)]$ Hyperfine structure splitting of the positron-helium ions $e^{+}[$He$(2^3S)]$

Alexei M. Frolov

The hyperfine structure splittings are determined for the lowest bound state in the positron-helium ion $e^{+}[^3$ He $(2^3S)]$ and $e^{+}[^4$ He $(2^3S)]$ . In particular, we have fond that for the $e^{+}[{}^3$ He $(2^3S)]$ ion one can observe the three following hyperfine structure splittinings: 5824.3986 $MHz$ , 76466.5308 $MHz$ and 5824.4019 $MHz$ . In the $e^{+}[{}^4$ He $(2^3S)]$ ion only one hyperfine structure splitting 82963.0427 $MHz$ can be observed. All these values can be measured in modern experiments.The hyperfine structure splittings are determined for the lowest bound state in the positron-helium ion $e^{+}[^3$He$(2^3S)]$ and $e^{+}[^4$He$(2^3S)]$. In particular, we have fond that for the $e^{+}[{}^3$He$(2^3S)]$ ion one can observe the three following hyperfine structure splittinings: 5824.3986 $MHz$, 76466.5308 $MHz$ and 5824.4019 $MHz$. In the $e^{+}[{}^4$He$(2^3S)]$ ion only one hyperfine structure splitting 82963.0427 $MHz$ can be observed. All these values can be measured in modern experiments.

Aug 20, 20120 citations

Hyperfine structure splitting of the positron-helium ions e +[3He(23 S)] and e +[4He(23 S)]

A. M. Frolov

arXiv:1208.4121Journal of Experimental and Theoretical Physics LettersDec 1, 20121 citation

Determination and applications of enhancement factors for positron and ortho-positronium annihilations

Jim Mitroy

Electron-positron annihilation rates calculated directly from the electron and positron densities are known to underestimate the true annihilation rate. A correction factor, known as the enhancement factor, allows for the local increase of the electron density around the positron caused by the attractive electron-positron interaction. Enhancement factors are given for positrons annihilating with the $1s$ electron in H, ${\mathrm{He}}^{+}$ , He, ${\mathrm{Li}}^{2+}$ , and ${\mathrm{Li}}^{+}$ . The enhancement factor for a free positron annihilating with ${\mathrm{He}}^{+}$ and He is found to be close to that of ortho-positronium (i.e., Ps in its triplet state) annihilating with these atoms. The enhancement factor for Ps-He scattering is used in conjunction with the known annihilation rate for pickoff annihilation to derive a scattering length of $1.47{a}_{0}$ for Ps-He scattering. Further, enhancement factors for ${e}^{+}$ -Ne and ${e}^{+}$ -Ar annihilation are used in conjunction with the pickoff annihilation rate to estimate scattering lengths of $1.46{a}_{0}$ for Ps-Ne scattering and $1.75{a}_{0}$ for Ps-Ar scattering.Electron-positron annihilation rates calculated directly from the electron and positron densities are known to underestimate the true annihilation rate. A correction factor, known as the enhancement factor, allows for the local increase of the electron density around the positron caused by the attractive electron-positron interaction. Enhancement factors are given for positrons annihilating with the $1s$ electron in H, ${\mathrm{He}}^{+}$, He, ${\mathrm{Li}}^{2+}$, and ${\mathrm{Li}}^{+}$. The enhancement factor for a free positron annihilating with ${\mathrm{He}}^{+}$ and He is found to be close to that of ortho-positronium (i.e., Ps in its triplet state) annihilating with these atoms. The enhancement factor for Ps-He scattering is used in conjunction with the known annihilation rate for pickoff annihilation to derive a scattering length of $1.47{a}_{0}$ for Ps-He scattering. Further, enhancement factors for ${e}^{+}$-Ne and ${e}^{+}$-Ar annihilation are used in conjunction with the pickoff annihilation rate to estimate scattering lengths of $1.46{a}_{0}$ for Ps-Ne scattering and $1.75{a}_{0}$ for Ps-Ar scattering.

Physical Review ADec 16, 200512 citations

Bound-state properties of the positronium negative ion Ps−

Alexei M. Frolov

Various geometrical and energetical (bound-state) properties of the positronium negative ion $({\mathrm{Ps}}^{\ensuremath{-}}$ or ${e}^{\ensuremath{-}}{e}^{+}{e}^{\ensuremath{-}})$ are determined by using highly accurate variational wave functions. These wave functions have been constructed by applying the advanced two-stage strategy proposed by Frolov [Phys. Rev. A 57, 2436 (1998)]. The determined total energy of the ground state $E=\ensuremath{-}0.2620050702329757\mathrm{a}.\mathrm{u}.$ is the lowest and most accurate value obtained for this system to date (the corresponding binding energy equals $\ensuremath{-}0.326674721317821\mathrm{eV}).$ The computation of the second-order relativistic corrections $(\ensuremath{\simeq}{\ensuremath{\alpha}}^{2})$ to the total energy is discussed also. The general form of the Breit-Pauli Hamiltonian in the relative coordinates for the ${\mathrm{Ps}}^{\ensuremath{-}}$ ion is presented.Various geometrical and energetical (bound-state) properties of the positronium negative ion $({\mathrm{Ps}}^{\ensuremath{-}}$ or ${e}^{\ensuremath{-}}{e}^{+}{e}^{\ensuremath{-}})$ are determined by using highly accurate variational wave functions. These wave functions have been constructed by applying the advanced two-stage strategy proposed by Frolov [Phys. Rev. A 57, 2436 (1998)]. The determined total energy of the ground state $E=\ensuremath{-}0.2620050702329757\mathrm{a}.\mathrm{u}.$ is the lowest and most accurate value obtained for this system to date (the corresponding binding energy equals $\ensuremath{-}0.326674721317821\mathrm{eV}).$ The computation of the second-order relativistic corrections $(\ensuremath{\simeq}{\ensuremath{\alpha}}^{2})$ to the total energy is discussed also. The general form of the Breit-Pauli Hamiltonian in the relative coordinates for the ${\mathrm{Ps}}^{\ensuremath{-}}$ ion is presented.

Physical Review AOct 1, 199972 citations

Cross-section for formation of the triplet positron-helium bound state

Joseph Di Rienzi, Richard J. Drachman

Bulletin of the American Physical SocietyMay 20, 20050 citations

The

({e}^{\ensuremath{-}},{e}^{+})

-pair annihilation is considered in the positron-helium

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

four-body ion, in which the positron forms a bound state with the helium atom in its lowest triplet state [i.e., in the

2\phantom{\rule{0.2em}{0ex}}^{3}S\phantom{\rule{0.3em}{0ex}}(L=0)

state]. A number of bound-state properties of this system have been determined for the

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

ions, where the

^{\ensuremath{\infty}}\mathrm{He}

^{4}\mathrm{He}

, and

^{3}\mathrm{He}

helium nuclei are considered. Some applications related to the positron annihilation in the

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

ion are also discussed.

Bound state properties, positron annihilation and hyperfine structure splittings in the four-body positron-helium

e^{+} [^{3}

He(

2^{3}S_e

)] and

e^{+} [^{4}

He(

2^{3}S_e

)] ions

Hyperfine structure splitting of the positron-helium ions

e^{+}[

(2^3S)]

The hyperfine structure splittings are determined for the lowest bound state in the positron-helium ion

e^{+}[^3

(2^3S)]

and

e^{+}[^4

(2^3S)]

. In particular, we have fond that for the

e^{+}[{}^3

(2^3S)]

ion one can observe the three following hyperfine structure splittinings: 5824.3986

MHz

, 76466.5308

MHz

and 5824.4019

MHz

. In the

e^{+}[{}^4

(2^3S)]

ion only one hyperfine structure splitting 82963.0427

MHz

can be observed. All these values can be measured in modern experiments.

1s

electron in H,

{\mathrm{He}}^{+}

, He,

{\mathrm{Li}}^{2+}

, and

{\mathrm{Li}}^{+}

. The enhancement factor for a free positron annihilating with

{\mathrm{He}}^{+}

and He is found to be close to that of ortho-positronium (i.e., Ps in its triplet state) annihilating with these atoms. The enhancement factor for Ps-He scattering is used in conjunction with the known annihilation rate for pickoff annihilation to derive a scattering length of

1.47{a}_{0}

for Ps-He scattering. Further, enhancement factors for

{e}^{+}

-Ne and

{e}^{+}

-Ar annihilation are used in conjunction with the pickoff annihilation rate to estimate scattering lengths of

1.46{a}_{0}

for Ps-Ne scattering and

1.75{a}_{0}

for Ps-Ar scattering.