Physical Review A

Auger transition rates for metastable states of antiprotonic helium He+p¯

V. I. Korobov, Isao Shimamura

Published Dec 1, 1997• 60 citations

Abstract

The rates of Auger transitions of antiprotonic helium ${}^{4}$He${}^{+}\overline{p}$ and ${}^{3}$He${}^{+}\overline{p}$ are calculated by using a variational scattering method with an elaborate three-body trial function. The shift of the energy levels of these systems due to the coupling with the Auger-decay channels is also obtained from this calculation. Thus an improvement is made over the previously calculated nonrelativistic energies. Together with the relativistic corrections calculated elsewhere, the theoretical transition wavelength between the states $(n,l)=(37,34)$ and $(38,33)$ of ${}^{4}$He${}^{+}\overline{p}$, for example, is significantly improved to be 713.593 nm, which compares well with the experimental value 713.578$\ifmmode\pm\else\textpm\fi{}$0.006 nm. The calculated Auger lifetime of the level (38,33) is 3.2 ps, as compared with the value 4.1$\ifmmode\pm\else\textpm\fi{}$0.2 ps deduced from the measured line broadening. Auger rates are calculated also using Fermi's golden-rule formula with a regular Coulomb function with no phase shift for the Auger electron. The results agree fairly well with the accurate variational results.

DOI: 10.1103/physreva.56.4587

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Physical Review A

Auger transition rates for metastable states of antiprotonic helium He+p¯

V. I. Korobov, Isao Shimamura

Published Dec 1, 1997• 60 citations

Publisher

Abstract

The rates of Auger transitions of antiprotonic helium

{}^{4}

{}^{+}\overline{p}

and

{}^{3}

{}^{+}\overline{p}

are calculated by using a variational scattering method with an elaborate three-body trial function. The shift of the energy levels of these systems due to the coupling with the Auger-decay channels is also obtained from this calculation. Thus an improvement is made over the previously calculated nonrelativistic energies. Together with the relativistic corrections calculated elsewhere, the theoretical transition wavelength between the states

(n,l)=(37,34)

and

(38,33)

{}^{4}

{}^{+}\overline{p}

, for example, is significantly improved to be 713.593 nm, which compares well with the experimental value 713.578

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

0.006 nm. The calculated Auger lifetime of the level (38,33) is 3.2 ps, as compared with the value 4.1

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

0.2 ps deduced from the measured line broadening. Auger rates are calculated also using Fermi's golden-rule formula with a regular Coulomb function with no phase shift for the Auger electron. The results agree fairly well with the accurate variational results.

DOI: 10.1103/physreva.56.4587

Related papers

Systematic study of the decay rates of antiprotonic helium states

H. Yamaguchi, R. Hayano, Takashi Ishikawa +8 more

A systematic study of the decay rates of antiprotonic helium ( ${\overline{p}}^{4}{\mathrm{He}}^{+}$ and ${\overline{p}}^{3}{\mathrm{He}}^{+}$ ) at CERN Antiproton Decelerator has been made by a laser spectroscopic method. The decay rates of some of its short-lived states, namely those for which the Auger rates ${\ensuremath{\gamma}}_{A}$ are much larger than their radiative decay rates $({\ensuremath{\gamma}}_{\mathrm{rad}}\ensuremath{\sim}1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}{s}^{\ensuremath{-}1})$, were determined from the time distributions of the antiproton annihilation signals induced by laser beams, and the widths of the atomic resonance lines. The magnitude of the decay rates, especially their relation with the transition multipolarity, is discussed and compared with theoretical calculations.A systematic study of the decay rates of antiprotonic helium (${\overline{p}}^{4}{\mathrm{He}}^{+}$ and ${\overline{p}}^{3}{\mathrm{He}}^{+}$) at CERN Antiproton Decelerator has been made by a laser spectroscopic method. The decay rates of some of its short-lived states, namely those for which the Auger rates ${\ensuremath{\gamma}}_{A}$ are much larger than their radiative decay rates $({\ensuremath{\gamma}}_{\mathrm{rad}}\ensuremath{\sim}1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}{s}^{\ensuremath{-}1})$, were determined from the time distributions of the antiproton annihilation signals induced by laser beams, and the widths of the atomic resonance lines. The magnitude of the decay rates, especially their relation with the transition multipolarity, is discussed and compared with theoretical calculations.

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M. Hori, H. A. Torii, R. Hayano +16 more

A laser spectroscopic method was developed to directly observe the lifetimes of individual states in metastable antiprotonic helium atoms $(\overline{p}{}^{4}{\mathrm{He}}^{+}).$ Collisional effects with surrounding helium atoms were studied in cryogenic gas targets at pressures between 0.1 and 9.0 bars and at temperatures between 5.5 and 7.0 K. The metastable state $(n,\mathcal{l})=(39,35)$ showed a lifetime of 1.5 $\ensuremath{\mu}\mathrm{s}$, regardless of density, whereas the lifetime of the energetically lower-lying state $(37,34)$ was found to shorten from 1.3 to 0.1 $\ensuremath{\mu}$s with increasing density. The lifetimes of the states $(38,34)$ and $(36,33)$ were determined to be 10 ns and 5 ns, respectively, showing the effects of the internal Auger process. When extrapolated to zero density, the measured lifetimes agreed with the results of calculations for the radiative and Auger widths. Using the fact that the state $(37,34)$ becomes short lived at high density, the resonance $(38,35)\ensuremath{\rightarrow}(37,34)$ at 529.62 nm was detected.A laser spectroscopic method was developed to directly observe the lifetimes of individual states in metastable antiprotonic helium atoms $(\overline{p}{}^{4}{\mathrm{He}}^{+}).$ Collisional effects with surrounding helium atoms were studied in cryogenic gas targets at pressures between 0.1 and 9.0 bars and at temperatures between 5.5 and 7.0 K. The metastable state $(n,\mathcal{l})=(39,35)$ showed a lifetime of 1.5 $\ensuremath{\mu}\mathrm{s}$, regardless of density, whereas the lifetime of the energetically lower-lying state $(37,34)$ was found to shorten from 1.3 to 0.1 $\ensuremath{\mu}$s with increasing density. The lifetimes of the states $(38,34)$ and $(36,33)$ were determined to be 10 ns and 5 ns, respectively, showing the effects of the internal Auger process. When extrapolated to zero density, the measured lifetimes agreed with the results of calculations for the radiative and Auger widths. Using the fact that the state $(37,34)$ becomes short lived at high density, the resonance $(38,35)\ensuremath{\rightarrow}(37,34)$ at 529.62 nm was detected.

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Anomalies in the decay rates of antiprotonic helium-atom states

H. Yamaguchi, Takashi Ishikawa, Jun Sakaguchi +8 more

Six resonance transitions of the antiprotonic helium atom in helium gas at densities of $3\ifmmode\times\else\texttimes\fi{}{10}^{20}--3\ifmmode\times\else\texttimes\fi{}{10}^{21} {\mathrm{cm}}^{\ensuremath{-}3}$ were studied at the antiproton decelerator (AD) of CERN. The decay rates of the daughter states of these transitions were determined either from the time distributions of the resonance spikes or from the widths of the resonance lines. Whereas most of the observed decay rates agree with theoretical calculations of Auger rates, two states, $(n,l)=(37,33)$ and (32,31), were found to have decay rates two orders of magnitude larger than predicted by these calculations. The effect of coupling with near-lying electron-excited states is considered to be the reason for the anomaly of the (37, 33) state, as pointed out by Kartavtsev et al. [Phys. Rev. A $61,$ 062507 (2000)].Six resonance transitions of the antiprotonic helium atom in helium gas at densities of $3\ifmmode\times\else\texttimes\fi{}{10}^{20}--3\ifmmode\times\else\texttimes\fi{}{10}^{21} {\mathrm{cm}}^{\ensuremath{-}3}$ were studied at the antiproton decelerator (AD) of CERN. The decay rates of the daughter states of these transitions were determined either from the time distributions of the resonance spikes or from the widths of the resonance lines. Whereas most of the observed decay rates agree with theoretical calculations of Auger rates, two states, $(n,l)=(37,33)$ and (32,31), were found to have decay rates two orders of magnitude larger than predicted by these calculations. The effect of coupling with near-lying electron-excited states is considered to be the reason for the anomaly of the (37, 33) state, as pointed out by Kartavtsev et al. [Phys. Rev. A $61,$ 062507 (2000)].

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Formation of antiprotonic helium p¯He+ and ionization in low-energy collisions of p¯ with He in the ground 1S1 and metastable 2S3 and 2S1 states

Kazuhiro Sakimoto

Calculations of low-energy collisions of antiprotons $\overline{p}$ with helium atoms in the ground $(1\phantom{\rule{4pt}{0ex}}^{1}\mathit{S})$ and metastable $(2\phantom{\rule{4pt}{0ex}}^{3}\mathit{S}$ and $2\phantom{\rule{4pt}{0ex}}^{1}\mathit{S})$ states are carried out by using a semiclassical method and by further assuming that one of the two electrons is passive. Antiproton capture to form antiprotonic helium $(\ensuremath{\rightarrow}\overline{p}{\mathrm{He}}^{+}+e)$ and breakup ionization $(\ensuremath{\rightarrow}\overline{p}+{\mathrm{He}}^{+}+e)$ are investigated. The energy dependence of the capture and ionization cross sections and the distributions of the product states are presented and compared with previous theoretical calculations. For the metastable helium targets, most of the $\overline{p}{\mathrm{He}}^{+}$ atoms produced in the capture have long lifetimes against subsequent Auger decays and can be observed experimentally. For the ground-state targets, however, the formation of such long-lived states is rather a rare event at low collision energies.Calculations of low-energy collisions of antiprotons $\overline{p}$ with helium atoms in the ground $(1\phantom{\rule{4pt}{0ex}}^{1}\mathit{S})$ and metastable $(2\phantom{\rule{4pt}{0ex}}^{3}\mathit{S}$ and $2\phantom{\rule{4pt}{0ex}}^{1}\mathit{S})$ states are carried out by using a semiclassical method and by further assuming that one of the two electrons is passive. Antiproton capture to form antiprotonic helium $(\ensuremath{\rightarrow}\overline{p}{\mathrm{He}}^{+}+e)$ and breakup ionization $(\ensuremath{\rightarrow}\overline{p}+{\mathrm{He}}^{+}+e)$ are investigated. The energy dependence of the capture and ionization cross sections and the distributions of the product states are presented and compared with previous theoretical calculations. For the metastable helium targets, most of the $\overline{p}{\mathrm{He}}^{+}$ atoms produced in the capture have long lifetimes against subsequent Auger decays and can be observed experimentally. For the ground-state targets, however, the formation of such long-lived states is rather a rare event at low collision energies.

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Transitions between hyperfine structure states of antiprotonic $^4 \mathrm{He}$ at collisions with medium atoms: interaction \emph{ab initio}Transitions between hyperfine structure states of antiprotonic $^4 \mathrm{He}$ at collisions with medium atoms: interaction \emph{ab initio}

Anton V. Bibikov, Grigory Ya. Korenman, S. N. Yudin

Collisions of metastable antiprotonic helium atoms with atoms of the medium induce, among other processes, transitions between hyperfine structure (HFS) states, as well as shifts and broadening of microwave M1 spectral lines. In order to obtain matrix potential of interaction between $(\mathrm{\bar{p} He} ^+)$ and $\mathrm{He}$ , we have calculated the potential energy surface (PES) in the framework of unrestricted Hartree-Fock method taking into account electron correlations in the second-order perturbation theory (MP2). With this potential, the system of close-coupling equations for HFS channels is solved numerically. Cross sections and transition rates, shifts and broadening of M1 spectral lines are calculated. They are used to obtain a numerical solution of the master equation that determines the time evolution of the HFS-states density matrix. The results are compared with the experimental data and with the results of model calculation.Collisions of metastable antiprotonic helium atoms with atoms of the medium induce, among other processes, transitions between hyperfine structure (HFS) states, as well as shifts and broadening of microwave M1 spectral lines. In order to obtain matrix potential of interaction between $(\mathrm{\bar{p} He} ^+)$ and $\mathrm{He}$, we have calculated the potential energy surface (PES) in the framework of unrestricted Hartree-Fock method taking into account electron correlations in the second-order perturbation theory (MP2). With this potential, the system of close-coupling equations for HFS channels is solved numerically. Cross sections and transition rates, shifts and broadening of M1 spectral lines are calculated. They are used to obtain a numerical solution of the master equation that determines the time evolution of the HFS-states density matrix. The results are compared with the experimental data and with the results of model calculation.

arXiv:1911.10619Nov 24, 20190 citations

Variational expansion for antiprotonic helium atoms

V. I. Korobov, D. Bakalov, Hendrik J. Monkhorst

A very accurate variational expansion is suggested for calculation of nonrelativistic energies of the metastable antiprotonic helium atoms ${\mathrm{He}}^{+}\overline{p}.$ This expansion reflects the dual atomic-molecular nature of the system. Convergence of the results as a function of the increasing sets of basis functions shows an accuracy better than ${10}^{\ensuremath{-}10}\mathrm{a}.\mathrm{u}.,$ two orders of magnitude better than in our previous calculations.A very accurate variational expansion is suggested for calculation of nonrelativistic energies of the metastable antiprotonic helium atoms ${\mathrm{He}}^{+}\overline{p}.$ This expansion reflects the dual atomic-molecular nature of the system. Convergence of the results as a function of the increasing sets of basis functions shows an accuracy better than ${10}^{\ensuremath{-}10}\mathrm{a}.\mathrm{u}.,$ two orders of magnitude better than in our previous calculations.

Physical Review AFeb 1, 199961 citations

The rates of Auger transitions of antiprotonic helium

{}^{4}

{}^{+}\overline{p}

and

{}^{3}

{}^{+}\overline{p}

(n,l)=(37,34)

and

(38,33)

{}^{4}

{}^{+}\overline{p}

, for example, is significantly improved to be 713.593 nm, which compares well with the experimental value 713.578

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

0.006 nm. The calculated Auger lifetime of the level (38,33) is 3.2 ps, as compared with the value 4.1

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

A systematic study of the decay rates of antiprotonic helium (

{\overline{p}}^{4}{\mathrm{He}}^{+}

and

{\overline{p}}^{3}{\mathrm{He}}^{+}

) at CERN Antiproton Decelerator has been made by a laser spectroscopic method. The decay rates of some of its short-lived states, namely those for which the Auger rates ${\ensuremath{\gamma}}_{A}$ are much larger than their radiative decay rates $({\ensuremath{\gamma}}_{\mathrm{rad}}\ensuremath{\sim}1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}{s}^{\ensuremath{-}1})$, were determined from the time distributions of the antiproton annihilation signals induced by laser beams, and the widths of the atomic resonance lines. The magnitude of the decay rates, especially their relation with the transition multipolarity, is discussed and compared with theoretical calculations.

A laser spectroscopic method was developed to directly observe the lifetimes of individual states in metastable antiprotonic helium atoms

(\overline{p}{}^{4}{\mathrm{He}}^{+}).

Collisional effects with surrounding helium atoms were studied in cryogenic gas targets at pressures between 0.1 and 9.0 bars and at temperatures between 5.5 and 7.0 K. The metastable state

(n,\mathcal{l})=(39,35)

showed a lifetime of 1.5 $\ensuremath{\mu}\mathrm{s}$, regardless of density, whereas the lifetime of the energetically lower-lying state

(37,34)

was found to shorten from 1.3 to 0.1 $\ensuremath{\mu}$s with increasing density. The lifetimes of the states

(38,34)

and

(36,33)

were determined to be 10 ns and 5 ns, respectively, showing the effects of the internal Auger process. When extrapolated to zero density, the measured lifetimes agreed with the results of calculations for the radiative and Auger widths. Using the fact that the state

(37,34)

becomes short lived at high density, the resonance $(38,35)\ensuremath{\rightarrow}(37,34)$ at 529.62 nm was detected.

(n,l)=(37,33)

and (32,31), were found to have decay rates two orders of magnitude larger than predicted by these calculations. The effect of coupling with near-lying electron-excited states is considered to be the reason for the anomaly of the (37, 33) state, as pointed out by Kartavtsev et al. [Phys. Rev. A

61,

062507 (2000)].

Calculations of low-energy collisions of antiprotons

\overline{p}

with helium atoms in the ground

(1\phantom{\rule{4pt}{0ex}}^{1}\mathit{S})

and metastable

(2\phantom{\rule{4pt}{0ex}}^{3}\mathit{S}

and

2\phantom{\rule{4pt}{0ex}}^{1}\mathit{S})

states are carried out by using a semiclassical method and by further assuming that one of the two electrons is passive. Antiproton capture to form antiprotonic helium $(\ensuremath{\rightarrow}\overline{p}{\mathrm{He}}^{+}+e)$ and breakup ionization $(\ensuremath{\rightarrow}\overline{p}+{\mathrm{He}}^{+}+e)$ are investigated. The energy dependence of the capture and ionization cross sections and the distributions of the product states are presented and compared with previous theoretical calculations. For the metastable helium targets, most of the

\overline{p}{\mathrm{He}}^{+}

atoms produced in the capture have long lifetimes against subsequent Auger decays and can be observed experimentally. For the ground-state targets, however, the formation of such long-lived states is rather a rare event at low collision energies.

Transitions between hyperfine structure states of antiprotonic

^4 \mathrm{He}

at collisions with medium atoms: interaction \emph{ab initio}

(\mathrm{\bar{p} He} ^+)

and

\mathrm{He}

, we have calculated the potential energy surface (PES) in the framework of unrestricted Hartree-Fock method taking into account electron correlations in the second-order perturbation theory (MP2). With this potential, the system of close-coupling equations for HFS channels is solved numerically. Cross sections and transition rates, shifts and broadening of M1 spectral lines are calculated. They are used to obtain a numerical solution of the master equation that determines the time evolution of the HFS-states density matrix. The results are compared with the experimental data and with the results of model calculation.

A very accurate variational expansion is suggested for calculation of nonrelativistic energies of the metastable antiprotonic helium atoms

{\mathrm{He}}^{+}\overline{p}.

This expansion reflects the dual atomic-molecular nature of the system. Convergence of the results as a function of the increasing sets of basis functions shows an accuracy better than ${10}^{\ensuremath{-}10}\mathrm{a}.\mathrm{u}.,$ two orders of magnitude better than in our previous calculations.