Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Exotic molecules consisting of an antiproton and a hydrogen atom

Kazuhiro Sakimoto

Published Oct 8, 2018• 3 citations
Publisher

Abstract

A theoretical study is conducted on the stability of exotic antiproton-hydrogen molecular anions ($\overline{p}\mathrm{H}$), which in the separated atom limit correlate with $\overline{p}+\mathrm{H}(n=2)$ ($n$ being the principal quantum number). The $\overline{p}\mathrm{H}$ molecule in the electronic ground state is highly unstable due to pair annihilation and autodetachment ($\ensuremath{\rightarrow}\overline{p}p+e$). However, if the $\overline{p}\mathrm{H}$ molecule is electronically excited, the molecular stability can be drastically improved. Since the excited states of the $\mathrm{H}$ atom have accidental degeneracy, the asymptotic form of the Born-Oppenheimer potential curve of $\overline{p}+\mathrm{H}(n=2)$ behaves as $1/{R}^{2}$ ($R$ being the relative distance), which can play a critical role in the bonding and stability of the molecule. It is found that the $\overline{p}\mathrm{H}$ molecule in the first electronic excited state and in a high rotational state is sufficiently stable and has a lifetime dominated by spontaneous radiative emission ($\ensuremath{\rightarrow}\overline{p}+\mathrm{H}+h\ensuremath{\nu}$). The $\overline{p}\mathrm{H}$ system is dynamically similar to ${\mathrm{H}}_{2}{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{-}}$, which had been commonly considered to be unstable due to autodetachment. However, recent measurements of ion-beam sputtering unambiguously verified the existence of long-lived ${\mathrm{H}}_{2}{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{-}}$ molecules in high rotational states. This suggests that the $\overline{p}\mathrm{H}$ molecules may actually be created if one employs experimental means such as the chemical sputtering of hydrogen-rich targets with $\overline{p}$ beams.

DOI
10.1103/physreva.98.042503

Related papers

Moleculelike metastable states of antiprotonic and mesic helium

Isao Shimamura

The exotic helium atom, consisting of a helium nucleus ${\mathrm{He}}^{2+}$, an electron ${\mathit{e}}^{\mathrm{\ensuremath{-}}}$, and a massive, negatively charged particle ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$, such as an antiproton (p\ifmmode\bar\else\textasciimacron\fi{}) or a kaon (${\mathit{K}}^{\mathrm{\ensuremath{-}}}$), is studied theoretically. This exotic atom is more like a polar molecule with two nuclei ${\mathrm{He}}^{2+}$ and ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$, if ${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ is in a low-lying orbital and ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ is in a highly excited orbital. Such states are generally formed in the capture of ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ by helium. The Born-Oppenheimer (BO) separation of the ${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ motion and the ${\mathrm{He}}^{2+}$-${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ motion is a good approximation for these states, and affords a transparent, unified perspective of exotic helium with different ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ and different isotopes of ${\mathrm{He}}^{2+}$. A propensity rule that favors small transition energies (except for the smallest one) is found for radiative emission by low vibrational and high rotational levels. This rule resembles the selection rule for infrared emission by the usual diatomic polar molecules, and contradicts the conventional expectation that radiative transitions in exotic atoms favor larger transition energies. The radiative lifetimes \ensuremath{\tau} of highly excited states formed immediately after the capture of ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ are of the order of \ensuremath{\mu}sec for $^{4}\mathrm{He}^{2+}$-p\ifmmode\bar\else\textasciimacron\fi{}-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ and $^{3}\mathrm{He}^{2+}$-p\ifmmode\bar\else\textasciimacron\fi{}-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$, and those for $^{4}\mathrm{He}^{2+}$-${\mathit{K}}^{\mathrm{\ensuremath{-}}}$-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ are about half the values for the antiprotonic helium.The effect of the electronic charge polarization by ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ on \ensuremath{\tau} is explained quantitatively in a simple picture in terms of the molecular dipole moment. Low vibrational, high rotational states are described as circular or near-circular states in the atomic picture. They are stable against Auger decay, which the nonadiabatic perturbation on the BO states induces. An infinite series of bound \ensuremath{\Sigma} electronic states of exotic helium negative ions (${\mathrm{He}}^{2+}$-${\mathit{X}}^{\mathrm{\ensuremath{-}}}$-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$)-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ exists for any ${\mathrm{He}}^{2+}$-${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ distances R beyond 0.819 a.u. in the BO approximation. An infinite \ensuremath{\Pi} series exists for R>3.811 a.u., and an infinite \ensuremath{\Delta} series for R>9.532 a.u.

Physical Review A•Oct 1, 1992•135 citations

Metastable compound states of an antiproton and a hydrogen atom

Kazuhiro Sakimoto

The stability of antiproton-hydrogen compound states $(\overline{p}\mathrm{H})$ is investigated theoretically. The $\overline{p}\mathrm{H}$ compound state has decay channels of atomic electron detachment $(\ensuremath{\rightarrow}{e}^{\ensuremath{-}}+\overline{p}p)$ and hadronic pair $(\overline{p}\text{\ensuremath{-}}p)$ annihilation, and hence it cannot be permanently stable even if the dissociation channel $(\ensuremath{\rightarrow}\overline{p}+\mathrm{H})$ is energetically closed. In this paper, information on the metastable $\overline{p}\mathrm{H}$ states at energies below the dissociation limit is obtained by analyzing low-energy resonances in ${e}^{\ensuremath{-}}+\overline{p}p$ scattering. The scattering calculation is carried out by using an R-matrix method, which also allows for the annihilation channel simultaneously. The metastable states are found to be identified as vibrational levels supported by a Born-Oppenheimer (BO) potential. The energy-level widths attributed to the electron detachment and the annihilation are also calculated using a model based on the BO picture.

Physical Review A•Sep 29, 2014•4 citations

Antiprotonic helium atomcules

Sébastien Sauge

About 3% of antiprotons () stopped in helium are long-lived with microsecond lifetimes, against picoseconds in all other materials. This unusual longevity has been ascribed to the trapping of on metastable bound states in He+ helium atom-molecules thus named atomcules. Apart from their unique dual structure investigated by laser spectroscopy – a near-circular quasi-classical Rydberg atom with l ~ n – 1 ~ 37 or a special diatomic molecule with a negatively charged nucleus in high rotational state with J = l – the chemical physics aspects of their interaction with other atoms or molecules constitute an interesting topic for molecular physics. While atomcules may resist to million collisions in helium, molecular contaminants such as H2 are likely to destroy them in a single one, down to very low temperatures. In the Born-Oppenheimer framework, we interpret the molecular interaction obtained by ab initio quantum chemical calculations in terms of classical reactive channels, with activation barriers accounting for the experiments carried out in He and H2. From classical trajectory Monte Carlo simulations, we show that the thermalization stage strongly quenches initial populations, thus reduced to a recovered 3 % trapping fraction. This work illustrates the pertinence of chemical physics concepts to the study of exotic processes involving antimatter. New insights into the physico-chemistry of cold interstellar radicals are anticipated.

EPJ Web of Conferences•Jan 1, 2012•0 citations

Molecular effects on antiproton capture by H2 and the states of p¯p formed

James S. Cohen

Complete five-body dynamical calculations of antiproton $(\overline{p})$ capture by the hydrogen molecule $({\mathrm{H}}_{2})$ have been carried out using a generalization of the Kirschbaum-Wilets method (belonging to a class of quasiclassical methods sometimes called fermion molecular dynamics). The differences between capture by ${\mathrm{H}}_{2}$ and the H atom are found to be dramatic. The effects due to the two-center structure, rotational motions, and vibrational motions are distinguished. Of particular importance, the vibrational degree of freedom enables the molecule to capture antiprotons having lab energies above 100 eV, whereas atomic capture cuts off sharply above the ionization threshold of 27 eV (in the lab system). Antiproton capture by the atom is calculated by the same method as well as by the classical-trajectory Monte Carlo method, which is applicable only to the atom. The initial quantum numbers (assigned quasiclassically) of the $\overline{p}p$ formed are found to be shifted to significantly smaller values for the molecular target; the $n$ distribution is also narrower for the molecular target as compared with the atomic target.

Physical Review A•Nov 1, 1997•85 citations

Coupled channel study of antihydrogen-hydrogen molecular resonance state

Takuma Yamashita, Yasushi Kino

We report a theoretical study of antihydrogen-hydrogen molecular resonance states consisting of a positron, an antiproton, an electron and a proton. The four particles strongly correlate and show different character from the hydrogen molecule. Because of the non-separability of the positron and electron motions from the antiproton and proton motions, the adiabatic approximation breaks down at the short antiproton-proton distance. Based on a non-adiabatic method, we directly solve the four-body problem and obtain the resonance energies and widths. In order to examine the roles of positron–antiproton and electron–proton correlations as well as positron–electron and antiproton–proton correlations, we introduce two different types of coordinate systems. One is suited for describing an antihydrogen–hydrogen configuration, and the other is a positronium–protonium configuration. The antihydrogen–hydrogen configuration contributes to the existence of the molecular resonance states, and the positronium–protonium configuration makes the resonance states unstable. Mixing of the two configurations results in an antihydrogen-hydrogen molecular resonance state, and the resonance state has an energy of −0.077 9(3) a.u. from the antihydrogen–hydrogen dissociation threshold with its lifetime 16 (2) fs.

•Jan 1, 2018•0 citations

Coupled channel study of antihydrogen-hydrogen molecular resonance state

Takuma Yamashita, Yasushi Kino

We report a theoretical study of antihydrogen-hydrogen molecular resonance states consisting of a positron, an antiproton, an electron and a proton. The four particles strongly correlate and show different character from the hydrogen molecule. Because of the non-separability of the positron and electron motions from the antiproton and proton motions, the adiabatic approximation breaks down at the short antiproton-proton distance. Based on a non-adiabatic method, we directly solve the four-body problem and obtain the resonance energies and widths. In order to examine the roles of positron–antiproton and electron–proton correlations as well as positron–electron and antiproton–proton correlations, we introduce two different types of coordinate systems. One is suited for describing an antihydrogen–hydrogen configuration, and the other is a positronium–protonium configuration. The antihydrogen–hydrogen configuration contributes to the existence of the molecular resonance states, and the positronium–protonium configuration makes the resonance states unstable. Mixing of the two configurations results in an antihydrogen-hydrogen molecular resonance state, and the resonance state has an energy of −0.077 9(3) a.u. from the antihydrogen–hydrogen dissociation threshold with its lifetime 16 (2) fs.

JJAP Conference Proceedings•Jan 1, 2018•1 citation
A theoretical study is conducted on the stability of exotic antiproton-hydrogen molecular anions (p‾H\overline{p}\mathrm{H}p​H), which in the separated atom limit correlate with p‾+H(n=2)\overline{p}+\mathrm{H}(n=2)p​+H(n=2) (nnn being the principal quantum number). The p‾H\overline{p}\mathrm{H}p​H molecule in the electronic ground state is highly unstable due to pair annihilation and autodetachment (\ensuremath→p‾p+e\ensuremath{\rightarrow}\overline{p}p+e\ensuremath→p​p+e). However, if the p‾H\overline{p}\mathrm{H}p​H molecule is electronically excited, the molecular stability can be drastically improved. Since the excited states of the H\mathrm{H}H atom have accidental degeneracy, the asymptotic form of the Born-Oppenheimer potential curve of p‾+H(n=2)\overline{p}+\mathrm{H}(n=2)p​+H(n=2) behaves as 1/R21/{R}^{2}1/R2 (RRR being the relative distance), which can play a critical role in the bonding and stability of the molecule. It is found that the p‾H\overline{p}\mathrm{H}p​H molecule in the first electronic excited state and in a high rotational state is sufficiently stable and has a lifetime dominated by spontaneous radiative emission (\ensuremath→p‾+H+h\ensuremathν\ensuremath{\rightarrow}\overline{p}+\mathrm{H}+h\ensuremath{\nu}\ensuremath→p​+H+h\ensuremathν). The p‾H\overline{p}\mathrm{H}p​H system is dynamically similar to H2\ensuremath−{\mathrm{H}}_{2}{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{-}}H2​\ensuremath−, which had been commonly considered to be unstable due to autodetachment. However, recent measurements of ion-beam sputtering unambiguously verified the existence of long-lived H2\ensuremath−{\mathrm{H}}_{2}{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{-}}H2​\ensuremath− molecules in high rotational states. This suggests that the p‾H\overline{p}\mathrm{H}p​H molecules may actually be created if one employs experimental means such as the chemical sputtering of hydrogen-rich targets with p‾\overline{p}p​ beams.
The exotic helium atom, consisting of a helium nucleus He2+{\mathrm{He}}^{2+}He2+, an electron ${\mathit{e}}^{\mathrm{\ensuremath{-}}}$, and a massive, negatively charged particle ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$, such as an antiproton (p\ifmmode\bar\else\textasciimacron\fi{}) or a kaon (${\mathit{K}}^{\mathrm{\ensuremath{-}}}$), is studied theoretically. This exotic atom is more like a polar molecule with two nuclei He2+{\mathrm{He}}^{2+}He2+ and ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$, if ${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ is in a low-lying orbital and ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ is in a highly excited orbital. Such states are generally formed in the capture of ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ by helium. The Born-Oppenheimer (BO) separation of the ${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ motion and the He2+{\mathrm{He}}^{2+}He2+-${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ motion is a good approximation for these states, and affords a transparent, unified perspective of exotic helium with different ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ and different isotopes of He2+{\mathrm{He}}^{2+}He2+. A propensity rule that favors small transition energies (except for the smallest one) is found for radiative emission by low vibrational and high rotational levels. This rule resembles the selection rule for infrared emission by the usual diatomic polar molecules, and contradicts the conventional expectation that radiative transitions in exotic atoms favor larger transition energies. The radiative lifetimes \ensuremath{\tau} of highly excited states formed immediately after the capture of ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ are of the order of \ensuremath{\mu}sec for 4He2+^{4}\mathrm{He}^{2+}4He2+-p\ifmmode\bar\else\textasciimacron\fi{}-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ and 3He2+^{3}\mathrm{He}^{2+}3He2+-p\ifmmode\bar\else\textasciimacron\fi{}-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$, and those for 4He2+^{4}\mathrm{He}^{2+}4He2+-${\mathit{K}}^{\mathrm{\ensuremath{-}}}$-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ are about half the values for the antiprotonic helium.The effect of the electronic charge polarization by ${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ on \ensuremath{\tau} is explained quantitatively in a simple picture in terms of the molecular dipole moment. Low vibrational, high rotational states are described as circular or near-circular states in the atomic picture. They are stable against Auger decay, which the nonadiabatic perturbation on the BO states induces. An infinite series of bound \ensuremath{\Sigma} electronic states of exotic helium negative ions (He2+{\mathrm{He}}^{2+}He2+-${\mathit{X}}^{\mathrm{\ensuremath{-}}}$-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$)-${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ exists for any He2+{\mathrm{He}}^{2+}He2+-${\mathit{X}}^{\mathrm{\ensuremath{-}}}$ distances R beyond 0.819 a.u. in the BO approximation. An infinite \ensuremath{\Pi} series exists for R>3.811 a.u., and an infinite \ensuremath{\Delta} series for R>9.532 a.u.
The stability of antiproton-hydrogen compound states (p‾H)(\overline{p}\mathrm{H})(p​H) is investigated theoretically. The p‾H\overline{p}\mathrm{H}p​H compound state has decay channels of atomic electron detachment $(\ensuremath{\rightarrow}{e}^{\ensuremath{-}}+\overline{p}p)$ and hadronic pair $(\overline{p}\text{\ensuremath{-}}p)$ annihilation, and hence it cannot be permanently stable even if the dissociation channel $(\ensuremath{\rightarrow}\overline{p}+\mathrm{H})$ is energetically closed. In this paper, information on the metastable p‾H\overline{p}\mathrm{H}p​H states at energies below the dissociation limit is obtained by analyzing low-energy resonances in ${e}^{\ensuremath{-}}+\overline{p}p$ scattering. The scattering calculation is carried out by using an R-matrix method, which also allows for the annihilation channel simultaneously. The metastable states are found to be identified as vibrational levels supported by a Born-Oppenheimer (BO) potential. The energy-level widths attributed to the electron detachment and the annihilation are also calculated using a model based on the BO picture.
About 3% of antiprotons () stopped in helium are long-lived with microsecond lifetimes, against picoseconds in all other materials. This unusual longevity has been ascribed to the trapping of on metastable bound states in He+ helium atom-molecules thus named atomcules. Apart from their unique dual structure investigated by laser spectroscopy – a near-circular quasi-classical Rydberg atom with l ~ n – 1 ~ 37 or a special diatomic molecule with a negatively charged nucleus in high rotational state with J = l – the chemical physics aspects of their interaction with other atoms or molecules constitute an interesting topic for molecular physics. While atomcules may resist to million collisions in helium, molecular contaminants such as H2 are likely to destroy them in a single one, down to very low temperatures. In the Born-Oppenheimer framework, we interpret the molecular interaction obtained by ab initio quantum chemical calculations in terms of classical reactive channels, with activation barriers accounting for the experiments carried out in He and H2. From classical trajectory Monte Carlo simulations, we show that the thermalization stage strongly quenches initial populations, thus reduced to a recovered 3 % trapping fraction. This work illustrates the pertinence of chemical physics concepts to the study of exotic processes involving antimatter. New insights into the physico-chemistry of cold interstellar radicals are anticipated.
Complete five-body dynamical calculations of antiproton (p‾)(\overline{p})(p​) capture by the hydrogen molecule (H2)({\mathrm{H}}_{2})(H2​) have been carried out using a generalization of the Kirschbaum-Wilets method (belonging to a class of quasiclassical methods sometimes called fermion molecular dynamics). The differences between capture by H2{\mathrm{H}}_{2}H2​ and the H atom are found to be dramatic. The effects due to the two-center structure, rotational motions, and vibrational motions are distinguished. Of particular importance, the vibrational degree of freedom enables the molecule to capture antiprotons having lab energies above 100 eV, whereas atomic capture cuts off sharply above the ionization threshold of 27 eV (in the lab system). Antiproton capture by the atom is calculated by the same method as well as by the classical-trajectory Monte Carlo method, which is applicable only to the atom. The initial quantum numbers (assigned quasiclassically) of the p‾p\overline{p}pp​p formed are found to be shifted to significantly smaller values for the molecular target; the nnn distribution is also narrower for the molecular target as compared with the atomic target.
We report a theoretical study of antihydrogen-hydrogen molecular resonance states consisting of a positron, an antiproton, an electron and a proton. The four particles strongly correlate and show different character from the hydrogen molecule. Because of the non-separability of the positron and electron motions from the antiproton and proton motions, the adiabatic approximation breaks down at the short antiproton-proton distance. Based on a non-adiabatic method, we directly solve the four-body problem and obtain the resonance energies and widths. In order to examine the roles of positron–antiproton and electron–proton correlations as well as positron–electron and antiproton–proton correlations, we introduce two different types of coordinate systems. One is suited for describing an antihydrogen–hydrogen configuration, and the other is a positronium–protonium configuration. The antihydrogen–hydrogen configuration contributes to the existence of the molecular resonance states, and the positronium–protonium configuration makes the resonance states unstable. Mixing of the two configurations results in an antihydrogen-hydrogen molecular resonance state, and the resonance state has an energy of −0.077 9(3) a.u. from the antihydrogen–hydrogen dissociation threshold with its lifetime 16 (2) fs.
We report a theoretical study of antihydrogen-hydrogen molecular resonance states consisting of a positron, an antiproton, an electron and a proton. The four particles strongly correlate and show different character from the hydrogen molecule. Because of the non-separability of the positron and electron motions from the antiproton and proton motions, the adiabatic approximation breaks down at the short antiproton-proton distance. Based on a non-adiabatic method, we directly solve the four-body problem and obtain the resonance energies and widths. In order to examine the roles of positron–antiproton and electron–proton correlations as well as positron–electron and antiproton–proton correlations, we introduce two different types of coordinate systems. One is suited for describing an antihydrogen–hydrogen configuration, and the other is a positronium–protonium configuration. The antihydrogen–hydrogen configuration contributes to the existence of the molecular resonance states, and the positronium–protonium configuration makes the resonance states unstable. Mixing of the two configurations results in an antihydrogen-hydrogen molecular resonance state, and the resonance state has an energy of −0.077 9(3) a.u. from the antihydrogen–hydrogen dissociation threshold with its lifetime 16 (2) fs.