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

Mass polarization effect on the resonant energies of p¯ -He + ions and the protonium formation in low-energy antiproton–hydrogen-atom collisions

Xiao‐Min Tong, Naoki Toshima

Published Mar 16, 2012• 3 citations
Publisher

Abstract

We present a time-dependent method to investigate the mass polarization effect on the resonant energies of $\overline{p}\ensuremath{-}{\text{He}}^{+}$ and the state-specified protonium formation in low-energy antiproton--hydrogen-atom collisions in Jacobi coordinates. Comparing with our previous calculations in the $\mathsf{V}$-shaped coordinates by neglecting the mass polarization, we confirm that the mass polarization effect on the protonium formation is negligibly small. We also calculated the resonant energies of $\overline{p}\ensuremath{-}{\text{He}}^{+}$ in the $\mathsf{V}$ coordinates and Jacobi coordinates. The differences of the resonant energies between the two calculations are less than 4 meV. This also confirms that the mass polarization effect is negligibly small even in the resonant region.

DOI
10.1103/physreva.85.032709

Related papers

Ultraslow p¯ -H collisions in hyperspherical coordinates: Hydrogen and protonium channels

Brett D. Esry, H. R. Sadeghpour

The collision of an antiproton and a hydrogen atom at ultralow energies is described in hyperspherical coordinates. An adiabatic approximation leads to potential-energy curves that can be used to describe the dynamics of capture in the $\overline{p}\ensuremath{-}\mathrm{H}(1s)$ collision. A unified formulation of the collision and capture processes leading to formation of $p\overline{p}$ bound states emerges. Both $\mathrm{Pn}{(\mathrm{nl})\ensuremath{-}e}^{\ensuremath{-}}$ ``atomic-type'' and $\overline{p}\ensuremath{-}\mathrm{H}{(n}^{\ensuremath{'}}{l}^{\ensuremath{'}})$ ``molecular-type'' states are represented. These potential curves are calculated to more than 10 000 protonium Bohr radii, where low-energy antiprotons are stopped in collisions with hydrogen atoms. Elastic and inelastic partial and total protonium formation cross sections in the mass-scaled $\overline{p}$-H system are calculated. The existence of protonium negative (or positive) ion in its ground and excited states is discussed.

Physical Review A•Jan 14, 2003•31 citations

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.

Physical Review A•Apr 9, 2015•9 citations

Resonance recombination of spin-polarized atomic hydrogen at low temperatures

M. W. Reynolds, W. N. Hardy

In sufficiently large magnetic fields, the weakly bound levels of H2 acquire finite lifetimes owing to hyperfine predissociation and become manifest as scattering resonances in spin-polarized atomic hydrogen (H↓). In this work we investigate in detail the contribution to the reaction kinetics in H↓ due to the resonance, denoted [Formula: see text], arising from the predissociation of the (v,J) = (14,4) level of H2. To characterize the formation and disintegration of [Formula: see text], we calculate the predissociation as a function of both the applied magnetic field and the dissociation energy, D, of the level. Recombination occurs when [Formula: see text] is stabilized in collisions that cause transitions to lower molecular levels. For low H↓, densities, collisions with atoms of the saturated 4He vapour dominate; we calculate the cross section in the distorted wave Born approximation and also use a coupled-channels approach. At higher densities, stabilization occurs in collisions with H↓ as well; the effect of proton exchange between the atom and the molecule is derived. Previous experiments, analyzed neglecting proton exchange, are reanalyzed including this; the dissociation energy D is not as well determined by the data as was previously thought. Prospects for future experiments are discussed.

Canadian Journal of Physics•May 1, 1988•13 citations

Isotope effects in complex scattering lengths for He collisions with molecular hydrogen

J. L. Nolte, Benhui Yang, Phillip C. Stancil +4 more

We examine the effect of theoretically varying the collision-system reduced mass in collisions of He with vibrationally excited molecular hydrogen and observe zero-energy resonances for select atomic ``hydrogen'' masses less than 1 u or a ``helium'' mass of $1.95$ u. Complex scattering lengths, state-to-state vibrational quenching cross sections, and a low-energy elastic scattering resonance are all studied as a function of collision-system reduced mass. Experimental observations of these phenomena in the cold and ultracold regimes for collisions of $^{3}\mathrm{He}$ and $^{4}\mathrm{He}$ with ${\mathrm{H}}_{2}$, HD, HT, and DT should be feasible in the near future.

Physical Review A•Jan 8, 2010•12 citations

Collisional Stark Transitions and Induced Annihilation of Cold Antiprotonic Helium Ions

Grigory Ya. Korenman, S. N. Yudin

Stark transitions and induced annihilation of antiproton in the collisions of antiprotonic helium ions (\bar{p}He^{+2})_{nl} with He atoms at very low energy (~ 10 K) are considered in the framework of quantum coupled-channels method taking into account all the states with different l at given n~30, including the annihilating ns and np-states. Elastic scattering, Stark transitions and induced annihilation during collisions are produced by scalar and dipole terms in the interaction. It is shown that the most important contribution to the processes comes from the long-range polarization interaction. Admixtures of the ns and np-states to the states with higher l during collisions induce the effective annihilation cross sections for the initial l up to 15, but don't affect the Stark cross sections for the initial states nearly to circular orbits. Total rates of the Stark transitions from the circular orbits with n=28 - 32, averaged over the thermal motion, are compatible with the recent ASACUSA data. Isotope effect as well as the dependence on n are also qualitatively agree with the experiment.

arXiv:0711.4505•Nov 28, 2007•0 citations

Collisions of cold antiprotonic helium atoms and ions with ordinary helium atoms

Grigory Ya. Korenman, S. N. Yudin

We consider two types of collisional processes with excited antiprotonic helium systems. (i) Transitions between hyperfine structure sublevels in ( He + ) n LFJ are considered at T ≤ 25 K using the coupled-channels method and a model of scalar and tensor interactions between antiprotonic and ordinary He atoms. Inelastic cross sections for the single and double spin-flip transitions are less than elastic ones by four and seven orders of magnitude, respectively. The cross sections show a resonance behaviour at E ∼ 1–4 K, and therefore the relaxation rates, density shift and broadening of the M1 spectral lines decrease with increasing temperature from 3 to 25 K. (ii) Stark transitions and induced annihilation during collisions of the ( He 2+ ) nl ion with He atoms at E ∼ 10 K are considered for all l -states at n ∼ 30 in the framework of the coupled-channels method. In order to take into account complex energy shifts of the ns and np -states, we introduce modified boundary conditions in these channels. The main contribution to elastic scattering, Stark transitions and induced annihilations during collisions comes from the long-range polarization interaction. Admixtures of ns and np -states to nl -states ( l ≥ 2) during collisions induce the effective annihilation cross sections for the initial l up to 15, but don't affect the Stark cross sections for states with nearly-circular orbits. The calculated values for both types of processes are compatible with recent experimental data.

Journal of Physics Conference Series•Nov 1, 2007•9 citations
We present a time-dependent method to investigate the mass polarization effect on the resonant energies of p‾\ensuremath−He+\overline{p}\ensuremath{-}{\text{He}}^{+}p​\ensuremath−He+ and the state-specified protonium formation in low-energy antiproton--hydrogen-atom collisions in Jacobi coordinates. Comparing with our previous calculations in the V\mathsf{V}V-shaped coordinates by neglecting the mass polarization, we confirm that the mass polarization effect on the protonium formation is negligibly small. We also calculated the resonant energies of p‾\ensuremath−He+\overline{p}\ensuremath{-}{\text{He}}^{+}p​\ensuremath−He+ in the V\mathsf{V}V coordinates and Jacobi coordinates. The differences of the resonant energies between the two calculations are less than 4 meV. This also confirms that the mass polarization effect is negligibly small even in the resonant region.
The collision of an antiproton and a hydrogen atom at ultralow energies is described in hyperspherical coordinates. An adiabatic approximation leads to potential-energy curves that can be used to describe the dynamics of capture in the $\overline{p}\ensuremath{-}\mathrm{H}(1s)$ collision. A unified formulation of the collision and capture processes leading to formation of pp‾p\overline{p}pp​ bound states emerges. Both $\mathrm{Pn}{(\mathrm{nl})\ensuremath{-}e}^{\ensuremath{-}}$ ``atomic-type'' and $\overline{p}\ensuremath{-}\mathrm{H}{(n}^{\ensuremath{'}}{l}^{\ensuremath{'}})$ ``molecular-type'' states are represented. These potential curves are calculated to more than 10 000 protonium Bohr radii, where low-energy antiprotons are stopped in collisions with hydrogen atoms. Elastic and inelastic partial and total protonium formation cross sections in the mass-scaled p‾\overline{p}p​-H system are calculated. The existence of protonium negative (or positive) ion in its ground and excited states is discussed.
Calculations of low-energy collisions of antiprotons p‾\overline{p}p​ with helium atoms in the ground (11S)(1\phantom{\rule{4pt}{0ex}}^{1}\mathit{S})(11S) and metastable (23S(2\phantom{\rule{4pt}{0ex}}^{3}\mathit{S}(23S and 21S)2\phantom{\rule{4pt}{0ex}}^{1}\mathit{S})21S) 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 p‾He+\overline{p}{\mathrm{He}}^{+}p​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.
In sufficiently large magnetic fields, the weakly bound levels of H2 acquire finite lifetimes owing to hyperfine predissociation and become manifest as scattering resonances in spin-polarized atomic hydrogen (H↓). In this work we investigate in detail the contribution to the reaction kinetics in H↓ due to the resonance, denoted [Formula: see text], arising from the predissociation of the (v,J) = (14,4) level of H2. To characterize the formation and disintegration of [Formula: see text], we calculate the predissociation as a function of both the applied magnetic field and the dissociation energy, D, of the level. Recombination occurs when [Formula: see text] is stabilized in collisions that cause transitions to lower molecular levels. For low H↓, densities, collisions with atoms of the saturated 4He vapour dominate; we calculate the cross section in the distorted wave Born approximation and also use a coupled-channels approach. At higher densities, stabilization occurs in collisions with H↓ as well; the effect of proton exchange between the atom and the molecule is derived. Previous experiments, analyzed neglecting proton exchange, are reanalyzed including this; the dissociation energy D is not as well determined by the data as was previously thought. Prospects for future experiments are discussed.
We examine the effect of theoretically varying the collision-system reduced mass in collisions of He with vibrationally excited molecular hydrogen and observe zero-energy resonances for select atomic ``hydrogen'' masses less than 1 u or a ``helium'' mass of 1.951.951.95 u. Complex scattering lengths, state-to-state vibrational quenching cross sections, and a low-energy elastic scattering resonance are all studied as a function of collision-system reduced mass. Experimental observations of these phenomena in the cold and ultracold regimes for collisions of 3He^{3}\mathrm{He}3He and 4He^{4}\mathrm{He}4He with H2{\mathrm{H}}_{2}H2​, HD, HT, and DT should be feasible in the near future.
Stark transitions and induced annihilation of antiproton in the collisions of antiprotonic helium ions (\bar{p}He^{+2})_{nl} with He atoms at very low energy (~ 10 K) are considered in the framework of quantum coupled-channels method taking into account all the states with different l at given n~30, including the annihilating ns and np-states. Elastic scattering, Stark transitions and induced annihilation during collisions are produced by scalar and dipole terms in the interaction. It is shown that the most important contribution to the processes comes from the long-range polarization interaction. Admixtures of the ns and np-states to the states with higher l during collisions induce the effective annihilation cross sections for the initial l up to 15, but don't affect the Stark cross sections for the initial states nearly to circular orbits. Total rates of the Stark transitions from the circular orbits with n=28 - 32, averaged over the thermal motion, are compatible with the recent ASACUSA data. Isotope effect as well as the dependence on n are also qualitatively agree with the experiment.
We consider two types of collisional processes with excited antiprotonic helium systems. (i) Transitions between hyperfine structure sublevels in ( He + ) n LFJ are considered at T ≤ 25 K using the coupled-channels method and a model of scalar and tensor interactions between antiprotonic and ordinary He atoms. Inelastic cross sections for the single and double spin-flip transitions are less than elastic ones by four and seven orders of magnitude, respectively. The cross sections show a resonance behaviour at E ∼ 1–4 K, and therefore the relaxation rates, density shift and broadening of the M1 spectral lines decrease with increasing temperature from 3 to 25 K. (ii) Stark transitions and induced annihilation during collisions of the ( He 2+ ) nl ion with He atoms at E ∼ 10 K are considered for all l -states at n ∼ 30 in the framework of the coupled-channels method. In order to take into account complex energy shifts of the ns and np -states, we introduce modified boundary conditions in these channels. The main contribution to elastic scattering, Stark transitions and induced annihilations during collisions comes from the long-range polarization interaction. Admixtures of ns and np -states to nl -states ( l ≥ 2) during collisions induce the effective annihilation cross sections for the initial l up to 15, but don't affect the Stark cross sections for states with nearly-circular orbits. The calculated values for both types of processes are compatible with recent experimental data.