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Physical Review A

Radiative association of atomic hydrogen with antihydrogen at subkelvin temperatures

Bernard Zygelman, Alejandro Sáenz, Piotr Froelich, S. Jonsell, A. Dalgarno

Published Apr 19, 2001• 28 citations
Publisher

Abstract

Partial and total cross sections for the radiative association process $\mathrm{H}+\mathrm{H}\stackrel{\ensuremath{\rightarrow}}{\ifmmode\bar\else\textasciimacron\fi{}}\mathrm{H}\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{}+h\ensuremath{\nu}$ in the sub-Kelvin temperature regime are reported. We calculate the emission spectra for this process and suggest its utility as a diagnostic. The cross section for radiative association is found to have the value $\ensuremath{\sigma}=6.85\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}22} {\mathrm{cm}}^{2}/\sqrt{T}$, where T is an effective temperature. It is significantly smaller than the in-flight annihilation and fragmentation cross sections. We discuss the role that radiative association plays in the formation of a quasibound system of the $\mathrm{H}\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{}$ molecule.

DOI
10.1103/physreva.63.052722

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Partial and total cross sections for the radiative association process H+H\ifmmode\elseˉ\textasciimacron\fi\ensuremath→HH\ifmmode\elseˉ\textasciimacron\fi+h\ensuremathν\mathrm{H}+\mathrm{H}\stackrel{\ensuremath{\rightarrow}}{\ifmmode\bar\else\textasciimacron\fi{}}\mathrm{H}\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{}+h\ensuremath{\nu}H+H\ifmmode\elseˉ​\textasciimacron\fi\ensuremath→​HH\ifmmode\elseˉ​\textasciimacron\fi+h\ensuremathν in the sub-Kelvin temperature regime are reported. We calculate the emission spectra for this process and suggest its utility as a diagnostic. The cross section for radiative association is found to have the value \ensuremathσ=6.85\ifmmode×\else\texttimes\fi10\ensuremath−22cm2/T\ensuremath{\sigma}=6.85\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}22} {\mathrm{cm}}^{2}/\sqrt{T}\ensuremathσ=6.85\ifmmode×\else\texttimes\fi10\ensuremath−22cm2/T​, where T is an effective temperature. It is significantly smaller than the in-flight annihilation and fragmentation cross sections. We discuss the role that radiative association plays in the formation of a quasibound system of the HH\ifmmode\elseˉ\textasciimacron\fi\mathrm{H}\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{}HH\ifmmode\elseˉ​\textasciimacron\fi molecule.
The main properties of the interaction of ultralow-energy antiprotons $(E<~{10}^{\ensuremath{-}6}$ a.u.) with atomic hydrogen are established. They include the elastic and inelastic cross sections and protonium (Pn) formation spectrum. The inverse Auger process $(\mathrm{Pn}+\stackrel{\ensuremath{\rightarrow}}{e}\mathrm{H}+\overline{p})$ is taken into account in the framework of a unitary coupled-channel model. The annihilation cross section is found to be several times smaller than the predictions made by the black sphere absorption models. A family of p‾H\overline{p}\mathrm{H}p​H near-threshold metastable states is predicted. The dependence of protonium formation probability on the position of such near-threshold SSS-matrix singularities is analyzed. An estimation for the $\mathrm{H}\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{}$ annihilation cross section is obtained.
We present a theory that describes the interaction of hydrogen atoms with antihydrogen at subkelvin temperatures. The formalism includes a nonlocal complex optical potential, whose imaginary component describes the breakup of the H-H‾\text{H-}\overline{\mathrm{H}}H-H complex into positronium and protonium fragments. Using ab inito methods, we construct the imaginary part of the optical potential and calculate the cross sections for fragmentation in ultracold collisions of H\mathrm{H}H and H‾\overline{\mathrm{H}}H. We find a 3535%35 reduction in the value of the scattering length from that obtained in the Born-Oppenheimer approximation. We estimate the lifetimes for quasibound states of this complex to fragment into a protonium-positronium pair.
Matter-antimatter interactions are investigated using hydrogen-antihydrogen collisions as an example. Cross sections for elastic scattering and for the antihydrogen loss (either through the rearrangement reaction, resulting in formation of protonium and positronium according to H+&Hmacr;-->p&pmacr;+e(+)e(-), or via annihilation in flight) are calculated for the first time in a fully quantum mechanical approach. Implications for experiments intending to trap and cool antihydrogen are discussed.
Matter-antimatter interactions are investigated using hydrogen-antihydrogen collisions as an example. Cross sections for elastic scattering and for the antihydrogen loss (either through the rearrangement reaction, resulting in formation of protonium and positronium according to $\mathrm{H}+\overline{\mathrm{H}}\ensuremath{\rightarrow}p\overline{p}{+e}^{+}{e}^{\ensuremath{-}}$, or via annihilation in flight) are calculated for the first time in a fully quantum mechanical approach. Implications for experiments intending to trap and cool antihydrogen are discussed.
The stability of antimatter in contact with matter has been investigated. The interaction between hydrogen and antihydrogen is considered as the prototype reaction. We have focused interest on the rates for proton-antiproton and/or electron-positron annihilation during hydrogen-antihydrogen collisions at low energies. In particular, we have concentrated on the calculation of the rates for the rearrangement reaction leading to formation of protonium and positronium, ending inevitably in particle-antiparticle annihilation. The cross section for the rearrangement collision has been calculated in a fully quantum-mechanical treatment. Additionally, we have calculated cross sections for direct annihilation during the collision process, which was found to be comparable to the rearrangement cross section. The elastic cross section and its low-energy limit, given by the scattering length, have been calculated, allowing, by comparison to the inelastic processes, a prediction for the efficiency of cooling antihydrogen via collisions with ultracold hydrogen atoms.
The radiative association processes for Na+{\mathrm{Na}}^{+}Na+ colliding with 87Rb(5s)^{87}\mathrm{Rb}(5s)87Rb(5s) atoms have been investigated by using the quantum-mechanical method. The total and partial cross sections that associate to the specific rovibrational states are calculated rigorously in the energy range of ${10}^{\ensuremath{-}13}\ensuremath{-}1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$. The association cross sections display rich resonance structures. The ratios of rotationally resolved cross sections to total association cross sections and the ratios of vibrationally resolved cross sections to rotationally resolved cross sections are calculated and presented. For energies less than ${10}^{\ensuremath{-}9}\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$, association to $X\phantom{\rule{0.16em}{0ex}}{}^{2}{\ensuremath{\Sigma}}^{+}$ (J=1J=1J=1) dominates over all other association states. As the energy increases, each resonance of the total cross sections is associated with the given angular component of specific bound states. In the energy range of ${10}^{\ensuremath{-}13}\ensuremath{-}1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$, the vibrational states v=27v\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}27v=27 and v=28v\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}28v=28 are the most probable final states. The probability for the formation of molecular ion NaRb+{\mathrm{NaRb}}^{+}NaRb+ in the rovibrational states is discussed. The existence of Cooper minima in the radiative association cross sections is found and illustrated.