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Atoms

Analytical Results for the Three-Body Radiative Attachment Rate Coefficient, with Application to the Positive Antihydrogen Ion H+

Jack C. Straton

Published Apr 20, 2020• 2 citations
Publisher

Abstract

To overcome the numerical difficulties inherent in the Maxwell–Boltzmann integral of the velocity-weighted cross section that gives the radiative attachment rate coefficient α R A for producing the negative hydrogen ion H − or its antimatter equivalent, the positive antihydrogen ion H ¯ + , we found the analytic form for this integral. This procedure is useful for temperatures below 700 K, the region for which the production of H ¯ + has potential use as an intermediate stage in the cooling of antihydrogen to ultra-cold (sub-mK) temperatures for spectroscopic studies and probing the gravitational interaction of the anti-atom. Our results, utilizing a 50-term explicitly correlated exponential wave function, confirm our prior numerical results.

DOI
10.3390/atoms8020013

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To overcome the numerical difficulties inherent in the Maxwell–Boltzmann integral of the velocity-weighted cross section that gives the radiative attachment rate coefficient α R A for producing the negative hydrogen ion H − or its antimatter equivalent, the positive antihydrogen ion H ¯ + , we found the analytic form for this integral. This procedure is useful for temperatures below 700 K, the region for which the production of H ¯ + has potential use as an intermediate stage in the cooling of antihydrogen to ultra-cold (sub-mK) temperatures for spectroscopic studies and probing the gravitational interaction of the anti-atom. Our results, utilizing a 50-term explicitly correlated exponential wave function, confirm our prior numerical results.
Abstract We provide an estimate of the cross section for the radiative attachment of a second positron into the state of the ion that uses a 200-term two-positron wave function composed of explicitly correlated exponentials. This is done by analytically integrating the six-dimensional, three body photoionization integrals that enter into this result (and those utilizing, the alternative, Hylleraas wave functions) and applying the principle of detailed balance. Finally, we obtain the rate coefficient for attaching a second positron to antihydrogen as a function of temperature via a numerical integral that is a Maxwell–Boltzmann distribution of the product of positron velocity and cross section. Our motivation in studying the production of lies in its potential use as an intermediate stage in the cooling of antihydrogen to ultra-cold (sub-mK) temperatures for spectroscopic studies and probing the gravitational interaction of the anti-atom. Estimates of the reaction rates are given for positron temperatures T e in the range from 50 K to 5 K.
On the production of the positive antihydrogen ion Hˉ+{{{\rm \bar{H}}}^{+}}Hˉ+ via radiative attachment
We provide an estimate of the cross section for the radiative attachment of a second positron into the state of the ion using Ohmura and Ohmura's (1960 Phys. Rev. 118 154 ) effective range theory and the principle of detailed balance. The ion can potentially be created using interactions of positrons with trapped antihydrogen, and our analysis includes a discussion in which estimates of production rates are given. Motivations to produce include its potential use as an intermediary to cool antihydrogen to ultra-cold (sub-mK) temperatures for a variety of studies, including spectroscopy and probing the gravitational interaction of the anti-atom.
Abstract We present a 4-body calculation of scattering between an antihydrogen atom ( H ¯ ) and a positronium (Ps) aiming at the prediction of cross sections for the production of antihydrogen positive ions H ¯ + . The antihydrogen positive ions are expected to be a useful source of ultra-cold anti-atoms for the test of matter-antimatter gravity. We convert the Schrödinger equation to a set of coupled integro-differential equations that involve intermediate states which facilitate the internal region description of the scattering wavefunction. They are solved using a compact finite difference method. Our framework is extended to scattering between an excited Ps and H. Cross sections of the reactions, Ps (1s/2s/3s) H ¯ → e − + H ¯ + , in s-wave collisions, are calculated. It is found that the reactions originating from Ps (1s/2s) + H ¯ produce H ¯ + with a constant cross section within 0.05 eV above the threshold while the reaction cross section from Ps (3s) decreases as the collision energy increases in the same energy interval. Just above the threshold, the cross section of H ¯ + production from Ps (3s) + H ¯ in s-wave collision is 7.8 times larger than that from Ps (1s) + H ¯ in s-wave and 2.3 times larger than that from Ps (2s) + H ¯ in s-wave. The near-threshold de-excitation reaction from Ps (3s) + H ¯ occurs more rapidly than the H ¯ + production.
Synopsis We present the 4-body calculation of the antihydrogen-positronium scattering aiming at the prediction of cross sections for the production of antihydrogen positive ions. The latter are expected to be a useful source of ultra-cold atoms for the test of matter-antimatter gravity. We convert the Schrödinger equation to a set of coupled integro-differential equations that involve intermediate states and are solved using the compact finite difference method. We will present the investigation of the rearrangement reaction between the ground-state antihydrogen atom and the excited positronium.
Antihydrogen is at the focus of antimatter research.One of the main aims is to perform a direct test of the fundamental CPT symmetry by comparing the spectroscopic properties of the ground-state antihydrogen atom with those of the hydrogen atom.In current experiments synthetized antihydrogen is formed mainly via the three-body recombination process after mixing positron and antiproton clouds together in a cryogenic trap.The major three-body formation process populates mainly highly excited Rydberg states, therefore before the antihydrogen atoms reach the ground-state additional processes may take place, such as collisional (de)excitation, ionization and spontaneous or stimulated radiative transitions.We have used a classical-trajectory Monte Carlo (CTMC) code along with regular atomic codes to generate a scattering database of rate coefficients in various experimentally achievable magnetic field strengths and in low temperature positron plasma conditions.We used these rates to calculate the evolution of level population of antihydrogen during formation, scattering and flight within our experimental conditions [1].The model and the results are presented.
Recent calculations have suggested that it may be feasible to produce antihydrogen molecular ions in the near future [Zammit et al., Phys. Rev. A 100, 042709 (2019)]. The proposed scheme would laser excite cold antihydrogen H‾(1s)\overline{\text{H}}(1s)H(1s) atoms held in a magnetic-field minimum trap and the resulting metastable H‾(2s)\overline{\text{H}}(2s)H(2s) atoms would interact to form the antihydrogen molecular ion, ${\overline{\text{H}}}_{2}{}^{\ensuremath{-}}$, by associative ionization. Estimates for the efficiencies of the proposed formation and depletion processes relied on low-energy extrapolations of rate coefficients that were computed at thermal energies. In the present work, we provide quantum calculations of the rate coefficients for associative ionization and for the competing Penning ionization process, which would deplete the population of trapped H‾\overline{\text{H}}H. In contrast to the low-energy extrapolations, it is found that Penning ionization is the dominant ionization process at all temperatures and the relative efficiency of associative ionization is within a factor of 3 at the low temperatures required by the experimental scheme. Rate constants for single and double excitation transfer are computed as possible loss mechanisms and all rates are found to be small compared to spin-flip decay rates from Stark-induced mixing with H‾(2p\overline{\text{H}}(2pH(2p) states.