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Physical Review A

Near-threshold behavior of positronium-antiproton scattering

I. I. Fabrikant, Alexander Bray, Alisher S. Kadyrov, Igor Bray

Published Jul 5, 2016• 23 citations
Publisher

Abstract

Using the convergent close-coupling theory we study the threshold behavior of cross sections for positronium (Ps) of energy $E$ scattering on antiprotons. In the case of $\mathrm{Ps}(1s$) elastic scattering, simple power laws are observed for all partial waves studied. The partial-wave summed cross section is nearly constant, and dominates the antihydrogen formation cross section at all considered energies, even though the latter is exothermic and behaves as $1/{E}^{1/2}$. For $\mathrm{Ps}(2s$), oscillations spanning orders of magnitude on top of the $1/E$ behavior are found in the elastic and quasielastic cross sections. The antihydrogen formation is influenced by dipole-supported resonances below the threshold of inelastic processes. Resonance energies form a geometric progression relative to the threshold. The exothermic antihydrogen formation cross sections behave as $1/E$ at low energies, but are oscillation free. We demonstrate that all these rich features are reproduced by the threshold theory developed by Gailitis [J. Phys. B: At. Mol. Phys. 15, 3423 (1982)].

DOI
10.1103/physreva.94.012701

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Using the convergent close-coupling theory we study the threshold behavior of cross sections for positronium (Ps) of energy EEE scattering on antiprotons. In the case of Ps(1s\mathrm{Ps}(1sPs(1s) elastic scattering, simple power laws are observed for all partial waves studied. The partial-wave summed cross section is nearly constant, and dominates the antihydrogen formation cross section at all considered energies, even though the latter is exothermic and behaves as 1/E1/21/{E}^{1/2}1/E1/2. For Ps(2s\mathrm{Ps}(2sPs(2s), oscillations spanning orders of magnitude on top of the 1/E1/E1/E behavior are found in the elastic and quasielastic cross sections. The antihydrogen formation is influenced by dipole-supported resonances below the threshold of inelastic processes. Resonance energies form a geometric progression relative to the threshold. The exothermic antihydrogen formation cross sections behave as 1/E1/E1/E at low energies, but are oscillation free. We demonstrate that all these rich features are reproduced by the threshold theory developed by Gailitis [J. Phys. B: At. Mol. Phys. 15, 3423 (1982)].
The two-center convergent close-coupling method is used to calculate antihydrogen (H‾)(\overline{\mathrm{H}})(H) formation via positronium (Ps) scattering on antiprotons (p‾)(\overline{p})(p​) at near threshold energies. For excited Ps of energy $\ensuremath{\varepsilon}$, the $1/\ensuremath{\varepsilon}$ behavior of the H‾\overline{\mathrm{H}}H formation cross sections is valid strictly only at the respective threshold, as is the $1/\sqrt{\ensuremath{\varepsilon}}$ behavior for Ps in the ground state. Simple equations are given for the $\overline{\mathrm{H}}(n\ensuremath{\le}4)$ formation cross sections from $\text{Ps}(n\ensuremath{\le}3)$ from zero to around 0.1 eV above threshold. Some of the implications of using p‾\overline{p}p​-Ps collisions to form antihydrogen in beams, and held in traps, are discussed.
We investigate the consequences of unexpectedly large elastic cross sections for the scattering of low-energy antiprotons from $n\ensuremath{\le}3$ positronium (Ps) on the experimental implementation of antihydrogen formation via Ps-antiproton collisions. The integrated elastic cross sections, obtained using the two-center convergent close-coupling theory, can be up to three orders of magnitude greater than their counterparts for antihydrogen formation. The differential momentum transfer cross sections, which suppress the large cross sections at forward scattering angles, show remarkably rich behavior across all scattering angles. We discuss the implications of these findings for the heating, via momentum transfer, of clouds of trapped antiprotons that are typically used for the creation of antihydrogen.
We investigate the elastic and inelastic scattering of positrons by sodium atoms in both the ground state, Na(3s3s3s), and excited states, Na*(3p3p3p, 4s4s4s, 3d3d3d), using the hyperspherical coordinate method with a model potential to represent the atomic core. The threshold behavior of positronium (Ps) formation cross sections is analyzed as the positron impact energy EEE approaches zero. Within this framework, we derive a generalized expression for partial-wave Ps-formation cross sections at low positron energies, which applies to both ground-state and excited-state sodium targets. Our results confirm that the total threshold behavior follows the expected power-law dependence: σPs∝E−1/2 σ_{\text{Ps}} \propto E^{-1/2} σPs​∝E−1/2 for exothermic reactions and σPs∝Ea σ_{\text{Ps}} \propto E^{a} σPs​∝Ea for endothermic reactions, where a>0 a > 0 a>0. Furthermore, we find that Ps-formation cross sections for positron scattering from excited Na states are significantly larger than those from the ground state in the low-energy region. A notable enhancement of Gailitis-Damburg oscillations is observed above the Ps(n=2n=2n=2) threshold, which may account for the increase observed in experimental data. Incorporating contributions from excited sodium targets improves agreement with experimental results and may help resolve discrepancies between theoretical predictions and measurements.
Abstract The interaction of antiprotons with low-energy positronium atoms is a fundamental three-body problem whose significance is its utility for formation of antihydrogen. Particular importance resides in understanding processes involving excited positronium states. Until recently such studies were performed using classical techniques. However, they become inapplicable in the low-energy domain. Here we report the results of comprehensive quantum calculations, which include initial excited positronium states with principal quantum numbers up to ni = 5. Contrary to expectation from earlier work, there are only muted increases in the cross-sections for antihydrogen formation for ni > 3. We interpret this in terms of quantum suppression of the reaction at higher angular momenta. Furthermore, the cross-sections for elastic scattering are around two orders of magnitude higher, which we attribute to the degeneracy of the positronium states. We outline some experimental consequences of our results.
Abstract The study of collision between metastable positronium (Ps) and antihydrogen ( H ¯ ) is crucial for precision experiments involving H ¯ . In this paper, we investigate the elastic scattering between H ¯ and Ps(2s) by combining the confined variational method with the projection method, for scattering energies from 0.0245 eV to 0.068 eV. Our calculations provide accurate phase shifts and cross sections for the 1,3 S and 1,3 P symmetries. Near the binding threshold, the rapid increase in the total cross section may be attributed to the P-wave resonance effect. Additionally, we determined the S-wave scattering lengths to be 9.34 a 0 and 5.81 a 0 for singlet and triplet elastic scattering, respectively.
Antihydrogen formation cross sections are calculated for low-energy collisions of antiproton with positronium by the hyperspherical coupled-channel method. The scattering wavefunctions are expanded in terms of a large number of sector-adiabatic states associated with the n=1-4 states of antihydrogen and n=1-3 states of positronium in the asymptotic separated-atom region. The present formation cross sections differ considerably from those of the unitarized Born approximation reported by Mitroy and Stelbovics (1994). The disagreement becomes larger with decreasing collision energy owing to the different energy dependence of the cross sections. The authors have confirmed that the formation cross sections from the 2s and 2p states are larger than that from the ground state by one order of magnitude.