The close-coupling equations for the positron-hydrogen system restricted to s-wave scattering from the l=0 levels of hydrogen and positronium are written as a set of coupled momentum space Lippmann-Schwinger equations. The matrix element for positronium formation is evaluated by integrating over the multipole projected components of the momentum space wave functions. Cross sections generated in the coupled static approximation provide a verification of the method. With a larger basis, including the 1s and 2s levels of hydrogen and the 1s and 2s levels of positronium, the broad s-wave resonance at 2.6 Ryd shifts position to 3.17 Ryd. An additional resonance is observed in the cross section at an energy of 1.10 Ryd.
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.
We investigate the elastic and inelastic scattering of positrons by sodium atoms in both the ground state, Na(
3s), and excited states, Na*(
3p,
4s,
3d), 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
E 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 for exothermic reactions and
σPs∝Ea for endothermic reactions, where
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=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.
The two-center convergent close-coupling method is used to calculate antihydrogen
(H) formation via positronium (Ps) scattering on antiprotons
(p) at near threshold energies. For excited Ps of energy $\ensuremath{\varepsilon}$, the $1/\ensuremath{\varepsilon}$ behavior of the
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-Ps collisions to form antihydrogen in beams, and held in traps, are discussed.
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.