Akinori Igarashi

Time-delay matrix analysis of resonances: application to the positronium negative ion

A procedure to analyse resonances in scattering and photoionization calculations is discussed. It is theoretically connected to a general relation between the trace of the time-delay matrix and the energy derivative of the eigenphase sum. This procedure is especially useful in analysing resonances with strong background contributions, such as shape resonances lying just above the threshold of a new channel with an overcritical dipole field. In this case the background eigenphase sum diverges towards the threshold, and it can easily change the time delay due to an S-matrix pole into a negative time delay, or time advance. As an application, we analyse results of hyperspherical close-coupling calculations of S-, P-, D-, F-, G- and H-wave resonances in the positronium negative ion Ps− near the Ps(n = 2, 3) thresholds. We find examples of a strong background leading to an overall time advance and the dipole oscillation in the cross section above and near a threshold.

Positronium formation in positron-helium collisions at intermediate energies

Abstract Positronium formation cross sections in the collision of a positron with a helium atom are calculated in the energy range from 50 to 300 eV. The target continuum distorted-wave (TCDW) amplitude is evaluated exactly within the framework of the single-electron approximation. The present TCDW cross sections are much smaller than the TCDW values of Deb et al., who obtained reasonable agreement with experiments employing some further approximations. We show that no existing theory for particle transfer can expalain the high-energy behavior of the measured cross sections and further extensive studies are required both theoretically and experimentally.

Hyperspherical coupled-channel calculation for antihydrogen formation in antiproton-positronium collisions

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.

Nonadiabatically coupled hyperspherical equations applied to the collisional spin flip of muonic hydrogen

Nonadiabatically coupled equations in terms of hyperspherical coordinates are solved for the elastic and hyperfine transitions F→F′ of muonic hydrogen isotopes pμ, dμ, and tμ in collisions pμ(F)+p→p+μp(F′), dμ(F)+d→d+μd(F′), and tμ(F)+t→t+μt(F′), as an extension of our previous work on pμ [Igarashi et al., Phys. Rev. A58 (1998), 1166]. Converged cross sections are obtained for collision energies 10−3 to 102 eV and for the total orbital angular momentum L=0 and 1 including the spin–spin interactions VS explicitly in the Hamiltonian, and for L≥2 neglecting VS because of the large interparticle separations. The inclusion of VS for L=0 and 1 reproduces the correct hyperfine-splitting energy Δ∈ in the separated-atom limit, and is found to be of vital importance for the calculation of the spin-flip cross sections for collision energies lower than Δ∈.

Resonance parameters for doubly excited states of H2

A close-coupling calculation for e− + H2+ scattering is implemented to obtain the resonance parameters for the Q1 and Q2 series of H2 for the symmetries , , and . The obtained results are overall in fairly good agreement with earlier works for low-lying resonances, but discrepancies are seen for some resonances depending on the symmetries and internuclear distances.