Calculations of positronium-atom scattering using a spherical cavity

Abstract

Positronium (Ps) scattering by noble-gas atoms (He, Ne, Ar, Kr, and Xe) is studied in the frozen-target approximation and with inclusion of the van der Waals interaction. Single-particle electron and positron states in the field of the target atom are calculated, with the system enclosed by a hard spherical wall. The two-particle Ps wave function is expanded in these states, and the Hamiltonian matrix is diagonalized, giving the Ps energy levels in the cavity. Scattering phase shifts, scattering lengths, and cross sections are extracted from these energies and compared with existing calculations and experimental data. Analysis of the effect of the van der Waals interaction shows that it cannot explain the recent experimental data of Brawley et al. for Ar and Xe [Phys. Rev. Lett. 115, 223201 (2015)].

Many-Body Theory for Positronium-Atom Interactions

“…As first applications of the theory, we calculate phase shifts, elastic-scattering and momentum-transfer cross sections, and the pickoff annihilation rate 1 Z eff for Ps on He and Ne. The cross sections are found to be in agreement with previous coupled-state [17] and model van der Waals [7] calculations. By accounting for And another one:…”

“…The MBT results for the momentum-transfer cross section [ Fig. 5 (c) and (d)], are close to the FT+vdW calculation [7], particularly for K > 0.3 a.u. For He, our calculation is within the error bars of the experimental result of Nagashima et al [44] but ∼30-45% larger than that of Canter et al [40], Rytsola et al [41], and Coleman et al [42].…”

“…becomes comparable at K ≈ 1 a.u. For He, the elastic cross section is close to the 9-Ps-9-He coupled-state calculation of Walters et al [17], and to the calculation [7] in which a model van-der-Waals potential was added to the FT Ps-atom interaction (FT+vdW) [47]. The MBT scattering length of 1.70 a.u.…”

“…Ref. [13] FT [7] MBT MBT-EF Exp. [ ground is much broader for Ne, which is possibly explains why the DBS data from Skalsey et al [43] are in good agreement with the MBT results.…”

“…They also partly cancel each other and can be neglected. We construct the Ps eigenstates with angular momentum J and parity Π from the single-particle Dyson states [7,39], as…”