Elastic Positronium-Atom Scattering Using the Stochastic Variational Method

One of the most difficult problems in atomic collision theory is the positronium-atom scattering problem. The source of the difficulty lies in the fact that both the projec- tile and the target are composite objects with an internal structure. This means that the interaction matrix elements involve multicenter integrals which are difficult and time consuming to evaluate (1). Particular sources of concern are the evaluation of the exchange matrix element involv- ing the electrons in the target and the electron forming part of the positronium. An even more formidable problem is the inclusion of the van der Waals interaction between the positronium (Ps) projectile and the atomic target. One can point to very few calculations that have included this ef- fect, and even then the calculations were restricted to Ps-H scattering. In this article, the stochastic variational method (2-5) is applied to the calculation of Ps-atom scattering for the Ps-H, Ps-Li1, Ps-He, and Ps-Ps systems. The Ps-H sys- tem is probably the best known from the theoretical point of view (6-9). There have been no scattering calcula- tions of the Ps-Li1 system as such, although there have been calculations of the alternate e1-Li entrance channel (10). The Ps-He system has been studied previously by a number of authors and at the moment there is a great deal of variation (a factor of 5) in the threshold cross section according to the different calculations (11-14) and differ- ent experiments (15-19). The present calculation includes all the physical Ps-helium interactions and to a large ex- tent resolves most of the theoretical issues surrounding the Ps-He scattering length. There has been no published cal- culation of Ps-Ps scattering even though knowledge of the scattering length is of vital importance to proposals to form a stable Bose-Einstein condensate (BEC) of spin-aligned triplet Ps atoms (20,21). Besides being half comprised of antimatter, a 3Ps BEC would also be unique because it could be formed at relatively high temperatures (150 K) (20,21).