Recent interest in the properties of the negative ion of positronium has encouraged us to compute its cross section for photodetachment.To simplify the calculation, we have used the asymptotic form of the bound-state wave function and a plane wave for the final-state wave function, following the work of Ohmura and Ohmura in the case of photodetachment of H . We have obtained the needed normalization constant from a very precise and extensive Hylleraas wave function for the three-particle bound state.The positronium negative ion (Ps ) has for years' been known to be particle stable and has been the subject of many theoretical investigations, 2 4 but only recently has it been produced in the laboratory. Further investigations have resulted in good measurements of its annihilation lifetime, which agree ' within experimental uncertainty with theory.It has also been suggested' that Ps could be used to generate positronium (Ps) beams of controlled energy; this~ould involve acceleration of Ps ions and photodetachment of one electron. For this application, as well as on general principles, it would be interesting to know the photodetachment cross section of Ps The formulation of the problem is straightforward:The dipole transition matrix element is calculated with use of a sufficiently accurate initial wave function of the bound ionic state as well as a p-wave continuum function describing the e -Ps final state. In this report we will describe a calculation which simplifies the description of the initial bound state by representing it by an asymptotic form whose normalization comes from the most accurate Hylleraas wave function of the ion. ' [This is justified by the very small binding energy (0.326 eV) of the Ps ion]. We make a further simplifying assumption by taking the final state to be a plane wave. (Note that some work designed to take into account the scattering has already been done. ')In Rydberg atomic units, the Hamiltonian of the system consisting of two electrons (pt, pz) and one positron (x) is2 2 2 2 + 2 Ipt -xl Ipz -«I Ipi -pzl For the initial bound state of Ps, it is convenient to transform to the following center-of-mass coordinate system: Omitting R, which describes uniform motion of the center of mass, we previously wrote a wave function for the Ps ground state in the Hylleraas form as follows: I +1 "2 "p;(rq, rz, r~z) = g C(l, m, n ) [rtrz e I, m, n I m "2 "j ] n and obtained an extremely accurate variationa1 energy. " For the final state of the photodetachment, on the other hand, itis more appropriate to describe the Ps+e system in an asymmetric form, since the correct kinematic description involves the motion of an electron relative to the center-ofmass of the Ps atom. That is, we use the coordinate Rz= rz -rt /2 in place of rz, while retaining the other coordinates as before. The Hamiltonian in these unsymmetric coordinates is 0"= -2 V, , +4VR + -+ 1 IRz+ -,r) I The final state, involving the relative motion of a free electron and Ps in the ground state, must be a p state. In this paper, we will as...
