Positronium formation as a three-body reaction. I. The second-order positron-electron interaction amplitude Abstract. The annihilation parameters Z eff of positrons in xenon atoms are calculated. The elastic cross sections for positron scattering from Xe atoms reported at low energy, below positronium (Ps) formation threshold. The bound wavefunctions of electrons are generated from Cowan program. The least-squares variational method (LSVM ) is used for determining the scattering wavefunction. The present results of annihilation parameters and cross sections are consisted with simiemprical and other theoretical results.

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The least-squares variational method (LSVM) is used for determining trial wavefunctions representing lowenergy positron-xenon elastic scattering, which are used to determine the positron lifetime. The trial function is taken to depend on several adjustable parameters, and is improved iteratively by increasing the number of terms. The bound state wavefunctions are obtained using Hartree-Fock-Slater method. The 2γ-rays annihilation rates of the positron in xenon atoms below Positronuim (Ps) formation threshold are calculated. Polarization potential V pl (r) is applied to enhance annihilation rates and lifetime. The present results of annihilation parameters are consistent with semiempirical, theoretical and experimental results.

The collisions of positrons with singly charged helium ion He + (1s) at ground state have been investigated using Harris-Nesbet variational method. This method is demonstrated for total elastic cross sections which corresponding to S-, P-, and D-wave scatterings below positronium formation threshold. The incident energies is considered up to 40 eV (positron momentum k  1.7 a.u.). The results show oscillating behavior of the cross sections in S-wave, where the existence of a resonance is expected, the first peak starts in S-wave and moving toward higher values of k as the angular momentum L increases. We encourage the experimental physicists to carry out further positron-ions experiments.