The effects of the positron ($e^{+}$) annihilation in $e^{+}$ scattering by the H atom are included directly in the Hamiltonian as an absorption potential, and hence the finite lifetimes ${\Gamma }_{ns}$ of positronium (Ps) in states $ns$ are automatically taken account of. The Schrödinger equation is solved using the hyperspherical close-coupling method. The annihilation and Ps formation are shown to be inseparable near the Ps($1s$) threshold $E_{\mathrm{t}\mathrm{h}}$; Ps formation constitutes just an indirect pathway to annihilation. The annihilation cross section, which would diverge near $E_{\mathrm{t}\mathrm{h}}$ if ${\Gamma }_{1s}$ were infinite, connects smoothly across $E_{\mathrm{t}\mathrm{h}}$ to the cross section for Ps formation, which is meaningful only at energies well above $E_{\mathrm{t}\mathrm{h}}$.

• Received 5 July 2002

DOI:https://doi.org/10.1103/PhysRevLett.89.123201