Absolute cross section for positron impact ionization of hydrogen near threshold

The hyperspherical hidden crossing method (HHCM) is used to investigate positron impact ionization of hydrogen near threshold. In this quantum calculation, the adiabatic Hamiltonian for arbitrary $L$ is expanded about the Wannier saddle point. The lowest order equation is solved analytically for the adiabatic eigenvalue; we use first and second order perturbation theory to calculate correction terms. We show that the Wannier threshold law and the extended threshold law are independent of $L. $We calculate absolute positron impact ionization cross sections for partial waves $L=0, 1, 2, 3$ in the energy range $0