Low-energy positron-argon collisions by using parameter-free positron correlation polarization potentials

We report differential, integral, and momentum-transfer cross sections and the scattering length ($A_0$) for positron ($e^{+}$)-argon scattering at low energies below the positronium formation threshold. An optical-potential approach is employed in which the repulsive Coulombic interaction is calculated exactly at the Hartree-Fock level and the attractive polarization and correlation effects are included approximately via a parameter-free positron correlation polarization (PCP) potential recently proposed by us. The PCP model is based on the correlation energy ${\varepsilon }_{\mathrm{corr}}$ of one positron in a homogeneous electron gas; in the outside region, the ${\varepsilon }_{\mathrm{corr}}$ is joined smoothly with the correct asymptotic form of the polarization interaction (-${\alpha }_0$/2$r^4$, where ${\alpha }_0$ is the target polarizability) where they cross each other for the first time. The total optical potential of the $e^{+}$-argon system is treated exactly in a partial-wave analysis to extract the scattering parameters. It is found that the PCP potential gives much better qualitative results, particularly for the differential cross sections and the scattering length, than the corresponding results obtained from an electron polarization potential used as such for the positron case. We also discuss the ‘‘critical’’ points (representing the minima in the differential scattering) in the low-energy $e^{+}$-Ar scattering. The present results involve no fitting procedure.