Convergent close-coupling approach to positron-helium collisions

Abstract

This thesis presents the theoretical studies of positron scattering on the helium atom using two-center Convergent Close-Coupling (CCC) theory.The thesis organized in the following way: In the Introduction (Chapter I) the motivation for the study and the current status of the positron-helium scattering problem are presented. Other theoretical methods that previously have been applied to this problem are reviewed and their limitations are indicated. The application of the two-centre CCC to positron-helium is presented in Chapter 2. The derivations of the scattering equations and transition matrix elements are given in detail. The results of the two-centre CCC calculations for positron scattering from the helium ground state are compared with available experimental data and the results of other calculations in Chapter 3. Chapter 4 presents CCC results of positron scattering from the metastable 2[superscript]3S excited state of helium. Finally, in Chapter 5, we draw conclusions arising from this work and indicate future directions for the research.Main results of this work • The two-centre Convergent Close-Coupling method is generalized to positron scattering on the helium atom. • Cross sections, free from pseudo-resonances, are obtained for all major channels of interest and over a wide range of scattering energy. The importance of the inclusion of pseudo-states from both centers is demonstrated. • The elastic cross section below the Ps-formation threshold is obtained, for the first time, by using a two-centre close-coupling approach. • A consistent agreement of the CCC calculations with the available integrated cross section measurements of Ps-formation has been achieved at energies from the threshold of 17.8 eV up to 150 eV.• The CCC calculations exhibit a qualitative agreement with the measurements of the total cross section for ionization of the ground state of helium by positron impact. • The separation of the spin part of the total wave function is demonstrated and possible ortho- to para- Ps formation ratios are derived from first principles without assumptions. • Calculations of positron scattering from the 2[superscript]3S metastable state of helium are done for the first time. Converged results for the total scattering, Psformation, helium and Ps excitation as well as breakup cross sections are obtained. • Both considered cases (scattering from the ground and the 2[superscript]3S metastable states) confirm the equal atomic and Ps contributions to near-threshold breakup cross section, a behavior previously observed in positron scattering from hydrogen.