Continuum Distorted Wave Method In The Positronium Formation Of Positron-atom Scattering

The study of positronium (Ps) formation process in positron-atom scattering is oneof the most fundamental topics in atomic and molecular physics. The difculty of describ-ing this two-center charge rearrangement channel provides new challenges to theoreticalwork. In this dissertation, we have applied the two-channel distorted wave method (EFS-CDW: Eikonal Final State-Continuum Distorted Wave initial state) to calculate the Psformation cross sections of atoms and ions by positron impact. A two-center continuumdistorted wave function is used in the initial channel to describe the interactions of targetcore and valence electron to the incident positron, while in the final channel, we use aneikonal wave function to represent the distortion efect of the target nucleus to the outgo-ing positronium atom. Such two-channel two-center distorted wave method can be suc-cessfully applied to from-low-to-high energy region in positron scattering. By applyingthis method to the hydrogen atom and hydrogen-like ions, we have successfully studiedthe detailed processes in the charge transfer reactions. The dissertation is organized asfollows:Firstly, we have presented the background information and current research sta-tus about the positron-atom scattering. Available experimental work in the literatureabout the Ps formation cross sections for various atoms are summarized. Several typ-ical powerful theoretical methods for Ps formation process in positron-atom scatteringare also introduced in this chapter, such as the Close-Coupling (CC) method, ConvergentClose-Coupling (CCC) method, Coupled-Channel Optical (CCO) method, perturbativeDistorted-Wave Born Approximation (DWBA) and single-channel Continuum DistortedWave (CDW) method.In Chapter2, we present the derivation and calculation details about the EFS-CDWmodel. The multi-dimensional integration of the transition matrix was transformed toseveral three-dimensional Nordsieck integration by utilizing the Fourier transformationtechniques. Through the coordinate rotation method, we have successfully obtained thearbitrary final Ps state (Ps(nlm)) formation cross sections. Due to the fact that EFS-CDWmodel includes the first two and part of the three orders of Born approximation and theThomas double-scattering process can be completely described by the second-order Born approximation, the Thomas double-scattering terms appear naturally in the present EFS-CDW model.As a preliminary test to the present method, we have applied it to the positron-hydrogen atom system. The calculated Ps(1s) and Ps(n=2) formation cross sections arein good agreement with various state-of-art method calculations, such as variational, CC,CCC and CCO methods. However, in the low energy region, the present Ps(2s) results arehigher than CC and CCC methods while the Ps(2p) are lower than them. It is probablydue to the fact that the Ps(2s) and Ps(2p) are strongly coupled due to the energy degen-eracy and the present uncoupling perturbative method could not describe such couplings.Summing up the Ps(n) formation cross sections, the obtained total Ps formation cross sec-tions are in good agreement with available experimental observations in the entire energyrange. Additionally, we have obtained the scaling law of Ps(n) cross sections correspond-ing to the principle number n. The exponential scaling factor decreases from infinity to3from the ionization threshold13.6eV to30eV. At intermediate and high energies, thescaling law does not change.The EFS-CDW model can be easily extended to the positron-ion scattering systems.In Chapter4, we have applied the present method to the positron scattering with H-likeiso-electron sequence (Z=1-9). A scaling law of the Ps formation cross sections withrespect to the target nuclear charge Z was derived according the scaling behavior of ve-locity and coordinate. The scaling law can be applied to both diferential and integratedcross sections. Comparing the scaled results with diferent charge Z and diferent scaledincident energies, we can generally obtained that the scaling behavior of the cross sec-tions improves with the incident energy and Z increase. We have also investigated themaximum positions of the Ps formation cross sections for various H-like ions. The crosssections for Ps formation are largest when the positron incident energy is in the vicinityof twice the corresponding threshold energy. Therefore, we have theoretically identifiedthat the wave vector matching model presented by Charlton is applicable in positron-ionscattering systems.In the last Chapter, we did some preliminary researches about extending the presentEFS-CDW method to multi-electron targets. The most simplest model is the efective-charge EFS-CDW model, which uses the frozen core approximation and treats the targetas a single-valence-electron atom. All the left electrons and the nucleus are treated asa single particle with an efective charge Z. However, the disadvantage of this model is that the scattering wave function in the initial channel does not satisfy the outgoingboundary condition. In the dynamic screening EFS-CDW model, the interactions betweenthe incident positron and target ion, as well as the interactions between the outgoingPs atom and target ion in the final state, both change dynamically with respect to thecorresponding distances. The nuclear charge changes gradually to unity at large distancesand therefore the boundary conditions are satisfied naturally.