Ravshanbek Utamuratov

Multiconfigurational two-centre convergent close-coupling approach to positron scattering on helium

The convergent close-coupling method with two-centre expansions has been developed to calculate positron scattering on helium. The method utilizes a multiconfigurational description of helium wavefunctions. Positronium formation is taken into account explicitly as electron capture into the positronium states. Direct-scattering, positronium-formation and breakup cross sections are calculated at all energies of practical relevance. Convergence in the calculated cross sections is demonstrated by increasing the basis size and orbital quantum number of the included states for each of the centres. Better agreement with experimental data is found when a multiconfigurational description is used for the helium wavefunctions in comparison with the recent frozen-core results.

A two-centre convergent close-coupling approach to positron?helium collisions

A two-centre convergent close-coupling method, which includes the positronium-formation channel, has been developed for positron scattering on helium. Convergent, pseudoresonance-free cross sections have been obtained. This is only possible if complete expansions are used on both the positronium and helium centres. The method is valid for all projectile energies and all transitions, including breakup, which is associated with excitation of positive-energy helium and positronium pseudostates. Generally, good agreement between calculated cross sections and available experimental data has been found across all incident energies.

Positron scattering on atoms and molecules

An overview is given of recent progress in the calculation of positron scattering on atoms and molecules using the convergent close-coupling method. Particular emphasis is given to those cases where positronium formation is one of the reaction channels, as well as the importance of demonstrating convergence with increasing orbital angular momentum of the bases used. Targets considered are atomic hydrogen, lithium, and molecular hydrogen. The last two decades have seen extraordinary progress in the field of electron, positron and photon scattering on atoms and ions. The problems of electron and photon scattering on atoms are very closely related. In the typical case of single photon absorption, the interaction proceeds by the resulting photo-electron scattering on the residual ion. For example, photon-helium scattering is essentially electron scattering on the singly charged helium ion. Positron-atom scattering is a little more interesting due to the possibility of positronium (Ps) formation. This is a rearrangement collision that considerably increases the complexity of the problem. Though it has been often claimed that positron-atom scattering is simpler than the corresponding electron-scattering problem due to the absence of exchange, in practice the introduction of the Ps-formation channel creates considerably more significant challenges. Historically, computational approaches to the problems have been subdivided into the low-, intermediate- and high-energy regimes. In addition, excitation and ionisation processes have also received different treatments. However, our interest in developing the convergent close-coupling (CCC) method has been to unify the approach to all such problems to be valid for the three projectiles across all energies and for the major excitation and ionisation processes. In developing the CCC method for excitation we took note of the techniques used specifically in their regimes of validity. At low energies the R-matrix close-coupling approach (1) has yielded outstanding results. At the higher energies the perturbative approach (2) has been particularly successful. The CCC method (3) combines the two techniques because it formulates close- coupling as coupled Lippmann-Schwinger equations in momentum space, which may be readily expanded in a perturbative series. Furthermore, the coupled equations may be solved in a distorted-wave formalism (4). However, unlike distorted-wave approximations the CCC results are independent of the choice of the distorting potential. In this sense the usage of such a potential is solely for numerical ease of solution. Following the pioneering implementation of the close-coupling method to ionisation processes (5), we developed an even simpler CCC approach (6). Rather than reconstructing the total wavefunction of the electron-atom system, we associated ionisation amplitudes with excitation of the positive-energy pseudostates. In other words, we extracted the required

Convergent close-coupling approach to positron and antiproton collisions with atoms

Recent developments in application of the convergent close-coupling approach to antimatter-matter scattering are outlined. These include positron collisions with alkalis and helium, in the ground or metastable states, as well as extension of the method to heavy projectiles, such as antiprotons.

Convergent close-coupling calculations of positron-helium collisions

The convergent close-coupling method, which includes positronium formation, is used to calculate positron-helium scattering. Low-energy elastic cross sections and Ore-gap total cross sections are calculated using equal number of pseudo-states from the atomic and positronium centers. We show that in the Ore-gap region only two-center expansions can give convergent results.

Convergent close coupling calculations for positron-magnesium scattering

While a two-centre convergent close-coupling approach to positron-magnesium scattering is developed, a single-centre method has been used to calculate total cross sections up to incident energies of 100 eV. The results agree very well with the measurements of Stein et al. [1] for positron energies above the ionisation threshold (7.6 eV). Similar accuracy is expected for energies below the positronium formation threshold (0.8 eV) where presently there are no experimental data to compare to. In this energy region we find a large p-wave resonance at 0.17 eV. Similar resonance behaviour was found in calculations by Mitroy and Bromley [2] at an energy of 0.1 eV.

Convergence study of the close-coupling approach to positron-helium collisions

Positron-helium collisions have been studied using a two-center close-coupling method. Convergent, pseudoresonance-free cross sections have been obtained by using complete expansions on both the helium and positronium centers. The low energy elastic cross sections, phase-shifts and total cross sections are compared with experimental data and results of other theories.