Impact-parameter convergent close-coupling approach to antiproton-atom collisions
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This thesis is devoted to extension of the convergent close-coupling (CCC) method to heavy projectiles and its application to the theoretical studies of antiproton scattering on the hydrogen and helium targets.In the Introduction (Chapter 1) the motivation for the study and the current status of antiproton scattering on hydrogen and helium are presented. Other theoretical methods that previously have been applied to these problems are reviewed and their limitations are indicated. The extension of the fully quantummechanical CCC method to ion-atom collisions is presented in Chapter 2. The derivations of the momentum-space coupled-channel Lippmann-Schwinger integral equations from the exact Schr¨odinger equation is given in detail. Transition matrix elements are derived in momentum-space. In Chapter 3 a direct method for solving multi-dimensional Lippmann-Schwinger integral equations without recourse to partial-wave expansion or any other transformation scheme will be described. A direct method has been applied to the antiproton-hydrogen as well as to the proton-hydrogen collisions. In Chapter 4 we solve the full multichannel problem by transforming the coupled-channel integral equations into the impactparameter representation. The scattering amplitude necessary to calculate the differential and total cross sections will be derived from the transition matrix elements. The results of the CCC calculations for antiproton scattering from atomic hydrogen and helium are presented and compared with available experimental data and the results of other calculations in Chapter 5 and Chapter 6, respectively. Finally, in Chapter 7, we draw conclusions arising from this work and indicate future directions for the research.Main results of this work • The convergent close-coupling method has been extended to heavy projectiles and applied to antiproton scattering on atomic hydrogen and helium. • For the first time, the relative motion of the heavy particles in antiproton collisions with atomic hydrogen and helium has been treated quantummechanically. • A direct method to solving the three-dimensional momentum-space coupledchannel Lippmann-Schwinger integral equations has been developed. • A scheme for transforming the three-dimensional Lippmann-Schwinger integral equations into the impact-parameter representation has been developed. The fully off-shell transition matrix elements in the impactparameter space have been derived. • For the first time, the fully quantum mechanical calculations of the cross sections for all the major channels of interest in antiproton collisions with hydrogen and helium have been performed over a wide range of scattering energies. • The total ionization cross sections for the H target has been calculated. The results are in excellent agreement with the available experiment. An overall agreement of the present results with the semiclassical calculations by other groups has practically confirmed the validity of the semiclassical approximation imposed on the relative heavy particle motion. • The total cross section for the He single ionization has been calculated using frozen-core (FC) and multi-configuration (MC) approximation for the target. As opposed to rather sophisticated and rigorous MC calculations the FC results agree with the experimental data at a wider energy range. • For the first time, based on the fully quantum-mechanical treatment of the problem the triple differential cross sections have been calculated for antiproton scattering on both H and He.• The p−H results for the various differential ionization cross sections agree reasonably well with the results of the semiclassical close-coupling and the continuum-distorted-wave-eikonal-initial-state (CDW-EIS) approaches, particularly at high energies. • The longitudinal ejected electron and recoil-ion momentum distributions for the single ionization of helium have been calculated. The results are in good agreement with the available experimental data.
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Abdurakhmanov, Ilkhom; Kadyrov, Alisher; Bray, Igor; Stelbovics, Andris (2011)A fully quantal integral-equation approach to ion–atom collisions is developed along the lines of the convergent close-coupling approach to electron–atom scattering. The approach starts from the exact three-body Schrödinger ...
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Solution of the proton-hydrogen scattering problem using a quantum-mechanical two-center convergent close-coupling methodAbdurakhmanov, Ilkhom; Kadyrov, Alisher; Avazbaev, S.; Bray, Igor (2016)Details of the recently developed quantum-mechanical two-center convergent close-coupling approach (Abdurakhmanov et al 2016 J. Phys. B: At. Mol. Phys. 49 03LT01) to proton-hydrogen scattering are presented. The formulation ...