Alisher Kadyrov

Trojan Horse as an indirect technique in nuclear astrophysics

The Trojan Horse method is a powerful indirect technique that provides information to determine astrophysical factors for binary rearrangement processes x + A → b + B at astrophysically relevant energies by measuring the cross section for the Trojan Horse reaction a + A → y + b + B in quasi-free kinematics. We present the theory of the Trojan Horse method for resonant binary subreactions based on the half-off-energy-shell R matrix approach which takes into account the off-energy-shell effects and initial and final state interactions.

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.

Recent progress in the description of positron scattering from atoms using the convergent close-coupling theory

Much progress in the theory of positron scattering on atoms has been made in the ten years since the review of Surko, Gribakin and Buckman [J. Phys. B 38, R57 (2005)]. We review this progress for few-electron targets with a particular emphasis on the two-centre convergent close-coupling and other theories which explicitly treat positronium (Ps) formation. While substantial progress has been made for Ps formation in positron scattering on few-electron targets, considerable theoretical development is still required for multielectron atomic and molecular targets.

Convergence of two-centre expansions in positron-hydrogen collisions

The question of convergence in two-centre expansions is addressed via the study of positron-hydrogen scattering within the s-wave model. Direct scattering, positronium formation, and breakup cross sections are found to converge if a sufficient number of states, centred on the hydrogen atom and positronium, are used to expand the total scattering wavefunction. Moreover, this occurs only if pseudostate expansions are applied to both the atomic and positronium centres.

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.

Coupled-channel integral-equation approach to antiproton–hydrogen collisions

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 Schrodinger equation for the scattering wavefunction and leads to coupled-channel Lippmann–Schwinger equations for the transition amplitudes in the impact-parameter representation, with the relative motion of the heavy particles treated quantum mechanically. The method is applied to calculate antiproton collisions with atomic hydrogen. Integrated total, excitation and ionization cross sections are calculated in the energy range from 1 keV to 1 MeV.

Direct solution of the three-dimensional Lippmann–Schwinger equation

A standard technique for solving three-dimensional momentum-space integral equations in scattering theory is their transformation into one-dimensional equations in terms of partial waves. However, for some scattering systems where a large number of partial waves contribute this technique is not efficient. In this work we explore the alternative approach of solving these equations directly without partial-wave expansion. For illustrative purposes we adopt the coupled-channel approach and consider a well-studied static-exchange model of electron-hydrogen scattering.

Scattering theory for arbitrary potentials

The fundamental quantities of potential scattering theory are generalized to accommodate long-range interactions. Definitions for the scattering amplitude and wave operators valid for arbitrary interactions including potentials with a Coulomb tail are presented. It is shown that for the Coulomb potential the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure.

Extrapolation of scattering data to the negative-energy region

Explicit analytic expressions are derived for the effective-range function for the case when the interaction is represented by a sum of the short-range square-well and long-range Coulomb potentials. These expressions are then transformed into forms convenient for extrapolating to the negative-energy region and obtaining the information about bound-state properties. Alternative ways of extrapolation are discussed. Analytic properties of separate terms entering these expressions for the effective-range function and the partial-wave scattering amplitude are investigated.

Quantum suppression of antihydrogen formation in positronium-antiproton scattering

The interaction of antiprotons with low-energy positronium atoms is a fundamental three-body problem whose significance is its utility for formation of antihydrogen. Particular importance resides in understanding processes involving excited positronium states. Until recently such studies were performed using classical techniques. However, they become inapplicable in the low-energy domain. Here we report the results of comprehensive quantum calculations, which include initial excited positronium states with principal quantum numbers up to ni = 5. Contrary to expectation from earlier work, there are only muted increases in the cross-sections for antihydrogen formation for ni > 3. We interpret this in terms of quantum suppression of the reaction at higher angular momenta. Furthermore, the cross-sections for elastic scattering are around two orders of magnitude higher, which we attribute to the degeneracy of the positronium states. We outline some experimental consequences of our results.The intriguing behaviour of positronium scattering has its role in antimatter studies. Here the authors have predicted the quantum suppression of the cross-section for antihydrogen formation in positronium scattering with antiprotons, by including the excited states and using convergent close-coupling calculations.