D. I. Abramov

THE LOCAL CHARACTERISTICS OF THE BOUND STATES OF MUONIC MOLECULES

The sticking probabilitiesΩJv,G- andγ-factors for all bound states of mesic molecules ppµ, pdµ, ptµ, ddµ, dtµ, and ttµ withJ=0 andv=0, 1 have been calculated in the adiabatic hyperspherical approach (AHSA).

Reduced adiabatic hyperspherical basis in the Coulomb three-body bound state problem

A new version of the adiabatic hyperspherical approach (AHSA) is suggested which has significant advantages for the calculation of three-body states with total angular momentumJ> 0. The binding energies of all bound states of mesic molecules with normal parity are calculated by the suggested method. Comparison with results of variational calculations and the fast convergence of the method confirm its high efficiency.

Hyperspherical Coulomb spheroidal basis in the Coulomb three-body problem

A hyperspherical Coulomb spheroidal (HSCS) representation is proposed for the Coulomb three-body problem. This is a new expansion in the set of well-known Coulomb spheroidal functions. The orthogonality of Coulomb spheroidal functions on a constant-hyperradius surface ρ = const rather than on a constant-internuclear-distance surface R = const, as in the traditional Born-Oppenheimer approach, is a distinguishing feature of the proposed approach. Owing to this, the HSCS representation proves to be consistent with the asymptotic conditions for the scattering problem at energies below the threshold for three-body breakup: only a finite number of radial functions do not vanish in the limit of ρ→∞, with the result that the formulation of the scattering problem becomes substantially simpler. In the proposed approach, the HSCS basis functions are considerably simpler than those in the well-known adiabatic hyperspherical representation, which is also consistent with the asymptotic conditions. Specifically, the HSCS basis functions are completely factorized. Therefore, there arise no problems associated with avoided crossings of adiabatic hyperspherical terms.

Symmetric Elastic and Spin-Flip Low-Energy Collisions of the Hydrogen-Isotope Mesic Atoms in the Adiabatic Hyperspherical Approach *

The reduced adiabatic hyperspherical (RAHS) basis suggested previously is used to calculate elastic and spin-flip cross sections in the processes (aμ)F+a → (aμ)F′+a, a=(p, d, t), for collision energies 10−3≤ɛ≤102 eV. The rapid convergence of the method is demonstrated: to achieve an accuracy of ⋍1% in the calculated cross sections, it is sufficient to use N≤10 of the basis RAHS functions. The comparison of the obtained results with the previous ones is presented.

Elastic scattering, muon transfer, bound states and resonances in the three-body mesic molecular systems in the reduced adiabatic hyperspherical approach

The uniform method of numerical investigation of bound states and scattering processes 2→ 2 (including resonance states) in the Coulomb three-body (CTB) systems is developed. It is based on the adiabatic hyperspherical approach (AHSA) and includes the numerical realization and applications to the three-body mesic atomic systems. The results of calculations of bound states of these systems (including the local characteristics of the wave functions) and the scattering processes 2→ 2 (including the characteristics of the resonance states) are presented.

Adiabatic hyperspherical approach to describing low-energy mesic-atom scattering

The adiabatic hyperspherical approach developed previously is used to describe the asymmetric mesic-atom scattering aμ+b → aμ+b, a+bμ (a, b=p, d, t) in the collision-energy range 10−3≤ɛ≤102 eV. Boundary conditions for J≠0 scattering states are formulated, and partial cross sections for J=0–3 are calculated. Effective numerical codes are developed, and a fast convergence of the adiabatic hyperspherical approach is demonstrated: to achieve a precision of about 1% in the calculated cross sections, it is sufficient to use a basis of not more than ten adiabatic hyperspherical functions. The results that we obtained are compared with the previous ones.

Uniform Description of the Bound, Quasistationary and Scattering States in the Coulomb three-Body Systems Using Adiabatic Hyperspherical Basis

The method, its numerical realization and applications for the calculations of the different characteristics of the Coulomb three-body (CTB) problem are presented. The method was successfully applied for the description of the three-body bound states (including the local characteristics of the wave function) as well as for the scattering processes 2 → 2 (including the characteristics of the resonance states).

The quantum Coulomb three-body problem - Visualization of simulation results and numerical methods

Some years ago it was established that the muon catalyzed fusion phenomenon could be used for the production of energy. This fact has been causing a rebirth of interest in the universal methods of solving the quantum Coulomb three-body problem. The adiabatic hyperspherical (AHS) approach considered in this joint project has definite advantages in comparison with other methods. The case study proposed focuses on the study of the structure and behavior of the wave function of bound states of a quantum three-body system as well as of the basis functions of the AHS approach. Adapted scientific visualization tools such as surface rendering, volume ray tracing and texturing will be used. Visualization allows to discover interesting features in the behavior of the basis functions and to analyze the convergence of the AHS-expansion for the wave functions.<<ETX>>

Spin-Flip and Elastic Processes in Slow Collisions of Mesic Atoms

AbstractThe reduced adiabatic hyperspherical (RAHS) basis suggested previously is used for the calculation of elastic and spin-flip cross sections in the processes (aμ)F + a → (aμ)F′ + a, a = (p, d, t), for collision energies 10−3 ≤ ε ≤ 102 eV. The rapid convergence of the method is demonstrated. A comparison of the obtained results with previous ones is presented.

Adiabatic hyperspherical approach to the problems of muon catalyzed fusion

AbstractThe adiabatic hyperspherical approach (AHSA) is applied for the numerical investigation of the scattering processes and resonances in Coulomb three-body mesic atomic systems. The results of the calculations of elastic and inelastic cross sections in low-energy collisions aμ + b (a, b = p, d, t), energies, lifetimes and local characteristics of resonant states of mesic molecular ions nHeaμ+ (n = 3, 4) are presented.