High resolution calculations of low energy scattering in e⁻e⁺p¯ and e⁺e⁻He⁺⁺ systems via Faddeev–Merkuriev equations

Abstract

The potential splitting approach incorporated into the framework of Faddeev-Merkuriev equations in the differential form is used for calculations of multichannel scattering in e − e +p and e + e − He ++ systems. Detailed calculations of all possible Swave cross-sections are performed in the low-energy region which supports up to seven open channels including the rearrangement channels of ground and excited states of antihydrogen, positronium and helium ion formations. All known sharp resonances of the systems obtained and approved by a number of authors are clearly reproduced in the calculated cross sections. In cross sections for energies above the threshold corresponding to n = 2 state of antihydrogen the prominent oscillations of Gailitis Damburg type have been found.

Solving the Faddeev-Merkuriev Equations in Total Orbital Momentum Representation via Spline Collocation and Tensor Product Preconditioning

“…However, our usage of the method presented in the next section (see also [33]) shows that a fast convergence is achieved.…”

“…The parameters x 0α , y 0α and ν α > 2 can in principle be chosen arbitrarily, but their choice changes the properties of components ψ α that are important from both theoretical and computational points of view [31]. In the papers [33,34] we have discussed the choice of the cut-off function and have presented some practical algorithm of how to choose its parameters efficiently. In the bound state calculations the splitting can be omitted, that is one can take V [33].…”

“…In the papers [33,34] we have discussed the choice of the cut-off function and have presented some practical algorithm of how to choose its parameters efficiently. In the bound state calculations the splitting can be omitted, that is one can take V [33]. Then the set of Eqs.…”

“…The scattering problem gives rise to much more complicated radiation boundary conditions and a subsequent boundary value problem. The exact asymptotic form of each component depends on the total energy E. Comprehensive descriptions of scattering boundary conditions can be found in [30] (for the total energy E of the system below the three-body breakup threshold see also formula (8) of [33] and discussion therein). Summarizing, for Eqs.…”

The Faddeev–Yakubovsky Symphony

“…The long range part is kept in the left hand side of the Faddeev equations to define the Coulomb asymptotes and the short range parts appear in the right hand side ensuring the decoupling of the equations. Merkuriev approach has proven to be very successful in several nuclear physics problems like p-d reactions [17] as well as handling purely atomic problems [18,19,20]. 3.…”