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 is based on the exact (fully quantum-mechanical) three-body Schrödinger equation. The total scattering wavefunction is expanded using a two-center pseudostate basis. This allows one to include all underlying processes, namely, direct scattering and ionization, electron capture into bound and continuum states of the projectile. The off-shell integration in the coupled-channel Lippmann–Schwinger integral equations emerging from the three-body Schrödinger equation for the scattering wavefunction is taken analytically which greatly reduces computational effort. While the calculated electron capture cross sections are in a good agreement with experiment, some discrepancy exists for the ionization cross sections.

We show, using quasi-exact numerical simulations, that Anderson localization in a disordered one-dimensional potential survives in the presence of attractive interaction between particles. The localization length of the particles' center of mass-computed analytically for weak disorder-is in good agreement with the quasi-exact numerical observations using the time evolving block decimation algorithm. Our approach allows for simulation of the entire experiment including the final measurement of all atom positions. IOP Publishing Ltd and Deutsche Physikalische Gesellschaft to a recent revival of interest in localization properties in general, and in AL in particular. AL is characterized by the inhibition of transport in a quantum system, whose classical counterpart behaves diffusively. It is accompanied by an exponential localization of eigenstates in the configuration space, |ψ(r )| 2 ∝ exp(−|r |/L), where L is the localization length. AL is due to the interference between various multiple scattering paths which favors the return of the particle to its initial position and thus decreases the probability of it traveling a long distance. As the geometry of these paths depends on the system dimension, so AL features depend on the dimension too. For one-dimensional (1D) systems, AL is a generic single-particle behavior even for very small disorder when the particle 'flies' above the potential fluctuations.A fundamental question is to understand how interaction between particles affects AL. Presently, there is no consensus on the possible existence and properties of many-body localization. Some results suggest that AL survives for few-body systems, although with a modified localization length [3]; studies of cold bosonic systems in the mean-field regime show that AL is destroyed and replaced by a sub-diffusive behavior [4,5], but the validity of the meanfield approximation at long times is questionable. There are even predictions that AL survives at finite temperature in the thermodynamic limit, in the presence of interactions [6]. In this paper, we show, using a specific example, that 1D AL survives in the presence of attractive interactions and is even a rather robust phenomenon. The novelty of our approach is that it uses a quasi-exact numerical scheme to solve the full many-body problem in the presence of disorder. Here, quasiexact means that all numerical errors can be controlled and reduced below an arbitrary value, just at the cost of increased computational resources. The big advantage of this approach is not to rely on neglecting a priori any physical process.Atomic matter waves have several advantages that made possible an unambiguous demonstration of single-particle AL in 1D [7,8]: atom-atom interaction can be reduced by either diluting the atomic gas or using Feshbach resonances, ensuring a very long coherence time of the atomic matter wave; the spatial and temporal orders of magnitude are very convenient, allowing a direct spatio-temporal visualization of the dynamics; all microscopic ingredients are well c...