Abstract:
We discuss the regularization of attractive singular potentials $-\alpha _{s}/r^{s}$, $s\geq 2$ by infinitesimal imaginary addition to interaction constant $\alpha_{s}=\alpha_{s}\pm i0$. Such a procedure enables unique definition of scattering observables and is equal to an absorption (creation) of particles in the origin. It is shown, that suggested regularization is an analytical continuation of the scattering amplitudes of repulsive singular potential in interaction constant $\alpha_{s}$. The nearthreshold properties of regularized in a mentioned way singular potential are examined. We obtain expressions for the scattering lengths, which turn to be complex even for infinitesimal imaginary part of interaction constant. The problem of perturbation of nearthreshold states of regular potential by a singular one is treated, the expressions for level shifts and widths are obtained. We show, that the physical sense of suggested regularization is that the scattering observables are insensitive to any details of the short range modification of singular potential, if there exists sufficiently strong inelastic short range interaction. In this case the scattering observables are determined by solutions of Schrodinger equation with regularized potential $-(\alpha_{s}\pm i0)/r^{s}$. We point out that the developed formalism can be applied for the description of systems with short range annihilation, in particular low energy nucleon-antinucleon scattering.

Abstract:
We consider the spin-exchange in ultracold collisions of hydrogen ($H$) and antihydrogen ($\bar{H}$) atoms. The cross sections for transitions between various hyperfine states are calculated. We show that the process of spin exchange in $\bar{H}-H$ collisions is basically driven by the strong force between proton and antiproton, that spin-exchange cross-sections are proportional to the difference of singlet and triplet strong force S-wave scattering lengths, while the strong force effects are enhanced about $10^9$ times due to long range atomic forces. We show that any difference in hyperfine structure of $H$ and $\bar{H}$ (CPT violation) manifests itself in radical change of spin-exchange cross-sections energy behavior.

Abstract:
We present a treatment of cold hydrogen-antihydrogen collisions based on the asymptotic properties of atom-antiatom interactions. We derive general formulas for the elastic and inelastic cross sections and for the scattering lengths and analyze their sensitivity to the parameters characterizing the inelasticity of the collision process. Given the inelasticity, we obtain bounds for the complex scattering length. We investigate the influence of strong nuclear forces and the isotope effects in $\bar{\rm H}{\rm H}$ and $\bar{\rm H}{\rm D}$ collisions and demonstrate enhancement of these effects due to the presence of the near-threshold narrow ${\rm H}\bar{\rm H}$ ($\bar{\rm H}{\rm D}$) states. The values of the elastic and inelastic cross-sections with simultaneous account of rearrangement and strong forces are presented. General expressions for the (complex) energies of the near-threshold $\rm{H}\bar{\rm H}$ states are obtained.

Abstract:
Annihilation cross-section of ultra low-energy atomic antihydrogen ($% E\le10^{-5}$ a.u.) on atomic hydrogen are calculated within a quantum mechanical coupled channels approach. The results differ from the extrapolations of semiclassical models to low energies. The main features of the observables are found to be determined by a family of $H\bar{H}$ nearthreshold states.

Abstract:
The main properties of the interaction of ultra low-energy antiprotons ($% E\le10^{-6}$ a.u.) with atomic hydrogen are established. They include the elastic and inelastic cross sections and Protonium (Pn) formation spectrum. The inverse Auger process ($Pn+e \to H+\bar{p}$) is taken into account in the framework of an unitary coupled-channels model. The annihilation cross-section is found to be several times smaller than the predictions made by the black sphere absorption models. A family of $\bar{p}H$ nearthreshold metastable states is predicited. The dependence of Protonium formation probability on the position of such nearthreshold S-matrix singularities is analysed. An estimation for the $H\bar{H}$ annihilation cross section is obtained.

Abstract:
We investigate the interaction of ultracold antihydrogen with a conducting surface. Our discussion focuses on the physical regime where the phenomenon of quantum reflection manifests. We calculate the reflection probability as function of incident atom energy. We find that, for ground state $\bar{H}$ atoms (with $T< 10^{-5}$ K), the probability of reflection is $R \simeq 1-k b$, where $k$ is the momentum of the atom and $b = 2174.0$ a.u. is a constant determined solely by the van der Waals-Casimir tail of the atom-wall interaction. We show that quantum reflection, which suppresses the direct contact of ultra-cold atoms with the surface, allows for the possibility of confinement and storage of cold antihydrogen atoms. We calculate the life-time of confinement as a function of antihydrogen energy. We develop a theory of $\bar{H}$ in a wave-guide and propose its application to fundamental measurements. In particular, for measurement of retardation corrections in the long-range component of the antiatom - wall potential. We demonstrate, for $\bar{H}$ falling in the gravitational field of Earth onto a conducting surface, the existence of quantized $\bar{H}$ states. We calculate that the lifetime of ultracold $\bar{H}$ in its lowest gravitational state and obtain $\tau=(Mg b/2\hbar)^{-1}\simeq 0.1$ s, where $Mg$ is a gravitational force acting on the antiatom. We propose that measurement of this lifetime may provide a new test for the gravitational properties of antimatter.

Abstract:
We suggest a method of singular terms regularization in potential model of $N\bar{N}$ interaction. This method is free from any uncertainties, related to the usual cut-off procedure and based on the fact, that in the presence of sufficiently strong short-range annihilation $N$ and $\bar{N}$ never approach close enough to each other. The effect of mentioned singular terms of OBE potential, modified by annihilation is shown to be repulsive. The obtained results for S- and P-wave scattering lengths are in agreement with existing theoretical models.

Abstract:
We suggest a regular potential model of $N\bar{N}$ interaction without any cut-off. The effect of singular terms of OBE potential, modified by annihilation is shown to be repulsive. The experimental data for S- and P-wave scattering lengths are well reproduced.

Abstract:
Hadron electromagnetic form factors of hadrons in the time-like region at the boundary of the physical region is considered. The energy behaviour of the form factor is shown to be dominantely determined by the strong hadron-antihadron interaction. The scattering length imaginary part for $p-\bar{p}$, $\Lambda-\bar{\Lambda}$, $\Sigma^0-\bar{\Sigma^0}$ are evaluated. We propose experiments to extract the information on the nearthreshold baryon-antibaryon interaction by using of hadron form foctors.

Abstract:
Hadron electromagnetic form factor in the time-like region at the boundary of the physical region is considered. The energy behavior of the form factor is shown to be determined by the strong hadron-antihadron interaction. Imaginary parts of the scattering lengths for $p\bar{p}$, $\Lambda\bar{\Lambda}$, $\Lambda\bar{\Sigma}^0 (\bar{\Lambda}{\Sigma}^0)$ and ${\Sigma}^0\bar{\Sigma}^0$ are estimated. Developed approach enables us to estimate imaginary part of the scattering volume from $D^*\bar{D^*}$ experimental data. The form factor energy behavior away from the threshold is obtained within a semiphenomenological model of hadron-antihadron interaction.