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In this paper we present the first pilot calculation of the elastic and inelastic cross sections for the 5-body scattering of antihydrogen ions with positronium atoms. These cross sections have not been calculated before and are not known experimentally. In particular, we focus on the collisional rearrangement reactions H(+)+Ps -> HPs+e(+) which deplete the H+ions and result in stable atomcules HPs. To better understand the mechanism of this rearrangement, we study the 3-dimensional, angle resolved positron densities of the 3- and 4-body fragments in the initial and final states of the rearrangement collision.

We report on the first production of an antihydrogen beam by charge exchange of 6.1 keV antiprotons with a cloud of positronium in the GBAR experiment at CERN. The 100 keV antiproton beam delivered by the AD/ELENA facility was further decelerated with a pulsed drift tube. A 9 MeV electron beam from a linear accelerator produced a low energy positron beam. The positrons were accumulated in a set of two Penning-Malmberg traps. The positronium target cloud resulted from the conversion of the positrons extracted from the traps. The antiproton beam was steered onto this positronium cloud to produce the antiatoms. We observe an excess over background indicating antihydrogen production with a significance of 3-4 standard deviations., Correction in: European Physical Journal C, Volume 83, article number 1069, (2023) DOI: 10.1140/epjc/s10052-023-12244-w

We have performed a comprehensive numerical investigation of the scattering of antihydrogen (H¯) and positronium (Ps) atoms, at collision energies just above the threshold for the rearrangement reaction resultingin H¯ + ions. Formation of H¯ + in H¯ + Ps collisions is of vivid interest for experiments with H¯ at CERN. We treat all open channels below the threshold for the rearrangement into H¯ + Ps (which includes elastic scattering, excitation and deexcitation of positronium to and from the excited states with n = 2, 3, polarization and depolarization of Ps(n, l), rearrangement into H¯ + + e−, and formation of Ps and H¯ in the reverse reaction). Our method is a combination of the variational calculation with the coupled rearrangement channel method. The four-body solutions of the Schrödinger equation, obtained via diagonalization of the full Hamiltonian, are combined with the channel functions that satisfy the correct asymptotic boundary conditions, in a procedure that delivers the scattering matrix S. The complete set of S-matrix elements for all allowed scattering processes is calculated (both in forward and reverse directions, without assumption of the detailed balance). The scattering cross sections are obtained from the S-matrix elements calculated for the total angular momenta J = 0–6, and for the positronic spin S = 0, required for the formation of H¯ +. The numerical accuracy of the calculation is checked using the criterion of unitarity of the S matrix. Convergence of the cross section is examined with respect to the partial wave contributions, under the constraint of conservation of total angular momentum and parity. We show that the energy behavior of the cross sections near thresholds is consistent with the Wigner laws. The cross sections for processes that compete with H¯ + formation are presented.

Near-threshold production of antihydrogen ion (H+) in positronium-antihydrogen collisions is predicted by a rigorous four-body scattering calculation. The convergence of the cross sections for the rearrangement and for all competing reactions (elastic scattering, de/excitation and de/polarization of positronium) is carefully examined against partial waves. The multi-channel scattering solutions are composed of functions that diagonalize the four-body Hamiltonian, and scattering functions that satisfy the correct asymptotic boundary conditions. The production rates of H+ show large discrepancies compared to more approximate calculations.

We present the 4-body calculation of the antihydrogen-positronium scattering aiming at the prediction of cross sections for the production of antihydrogen positive ions. The latter are expected to be a useful source of ultra-cold atoms for the test of matter-antimatter gravity. We convert the Schrodinger equation to a set of coupled integro-di fferential equations that involve intermediate states and are solved using the compact finite di fference method. We will present the investigation of the rearrangement reaction between the ground-state antihydrogen atom and the excited positronium.

We present a 4-body calculation of scattering between an antihydrogen atom ((H) over bar) and a positronium (Ps) aiming at the prediction of cross sections for the production of antihydrogen positive ions (($H) over bar (+)). The antihydrogen positive ions are expected to be a useful source of ultra-cold anti-atoms for the test of matter-antimatter gravity. We convert the Schrodinger equation to a set of coupled integro-differential equations that involve intermediate states which facilitate the internal region description of the scattering wavefunction. They are solved using a compact finite difference method. Our framework is extended to scattering between an excited Ps and (H) over bar. Cross sections of the reactions, Ps (1s/2s/3s) + (H) over bar -> e(-) + (H) over bar (+), in s-wave collisions, are calculated. It is found that the reactions originating from Ps (1s/2s) + H produce (H) over bar (+) with a constant cross section within 0.05 eV above the threshold while the reaction cross section from Ps (3s) decreases as the collision energy increases in the same energy interval. Just above the threshold, the cross section of (H) over bar (+) production from Ps (3s) + (H) over bar in s-wave collision is 7.8 times larger than that from Ps (1 s) + (H) over bar in s-wave and 2.3 times larger than that from Ps (2s) + (H) over bar in s-wave. The near-threshold de-excitation reaction from Ps (3s) + (H) over bar occurs more rapidly than the (H) over bar (+) production.

The aim of the GBAR (Gravitational Behavior of Antimatter at Rest) experiment is to measure the free fall acceleration of an antihydrogen atom, in the terrestrial gravitational field at CERN and therefore test the Weak Equivalence Principle with antimatter. The aim is to measure the local gravity with a 1% uncertainty which can be reduced to few parts of 10(-3).

The GBAR project (Gravitational Behaviour of Anti hydrogen at Rest) at CERN, aims to measure the free fall acceleration of ultracold neutral anti hydrogen atoms in the terrestrial gravitational field. The experiment consists preparing anti hydrogen ions (one antiproton and two positrons) and sympathetically cooling them with Be (+) ions to less than 10 mu K. The ultracold ions will then be photo-ionized just above threshold, and the free fall time over a known distance measured. We will describe the project, the accuracy that can be reached by standard techniques, and discuss a possible improvement to reduce the vertical velocity spread.

We study a method to induce resonant transitions between antihydrogen (H) quantum states above a material surface in the gravitational field of the Earth. The method consists in applying a gradient of magnetic field which is temporally oscillating with the frequency equal to a frequency of a transition between gravitational states of antihydrogen. Corresponding resonant change in a spatial density of antihydrogen atoms can be measured as a function of the frequency of applied field. We estimate an accuracy of measuring antihydrogen gravitational states spacing and show how a value of the gravitational mass of the H atom can be deduced from such a measurement.

We present a nonadiabatic treatment of the hydrogen-antihydrogen system. The technique used to describe H-(H) over bar collisions is based on the coupled-rearrangement-channel method. Within this approach the total, nonadiabatic wave function of the system is divided into two parts: an inner and an outer one. To describe the inner part a set of square-integrable four-body functions is used. These functions are obtained by a diagonalization of the total Hamiltonian projected on a chosen L-2 subspace; they explicitly contain components of various arrangement channels expressed in terms of corresponding Jacobi coordinates. The outer part of the total wave function reflects its asymptotic character. Our procedure leads to a system of nonlocal integrodifferential equations that are solved iteratively and simultaneously determine the outer part of the solution and the coefficients in the four-body expansion of the inner part. To solve these equations the compact fine difference method was applied. Using this formalism we perform a one-channel calculation of the elastic scattering to obtain the S matrix, the nonadiabatic scattering length, and the cross section for the low-energy elastic scattering in the H-(H) over bar channel.

We present a theoretical study of the motion of antihydrogen atoms in the Earth's gravitational field near a material surface. We predict the existence of long-living quasistationary states of antihydrogen in a superposition of the gravitational and Casimir-van der Waals potentials of the surface. We suggest an interferometric method of measuring the energy difference between such gravitational states, hence the gravitational mass of antihydrogen.

We present a theoretical study of the motion of the antihydrogen atom ((H) over bar) in the gravitational field of Earth above a material surface. We predict that the (H) over bar atom, falling in the gravitational field of Earth above a material surface, would settle into long-lived quantum states. We point out a method of measuring the difference in the energy of (H) over bar in such states. The method allows for spectroscopy of gravitational levels based on atom-interferometric principles. We analyze the general feasibility of performing experiments of this kind. We point out that such experiments provide a method of measuring the gravitational force (Mg) acting on (H) over bar and that they might be of interest in the context of testing the weak equivalence principle for antimatter.

We consider the hyperfine transitions in ultracold collisions of hydrogen (H) and antihydrogen ((H) over bar) atoms. The cross sections for transitions between various spin states are calculated. We show that hyperfine transitions in (H) over bar -H collisions are basically driven by the strong force between proton and antiproton.

We consider spin exchange in ultracold collisions of hydrogen (H) and antihydrogen ((H) over bar) atoms. The cross sections for transitions between various hyperfine states are calculated. We show that the process of spin exchange in (H) over bar -H collisions is basically driven by the strong force between a proton and an antiproton.

The lifetime of the meta-stable hydrogen-antihydrogen molecule in various vibrational states is calculated. The partial lifetime with respect to the proton-antiproton annihilation is obtained from complex eigenvalues which arise upon inclusion of the strong force in the adiabatic formulation of the molecular decay problem. We study the influence of the strong force, which causes annihilation, on the transition probability for decay via Coulombic rearrangement to protonium and positronium.

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 H (H) over bar and D (H) over bar collisions and demonstrate enhancement of these effects due to the presence of the near-threshold narrow H (H) over bar (D (H) over bar) 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 H (H) over bar states are obtained.

Previous calculations of low-temperature cross sections for collisions between spin-polarized metastable hydrogen atoms are improved to include nonadiabatic radial and angular coupling at large interatomic separations. The electrostatic dipole-quadrupole interaction produces nonadiabatic radial coupling between (2s,2p) and (2p,2p) states, while the Coriolis interaction produces nonadiabatic angular coupling. Both of these long-range contributions are handled in a space-fixed atomic gauge that is particularly convenient for a spin-polarized system. The improved theoretical results are compared with an existing experiment.

A numerical investigation of the doubly excited states of H2 converging to the H(n=2)+H(n′=2) limit was performed. Special emphasis was put on the accurate description of the range of intermediate internuclear distances in order to correctly connect the short range with the asymptotic van der Waals regime where perturbation theory is applicable. The present nonperturbative calculation extends to internuclear separations R=200a0 and is sufficiently accurate to achieve a connection between the two extreme regimes without any need for an interpolation procedure. The high precision of the ab initio results revealed a long range dipole-quadrupole interaction that had been omitted in two earlier calculations. In addition to revised first-order perturbation theory results the leading second-order term varying as R−6 was obtained. The impact of the present findings for cold H(n=2) collisions is briefly discussed.

The scattering length for hydrogenic atoms with variable lepton mass, ranging from H to p mu, is calculated. The non-trivial sensitivity of the scattering length to non-adiabatic effects is investigated using the coupled-channel approach. The physical conditions for the Bose-Einstein condensation of exotic atoms are expressed in terms of this scattering length, which for the p mu atoms interacting via (3)Sigma(+)(u) potentials, is calculated to be 1.13 x 10(-2) au. The critical temperature for condensing the p mu atoms is estimated to be 0.5 K at a density of 2.2 x 10(20) cm(-3). Under these conditions the phonon velocity in the condensate is 2.2 m s(-1) and the coherence length is nearly 5 mu m.

We investigate two methods to include the strong nuclear force in hydrogen-antihydrogen scattering calculations. First, we construct a model optical potential with parameters determined by the measured shift and width of the protonium ground state. Although this potential is a very crude model for the strong nuclear force, its parameters may be adjusted to reproduce both bound states and low-energy annihilation cross sections to within the experimental accuracy. It is then shown that this potential may be reduced to a short-distance boundary condition in terms of the proton-antiproton strong-interaction scattering length. Elastic and annihilation cross sections for ground-state hydrogen-antihydrogen scattering are calculated for s- and p-waves, and collision energies up to 1 atomic unit. The two methods are found to agree to within about 1%. The main source of discrepancy is that the scattering-length approach does not account for vacuum polarization, relativistic, and finite-size corrections. We verify that the range of the strong interaction potential does not affect the hydrogen-antihydrogen s-wave scattering properties, and that the strong interaction has negligible influence on p-wave scattering.