Hydrogen–anti-hydrogen elastic scattering using fully quantal method

Abstract

Hydrogen-anti-hydrogen scattering has been studied at low energies using quantal method. We employ the close-coupling method using different atomic basis sets. The same method has also been used to investigate hydrogen-hydrogen scattering. s-wave phase shifts and integrated elastic cross-sections are reported for both the systems. There is a structure in the elastic cross-section for hydrogen-hydrogen scattering.European physicists were successful in preparing anti-hydrogen (H) at CERN [1] by using a low-energy anti-proton (p) ring in late December 1995, and more recently at Fermilab [2]. These atoms are moving with a speed close to that of light. Their future plan is to obtain H at thermal velocities and to trap H. Impressive progresses have been made in this direction [3][4][5].Availability of H at sub-milli-Kelvin energies will make it possible to compare directly matter and anti-matter properties with high precision [6][7][8]. It has been pointed out that the main cause of loss of H trapped in a magnetic gradient trap is due to H-H 2 and H-He collision processes. The scattering cross-sections for these processes will help to fabricate a technical know-how in slowing down and trapping H. Therefore, theoretical investigations of these processes are of great importance.To the best of our knowledge, no positive-energy calculation has so far been carried out for matter-anti-matter systems with anti-matter signature. On the other hand, different workers have studied atom-atom scattering. Bates and Griffing [9] have initiated the study on the H-H system using the first Born approximation. Shingal et al. [10] have investigated H-H scattering using a coupled-channel semi-classical impact parameter method with rectilinear trajectories and reported the excitation and ionization cross-sections in the energy range 1 to 100 keV. They have used a 22-state basis for each state of symmetry. The semi-classical impact parameter method is not expected to be valid at low energies. In heavy-particle collision a large number of partial waves unlike light particle scattering are required for convergent results. This requirement has restricted a full quantal calculation to investigate heavy-particle

Leptonic annihilation in hydrogen-antihydrogen collisions

“…Our calculations show that, in a certain energy range, the rate of the rearrangement reaction ͑H+H → Pn+ Ps͒ is comparable to the rate of proton-antiproton annihilation in flight (H+H → e + + e − + other products). This finding conforms with other calculations of the rearrangement process [8][9][10].…”

Resonant phenomena in antihydrogen-hydrogen scattering

“…Several model calculations have been performed to get elastic and annihilation crosssections in the case of H 1S −H 1S scattering [3,4,5,7,8,20,21,22,23,24,25,26,27,28].…”

Stability of few-charge systems in quantum mechanics

“…However, the work on the preparation of H described above has generated greater theoretical interest in this system, Armour et al [169,211,212,213,214,215] Jonsell, Froelich et al [216,217,218,219,220,221,222], Sinha and Ghosh [223], Voronin and Carbonell [224].…”