Corrections to the Born-Oppenheimer approximation as applied to a system made up of hydrogen and antihydrogen

Abstract

ABSTRACT:Interest in antihydrogen AH is increasing as it seems likely that it will soon be possible to observe it in its rest frame. The simplest atom with which antihydrogen atoms can interact is atomic hydrogen. We recently obtained an upper bound of 0.8 a for 0 the critical value of the distance between the proton and the antiproton below which the electron and positron cease to be bound to the nuclei. In this calculation, the nuclei were assumed to be fixed. In this article, we examine the effect on the energy of the electron and the positron of taking into account the motion of the nuclei. The corrections are found to be small.

Quenching of para-H2with an ultracold antihydrogen atomH¯1Sultanov1, Adhikari2, Guster3 2010Phys. Rev. A61230View full textAdd to dashboardCite

“…Fig. 1): The functions V k1 H−H (y) with k = 2(3) are represented as cubic spline interpolation functions for any value of y = x 21 or y = x 31 as follows:…”

“…Some theoretical studies have been carried out for the H + H system at thermal energies using quantum-mechanical methods [21][22][23][24][25][26]. Also, discussions on the importance and applications for this system, especially in connection with Bose-Einstein condensation [27], ultracold collisions [16,22], and its static and dynamic properties [28], can be found in the literature.…”

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].…”

Positron Physics in a New Perspective

“…We have carried out calculations to determine the effect of taking into account the omitted terms in treatments using the Born-Oppenheimer approximation. In the first set of calculations, we calculated the changes to the energy of the light particles, due to the coupling of the light particle and nuclear motion [45]. We will go on to consider the effect of this coupling on the calculated scattering parameters for low energy scattering.…”

“…However, these are not Jacobi coordinates for separation into positronium and protonium, for which the Hamiltonian takes the form [45] where, as before, is the position vector of the positron with respect to the electron and is the position vector of the centre of mass of the positronium with respect to the centre of mass of the nuclei.…”