Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics B Atomic Molecular and Optical Physics

On the existence of antihydrogen-deuterium and antihydrogen-tritium bound-states

M. A. Abdel-Raouf, Janos J. Ladik

Published Apr 28, 1992• 6 citations
Publisher

Abstract

A theorem is presented which proves the existence of a bound state composed of one hydrogen atom and one antihydrogen atom. The extension of the theorem to antihydrogen-deuterium and antihydrogen-tritium systems is discussed.
DOI
10.1088/0953-4075/25/8/001

Related papers

Possible Coexistence of Antihydrogen with Hydrogen, Deuterium and Tritium Atoms

Mohamed Assad Abdel-Raouf

Recent productions of large numbers of cold antiprotons as well as the formation of antihydrogens at CERN and Fermilab have raised basic questions about possible coexistence of matter and antimatter in nature. In the present work, previous mathematical considerations are revisited which support the possible coexistence of Antihydrogen with Hydrogen, Deuterium and Tritium atoms. In particular, the main objective of the present work is to present computational treatments which confirm the possible formation of these quasi molecules in laboratory. These treatments are based on a nonadiabatic picture of the system in which generalized basis functions are adjusted within the framework of Rayleigh-Ritz' variational method. Thus, it is ruled out in the present work the Born-Oppenheimer adiabatic picture of the system, which demands the existence of bound states composed of fixed quasi heavy atoms (containing at least two baryons, e.g. protonium (Pn), with mean lifetime 1.0x10^^-6 s) and quasi light atoms (composed of two leptons, e.g. positronium (Ps), with mean lifetime 125x10^^-12 s for para-Ps and 142.05x10^^-9 s for ortho-Ps). Our calculations of the binding energies and internal structure of Antihydrogen-Hydrogen, Antihydrogen-Deuterium and Antihydrogen-Tritium show that these quasi molecules are bound and could be formed in nature. On the other hand, having in mind the adiabatic picture of the systems, our results suggest the possible formation of these molecules as resonant states in Antihydrogen-Atom interaction. Nevertheless, several arguments are accumulated in the conclusion as consequences of the proposed bound states.

arXiv:0711.2283•Nov 14, 2007•2 citations

Atomic processes in antihydrogen experiments: a theoretical and computational perspective

F. Robicheaux

One possible route for a precision test of the CPT theorem is to perform spectroscopic measurements on the antihydrogen atom and compare the results with those from hydrogen. We present a review of the existing theoretical and computational treatments of atomic processes important for understanding the experiments to make and trap the antihydrogen atom. The emphasis of this review is on the behaviour and properties of the charged species in these devices (electrons, positrons and antiprotons) and the properties of the antihydrogen that can be formed.

Journal of Physics B Atomic Molecular and Optical Physics•Sep 10, 2008•56 citations

Hydrogen Atom

S. Rajasekar, R. Velusamy

The hydrogen atom is the simplest of all atoms consisting of proton of charge e and the electron of charge -e. It is a two particle system. A two-body problem can always be reduced to a one-body problem by choosing the centre of mass coordinate and the relative coordinates. The existence of degenerate energy eigenvalues implies that linear combination of the corresponding eigenfunctions are solutions of the wave equation with the same energy. The isotopes of atomic hydrogen, deuterium and tritium also provide examples of hydrogenic systems. Since the mass of deuterium is md˜2mp and that of tritium is mt˜3mp, the reduced masses of them will be slightly different from that of hydrogen. In addition to deuterium and tritium, there exists other hydrogenic systems in which the role of proton is played by another positive particle.

CRC Press eBooks•Sep 29, 2022•0 citations

One-Dimensional Hydrogen Atom

R. Loudon

The quantum-mechanical system which consists of a particle in one dimension subjected to a Coulomb attraction (the one-dimensional hydrogen atom) is shown to have a ground state of infinite binding energy, all the excited bound states of the system having a twofold degeneracy. The breakdown of the theorem that a one-dimensional system cannot have degeneracy is examined. The treatment illustrates a number of properties common to the quantum mechanics of one-dimensional systems.

American Journal of Physics•Dec 1, 1959•586 citations

COMPOSITE SYSTEMS IN MAGNETIC FIELD: FROM HADRONS TO HYDROGEN ATOM

B. O. KERBIKOV

We briefly review the recent studies of the behavior of composite systems in magnetic field. The hydrogen atom is chosen to demonstrate the new results which may be experimentally tested. Possible applications to physics of antihydrogen are mentioned.

arXiv:1312.3254•Jun 27, 2014•0 citations

MATTER-ANTIMATTER INTERACTIONS : The hydrogen-antihydrogen system and antiproton-matter interactions

Henrik Stegeby

Ever since antiparticles were discovered their nature has been something of a mystery. They were postulated to be identical to regular particles except for having opposite charge, but this would imply that an equal amount of antiparticles and particles should have been created at the beginning of time. However, everywhere we look the Universe seems to be constituted of regular particles, giving rise to the question whether there is something else that differentiates antiparticles from regular particles, or if there is something amiss in the Standard Model of particle physics. This thesis focuses on a central system of study in this field, the hydrogen-antihydrogen system and the theory surrounding it, as well as an expansion into systems with an antiproton interacting with small molecules, bridging the fields of quantum physics and quantum chemistry. Methods expanding on the Born-Oppenheimer approximation for the interaction between the two atoms are presented. The resulting 2-body interaction potential is then used for creating a part of the basis in a non-adiabatic 4-body method in order to look for resonance states whose existence could impact cross-sections of hydrogen-antihydrogen scattering. The eigenfunctions obtained from the non-adiabatic method are used by extracting the 2-body hadronic density function and comparing it to the adiabatic wave function, for measuring the adiabaticity of the hydrogen-antihydrogen system. The antiproton-matter interaction is first investigated by a quantum dynamical approach of an antiproton scattering on molecular hydrogen, common products in high-energy collision experiments, continued by a study of the potential energy surfaces of an antiproton interacting with a range of functional groups present in the human body.

•Jan 1, 2018•0 citations
Recent productions of large numbers of cold antiprotons as well as the formation of antihydrogens at CERN and Fermilab have raised basic questions about possible coexistence of matter and antimatter in nature. In the present work, previous mathematical considerations are revisited which support the possible coexistence of Antihydrogen with Hydrogen, Deuterium and Tritium atoms. In particular, the main objective of the present work is to present computational treatments which confirm the possible formation of these quasi molecules in laboratory. These treatments are based on a nonadiabatic picture of the system in which generalized basis functions are adjusted within the framework of Rayleigh-Ritz' variational method. Thus, it is ruled out in the present work the Born-Oppenheimer adiabatic picture of the system, which demands the existence of bound states composed of fixed quasi heavy atoms (containing at least two baryons, e.g. protonium (Pn), with mean lifetime 1.0x10^^-6 s) and quasi light atoms (composed of two leptons, e.g. positronium (Ps), with mean lifetime 125x10^^-12 s for para-Ps and 142.05x10^^-9 s for ortho-Ps). Our calculations of the binding energies and internal structure of Antihydrogen-Hydrogen, Antihydrogen-Deuterium and Antihydrogen-Tritium show that these quasi molecules are bound and could be formed in nature. On the other hand, having in mind the adiabatic picture of the systems, our results suggest the possible formation of these molecules as resonant states in Antihydrogen-Atom interaction. Nevertheless, several arguments are accumulated in the conclusion as consequences of the proposed bound states.
One possible route for a precision test of the CPT theorem is to perform spectroscopic measurements on the antihydrogen atom and compare the results with those from hydrogen. We present a review of the existing theoretical and computational treatments of atomic processes important for understanding the experiments to make and trap the antihydrogen atom. The emphasis of this review is on the behaviour and properties of the charged species in these devices (electrons, positrons and antiprotons) and the properties of the antihydrogen that can be formed.
The hydrogen atom is the simplest of all atoms consisting of proton of charge e and the electron of charge -e. It is a two particle system. A two-body problem can always be reduced to a one-body problem by choosing the centre of mass coordinate and the relative coordinates. The existence of degenerate energy eigenvalues implies that linear combination of the corresponding eigenfunctions are solutions of the wave equation with the same energy. The isotopes of atomic hydrogen, deuterium and tritium also provide examples of hydrogenic systems. Since the mass of deuterium is md˜2mp and that of tritium is mt˜3mp, the reduced masses of them will be slightly different from that of hydrogen. In addition to deuterium and tritium, there exists other hydrogenic systems in which the role of proton is played by another positive particle.
Ever since antiparticles were discovered their nature has been something of a mystery. They were postulated to be identical to regular particles except for having opposite charge, but this would imply that an equal amount of antiparticles and particles should have been created at the beginning of time. However, everywhere we look the Universe seems to be constituted of regular particles, giving rise to the question whether there is something else that differentiates antiparticles from regular particles, or if there is something amiss in the Standard Model of particle physics. This thesis focuses on a central system of study in this field, the hydrogen-antihydrogen system and the theory surrounding it, as well as an expansion into systems with an antiproton interacting with small molecules, bridging the fields of quantum physics and quantum chemistry. Methods expanding on the Born-Oppenheimer approximation for the interaction between the two atoms are presented. The resulting 2-body interaction potential is then used for creating a part of the basis in a non-adiabatic 4-body method in order to look for resonance states whose existence could impact cross-sections of hydrogen-antihydrogen scattering. The eigenfunctions obtained from the non-adiabatic method are used by extracting the 2-body hadronic density function and comparing it to the adiabatic wave function, for measuring the adiabaticity of the hydrogen-antihydrogen system. The antiproton-matter interaction is first investigated by a quantum dynamical approach of an antiproton scattering on molecular hydrogen, common products in high-energy collision experiments, continued by a study of the potential energy surfaces of an antiproton interacting with a range of functional groups present in the human body.