One-electron molecular systems in a strong magnetic field

This review paper is inspired by a recent discovery by Chandra X-ray observatory of two absorption features in the spectra of radiation of the isolated neutron star 1E1207.4-5209, which can be attributed to atomic-molecular content of the atmosphere. It can be easily anticipated that after the above-mentioned discovery other neutron stars characterized by enormous magnetic fields will also become the objects for astronomical observations and studies. In the review a detailed qualitative and quantitative consideration of the one-electron molecular systems H2+(ppe),H3++(pppe),H43+(ppppe) and (HeH)++(αpe),He23+(ααe) in a magnetic field ranging from 109 to 4.414x1013G (the Schwinger limit) is presented. The main emphasis is made on the question of the existence of the corresponding molecular ions in a magnetic field. The Born-Oppenheimer approximation of zero order (infinitely heavy protons and/or α-particles) is used throughout. It is shown that for a magnetic field B-bar 1011G the H2+-ion always exists for any inclination of the molecular axis with respect to the magnetic line. For B-bar 1011G and large inclinations the minimum in the total energy curve disappears and the molecular ion H2+ ceases to exist. The domain of inclinations where the H2+-ion exists, reduces as the magnetic field increases and finally becomes 0-25-bar at B=4.414x1013G. The optimal configuration of H2+ always corresponds to protons situated along the magnetic line (the parallel configuration). With magnetic field growth the ion H2+ becomes more and more tightly bound and compact, and the electronic distribution evolves from a two-peak to a one-peak pattern. It is always stable. Several low-lying excited states are studied. The fact that the system (pppe) can be bound in a strong magnetic field to form the H3++-ion was mentioned for the first time at 1999. In the range of magnetic fields 108<B<1011G the H3++-ion with the protons forming an equilateral triangle perpendicular to the magnetic line exists. This configuration is unstable under decays to H-atom+p+p and H2++p. The triangular configuration of H3++ complements the H3++-ion in the linear, parallel configuration which exists for B-bar 1010G. A study of several low-lying excited states for H3++ in the parallel configuration is presented. For B-bar 3x1013G another molecular ion H43+ can exist in parallel configuration. In general, the neutral system-the hydrogen atom-has the highest total energy among the one-electron linear systems in the parallel configuration, so is the least bound but stable one-electron system for the whole region of magnetic fields studied, 0<B-bar 4.414x1013G. Among one-electron systems containing protons, H2+ has the lowest total energy for 0<B-bar 1013G. However, for B-bar 1013G the exotic system H3++ has the lowest total energy and is stable. The exotic systems containing α-particles (HeH)++(αpe) and He23+(ααe) can exist in a magnetic field B-bar 1012G and B-bar 2.35x1011G, respectively. In general, the ion He23+ is characterized by the highest binding energy among known one-electron systems made from protons and/or α-particles. A variational method with an optimization of the form of the vector potential (optimal gauge fixing) is used as a main tool. Phase transition type behavior of variational parameters which appears for some interproton distances and which is related to the beginning of the chemical reaction, for example, H2+-bar H+p is investigated