One-electron molecular systems in a strong magnetic field

Abstract

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 H 2 + ( ppe ) , H 3 ++ ( pppe ) , H 4 3 + ( ppppe ) and ( HeH ) ++ ( α pe ) , He 2 3 + ( α α e ) in a magnetic field ranging from 10 9 to 4.414 × 10 13 G (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 ≲ 10 11 G the H 2 + -ion always exists for any inclination of the molecular axis with respect to the magnetic line. For B ≳ 10 11 G and large inclinations the minimum in the total energy curve disappears and the molecular ion H 2 + ceases to exist. The domain of inclinations where the H 2 + -ion exists, reduces as the magnetic field increases and finally becomes 0– 25 ∘ at B = 4.414 × 10 13 G . The optimal configuration of H 2 + always corresponds to protons situated along the magnetic line (the parallel configuration). With magnetic field growth the ion H 2 + 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 H 3 ++ -ion was mentioned for the first time at 1999. In the range of magnetic fields 10 8 < B < 10 11 G the H 3 ++ -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 H 2 + + p . The triangular configuration of H 3 ++ complements the H 3 ++ -ion in the linear, parallel configuration which exists for B ≳ 10 10 G . A study of several low-lying excited states for H 3 ++ in the parallel configuration is presented. For B ≳ 3 × 10 13 G another molecular ion H 4 3 + 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 ≲ 4.414 × 10 13 G . Among one-electron systems containing protons, H 2 + has the lowest total energy for 0 < B ≲ 10 13 G . However, for B ≳ 10 13 G the exotic system H 3 ++ has the lowest total energy and is stable. The exotic systems containing α -particles, ( HeH ) ++ ( α pe ) and He 2 3 + ( α α e ) can exist in a magnetic field B ≳ 10 12 G and B ≳ 2.35 × 10 11 G , respectively. In general, the ion He 2 3 + 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, H 2 + ↔ H + p is investigated.