Effect of antiprotons on hydrogen-like ions in external magnetic fields

TL;DR

This study investigates the electronic structure and magnetic field effects on antiproton-hydrogen-like ion compounds using advanced numerical methods, revealing Zeeman shifts up to 100 Tesla.

Contribution

It introduces a novel application of the dual-kinetically balanced finite-basis-set method to analyze antiproton-ion systems in magnetic fields.

Findings

Calculated adiabatic potential curves for various quasi-molecular compounds.

Determined Zeeman shifts of molecular terms in strong magnetic fields.

Demonstrated non-perturbative effects of magnetic fields on these systems.

Abstract

In the present work, quasi-molecular compounds consisting of one antiproton ($\bar{p}$) and one hydrogen-like ion are investigated: $\mathrm{He}^{+} - \bar{p}$, $\mathrm{Li}^{2+} - \bar{p}$, $\mathrm{C}^{5+} - \bar{p}$, $\mathrm{S}^{15+} - \bar{p}$, $\mathrm{Kr}^{35+} - \bar{p}$, $\mathrm{Ho}^{66+} - \bar{p}$, $\mathrm{Re}^{74+} - \bar{p}$, $\mathrm{U}^{91+} - \bar{p}$. For the calculations, the Dirac equation with two-center potential is solved numerically using the dual-kinetically balanced finite-basis-set method adapted to systems with axial symmetry (A-DKB). Adiabatic potential curves are constructed for the ground state of the above quasi-molecular compounds in the framework of the A-DKB approach. Calculations were also performed for the case of an external magnetic field (the field is taken into account non-perturbatively). Zeeman shifts of the quasi-molecular terms are obtained for a homogeneous magnetic field with a strength of the laboratory order (up to 100 Tesla) directed along the axis of the molecule.