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

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.

14 pages, 4 figures