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

In the present work, quasi-molecular compounds consisting of one antiproton $bar{p}$ and one hydrogen-like ion are investigated: He⁺ - bar{p}, Li²⁺ - bar{p}, C⁵⁺ - bar{p}, S¹⁵⁺ - bar{p}, Kr³⁵⁺ - bar{p}, Ho⁶⁶⁺ - bar{p}, Re⁷⁴⁺ - bar{p}, U⁹¹⁺ - 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.