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

In the present work, quasi-molecular compounds consisting of one antiproton (p̄) and one hydrogen-like ion are investigated: He⁺ - p̄, Li²⁺ - p̄, C⁵⁺ - p̄, S¹⁵⁺ - p̄, Kr³⁵⁺ - p̄, Ho⁶⁶⁺ - p̄, Re⁷⁴⁺ - p̄, U⁹¹⁺ - p̄. 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.