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

In the present work, quasi-molecular compounds consisting of one antiproton ( $ \bar {p} $ p<overline>) and one hydrogen-like ion are investigated: $ \mathrm {He}<^>{+} - \bar {p} $ He+-p<overline>, $ \mathrm {Li}<^>{2+} - \bar {p} $ Li2+-p<overline>, $ \mathrm {C}<^>{5+} - \bar {p} $ C5+-p<overline>, $ \mathrm {S}<^>{15+} - \bar {p} $ S15+-p<overline>, $ \mathrm {Kr}<^>{35+} - \bar {p} $ Kr35+-p<overline>, $ \mathrm {Ho}<^>{66+} - \bar {p} $ Ho66+-p<overline>, $ \mathrm {Re}<^>{74+} - \bar {p} $ Re74+-p<overline>, $ \mathrm {U}<^>{91+} - \bar {p} $ U91+-p<overline>. For the calculations, the Dirac equation with two-centre 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.