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Circular Rydberg states of atomic hydrogen in an arbitrary magnetic field

We report a theoretical scheme using a B-spline basis set to improve the poor computational accuracy of circular Rydberg states of hydrogen atoms in the intermediate magnetic field. This scheme can produce high accuracy energy levels and valid for an arbitrary magnetic field. Energy levels of hydrogen are presented for circular Rydberg states with azimuthal quantum numbers $|m|$ = 10 - 70 as a function of magnetic field strengths ranging from zero to 2.35 $\times$ 10$^9$ T. The variation of spatial distributions of electron probability densities with magnetic field strengths is discussed and competition between Coulomb and magnetic interactions is illustrated.