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We report a theoretical scheme using a B-spline basis set to improve the poorcomputational accuracy of circular Rydberg states of hydrogen atoms in theintermediate magnetic field. This scheme can produce high accuracy energylevels and valid for an arbitrary magnetic field. Energy levels of hydrogen arepresented 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 electronprobability densities with magnetic field strengths is discussed andcompetition between Coulomb and magnetic interactions is illustrated.

Circular Rydberg states of atomic hydrogen in an arbitrary magnetic field