Hydrogen atom in strong magnetic fields: summation of the weak field series expansion

Using the weak field expansion, we have calculated the ground-state energy of the hydrogen atom in a magnetic field for values of the field up to about 1013 G. The perturbative expansion has been summed by an order-dependent mapping method. We compare our results with previous calculations. Our method allows us to obtain: first, more accurate values of the binding energy for a field up to 1010 G, then good results in the transition region between the two sets of accurate calculations of the literature, and finally still reasonably accurate values up to 1010 G