We assess the partition function and ionization degree of magnetized hydrogen atoms at thermodynamic equilibrium for a wide range of field intensities , B \approx 10 ^ { 5 } – 10 ^ { 12 } G. Evaluations include fitting formulae for an arbitrary number of binding energies , the coupling between the internal atomic structure and the center-of-mass motion across the magnetic field , and the formation of the so-called decentered states ( bound states with the electron shifted from the Coulomb well ) .
Non-ideal gas effects are treated within the occupational probability method .
We also present general mathematical expressions for the bound state correspondence between the limits of zero-field and high-field .
This let us evaluate the atomic partition function in a continuous way from the Zeeman perturbative regime to very strong fields .
Results are shown for conditions found in atmospheres of magnetic white dwarf stars ( MWDs ) , with temperatures T \approx 5000 – 80000 K and densities \rho \approx 10 ^ { -12 } – 10 ^ { -3 } g cm ^ { 3 } .
Our evaluations show a marked reduction of the gas ionization due to the magnetic field in the atmospheres of strong MWDs .
We also found that decentered states could be present in the atmospheres of currently known hot MWDs , giving a significant contribution to the partition function in the strongest magnetized atmospheres .