Ionization equilibrium and equation of state of hydrogen plasmas in strong magnetic fields

We study hydrogen plasmas at magnetic fields B ~ 10^{12}-10^{13} Gauss, densities ~ 10^{-3}-10^3 g/cc and temperatures T ~ 10^{5.5}-10^{6.5} K, typical of photospheres of middle-aged cooling neutron stars. We construct an analytical free energy model of the partially ionized plasma, including into consideration the decentred atomic states, which arise due to the thermal motion across the strong field. We show that these states, neglected in previous studies, may contribute appreciably into thermodynamics of the outer atmospheric layers at density below 1 g/cc and typical B and T. We take into account Coulomb non-ideality of the ionized component of the plasma affected by intense magnetic field. Ionization degree, occupancies and equation of state are calculated, and their dependences on the temperature, density and magnetic field are studied.