Some of X-ray dim isolated neutron stars (XDINS) and central compact objects in supernova remnants (CCO) show absorption features in their thermal soft X-ray spectra. It has been hypothesized that these features could be due to the periodic peaks in
free-free absorption opacities, caused by either Landau quantization of electron motion in magnetic fields B<10^{11} G or analogous quantization of ion motion in magnetic fields B>10^{13} G. Here, I review the physics behind cyclotron quantum harmonics in free-free photoabsorption, discuss different approximations for their calculation, and explain why the ion cyclotron harmonics (beyond the fundamental) cannot be observed.
We briefly review analytic approximations of thermodynamic functions of fully ionized nonideal electron-ion plasmas, applicable in a wide range of plasma parameters, including the domains of nondegenerate and degenerate, nonrelativistic and relativis
tic electrons, weakly and strongly coupled Coulomb liquids, classical and quantum Coulomb crystals. We present improvements to previously published approximations. Our code for calculation of thermodynamic functions based on the reviewed approximations is made publicly available.
