Spin rearrangement of many-electron atoms in magnetic fields of arbitrary strength

A Thomas-Fermi equation for many-electron atoms in magnetic fields of arbitrary strength is derived. The equation determines self-consistently both the electron number density with spins parallel and that with spins antiparallel to the external magnetic fields, and describes the process of spin rearrangement of the ground state of atoms. By an appropriate scale change, the equation reduces to a universal form independent of the atomic number for neutral atoms. Numerical results are also shown for the total energy, the total spin, the atomic radius and so on as a function of the magnetic field strength.