  We calculate the spin flip rates for an electron in a homogeneous magnetic
field for low excitations ($N\le 5$). Our results apply for all field strengths
including those beyond the critical field strength at which the spin
contributes as much to the electron's energy as its rest mass. Existing
approximations either assume that the electron is in a sufficiently highly
excited state such that its orbit can be assumed to be classical or the
magnetic field be weak compared to the critical field. The regime of high
magnetic field strength and low excitations is therefore poorly covered by
them. By comparing our calculations to different approximations, we find that
in the high field, low excitation regime the spin flip rates are lower and the
equilibrium spin polarization is less pure then one would get by naively
applying existing approximations in this regime.
