  A formula for the electron spin relaxation rate of an electron-phonon system
is derived using a new spring-loop diagram method. The result contains the
distribution functions for the electrons and phonons properly. Therefore, all
the spin flip and conserving processes are explained from a microscopic point
of view, and a physical insight of the quantum dynamics of electron spin in a
solid is obtained from the diagram. Photons and phonons are classified
according to the spin flip and conserving processes. The formula is used to
calculate the electron spin relaxation rate in GaAs. The temperature dependence
of the relaxation rate is obtained by a comparison with the experimental
result.
