The Bethe-Salpeter equation for an electromagnetic bound system which consists of a spin 1/2 particle is derived and the approximate Bethe-Salpeter wavefunctions for total angular momentum J=1/2 and J=3/2 are obtained. Using these wavefunctions, the cross sections for process mu +d to (d mu )+ gamma are calculated. These cross sections are of the order of 10^-27 cm² in the rest frame of deuterium when the kinetic energy of the incident muon is of the order of keV.