  It is shown that the sharp peak in the $E_{2g}$ Raman spectrum of
superconducting $MgB_2$ is due to a bound state caused by the electron-phonon
coupling. Our theory explains why this peak appears only in the spectra with
$E_{2g}$ symmetry and only in the $\sigma$ but not $\pi$ bands. The properties
of the bound state and the Raman spectrum are investigated, also in the
presence of impurity scattering.
