Damping width of the double giant dipole resonance of Xe-136 excited i
n relativistic heavy ion collisions is calculated by diagonalizing a m
icroscopic Hamiltonian in a basis containing one-, two- and three-phon
on states. The coupling between these states is determined making use
of the fermion structure of the phonons. The resulting width of the do
uble giant dipole resonance is close to root 2 times the width of the
single giant dipole resonance.