Electromagnetic excitation of the double giant dipole resonance in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Xe</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>136</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>

The nuclear response of a medium-mass nucleus ${(}^{136}$Xe) to electromagnetic excitation in a near-relativistic heavy-ion collision was investigated in the ${\mathrm{reaction}}^{136}$Xe(0.7A GeV)+Pb. From an exclusive measurement of the neutron decay of the excited $^{136}\mathrm{Xe}$ projectiles, strong excitations of giant resonances and, in particular, of the double isovector giant dipole resonance were identified. A resonance energy of 28.3\ifmmode\pm\else\textpm\fi{}0.7 MeV, a width of 6.3\ifmmode\pm\else\textpm\fi{}1.6 MeV, and a total cross section of 215\ifmmode\pm\else\textpm\fi{}50 mb were found for the double giant dipole resonance.