A standard time-dependent neutron transport computer code, TDA, is modified to allow time-varying material density to calculate the neutron spectrum from exploding inertial confinement fusion pellets with ρR values of 0 to 6 g/cm2. Softening of the spectra due to neutron-fuel interactions causes a time-of-flight broadening of the neutron arrival time distribution at the chamber wall. It is found that the total number of displacements per atom (dpa) produced in a graphite first wall increases with the ρR of the pellet over the ρR range investigated because the dpa cross section is larger at lower neutron energy. However, the total helium production decreases with increasing ρR, as does the peak damage rate. Neutron-induced radioactivity generated in a 10-mg iron tamper is of the same magnitude as that produced in the rest of an entire reactor system.