We describe a radiochemical measurement of the ratio of isotope concentrations produced in a gold hohlraum surrounding an Inertial Confinement Fusion capsule at the National Ignition Facility (NIF). We relate the ratio of the concentrations of (n,γ) and (n,2n) products in the gold hohlraum matrix to the down-scatter of neutrons in the compressed fuel and, consequently, to the fuel's areal density. The observed ratio of the concentrations of (198m+g)Au and (196g)Au is a performance signature of ablator areal density and the fuel assembly confinement time. We identify the measurement of nuclear cross sections of astrophysical importance as a potential application of the neutrons generated at the NIF.