[en] A method to measure the density distribution of a dense hydrogen gas jet is presented. A Mach 5.5 nozzle is cooled to 80K to form a flow capable of molecular cluster formation. A 250V, 10mA electron beam collides with the jet and produces H_α emission that is viewed by a fast camera. The high density of the jet, several 10¹⁶cm^-3, results in substantial electron depletion, which attenuates the H_α emission. The attenuated emission measurement, combined with a simplified electron-molecule collision model, allows us to determine the molecular density profile via a simple iterative calculation.