[en] This patent describes a method for detecting explosive materials in a target, the explosive materials containing characteristically large or small amounts of one or more nuclear species of interest. It comprises resonantly exciting nuclei of the target with a beam of bremsstrahlung radiation, resonantly exciting nuclei of one or more reference scatterers with the beam of bremsstrahlung radiation transmitted through the target, each the reference scatterer comprising one or more of the nuclear species of interest, measuring the intensity of photons at energies of interest scattered from each the reference scatterer in a direction or directions, the energies of interest for each reference scatterer corresponding to the spacings between the quantized energy states of the nuclear species of interest of which the reference scatterer is comprised, and estimating the abundance of each nuclear species of interest in the target from the measured intensity of photons scattered from the reference scatterer or scatterers comprising the nuclear species