Calculation of recoil spectra induced by fast neutron spectra in nuclear emulsions

In fast neutron spectroscopy using nuclear emulsions, the relation between the neutron spectrum and the proton spectrum is generally deduced from the properties of the neutron-proton scattering. From the experiments performed in our laboratory it appears that it is advantageous to measure the spectrum of the range projected on the plane of the emulsion only, taking into account the geometry of the exposure. The present paper provides a mathematical basis for the analysis of data obtained under such conditions, in the case of complex neutron spectra ; range straggling in the emulsion is accounted for. Both the analytical and the Monte-Carlo method are dealt with. Finally a correlated sampling method is described which yields a very accurate calculation of the recoil spectrum induced by a fission spectrum.