On the significance of the energy correlations of spallation neutrons on the neutron fluctuations in accelerator-driven subcritical systems

Studies of neutron fluctuations in spallation-driven subcritical systems require the use of energy-dependent master equations. In particular, calculation of the second moment of the neutron distribution requires knowledge on the energy correlations (two-point distributions) of the source particles. It is shown here that such correlations will exist even if the energies of all neutrons, generated in any single spallation event, are independent, provided that the energy distribution of the neutrons for separate spallation events is dependent on the number of neutrons generated. A simple model of number dependence of the energy spectrum is constructed, and the arising energy correlations are calculated. The error in calculating the second moment of the neutron distribution, arising when assuming zero correlations (i.e. using only one-particle energy spectra), is estimated in a simple model of neutron slowing down.