Calculation of the multiplicity moments in nuclear safeguards with forward transport theory

The theoretical basis of multiplicity counting of nuclear safeguards lies in the calculation of the factorial moments of the number of neutrons emitted from the item. While the traditional method to derive these moments uses the so-called point model in which the spatial transport of neutrons in the item is neglected, the theoretical framework has recently been re-derived in a one-speed transport model, which is inherently of the backward (adjoint) type. The arising integral equations for the moments were solved numerically with a collision number type (iterated kernel or Neumann-series) expansion. In this paper, we show that effective methods of analytical character, originally developed for direct (forward-type) transport problems, can be associated with the solution of the adjoint-type moment equations. The theory is described, and quantitative results are given for selected representative cases. The accuracy and computational speed of the method is investigated and compared favourably with those of the collision number expansion method. The quantitative results also lend some new insight into the properties of statistics of the multiplicative process for the exiting neutrons.