Passive methods of nuclear safeguards determine the important parameters of an unknown sample from the statistics of the detection of the neutrons emitted from the item. These latter are due to spontaneous fissions and ($\alpha$,n) reactions, enhanced by internal multiplication before leaking out. Based on the original work of Böhnel, the methodology of traditional multiplicity counting is based on the first three factorial moments of the number of neutrons, emitted from the sample due to one source event. These “Böhnel moments” were derived in the so-called “point model”, in which no space-dependence is accounted for, rather a uniform first collision probability is assumed for each neutron, irrespective of the position of its birth and its velocity direction, and, more important, it is assumed to be the same for all generations in the fission chain as for the source neutrons. The purpose of the present work is to derive the same factorial moments in a one-speed space-dependent model, in which the position and direction of the neutrons is accounted for, but (similarly to the original Böhnel model), no energy dependence is assumed. The integral equations for the moments are solved numerically with a collision number expansion. It is shown that compared to the space-dependent calculations, the unfolding method using the point model underestimates the fissile mass and the underestimation increases with increasing both of fissile mass and the value of $\alpha$.

核保障措施的被动方法根据从该物品发射的中子的检测统计数据确定未知样品的重要参数。后者是由于自发裂变和（$\alpha$，n）反应，在泄漏之前通过内部乘法得到增强。基于伯纳尔（Böhnel）的原始工作，传统的多重计数方法是基于由于一个源事件从样品中发出的中子数的前三个阶乘矩。这些“Böhnel矩”是在所谓的“点模型”中得出的，其中没有考虑空间依赖性，而是假定每个中子的统一初次碰撞概率均不考虑其出生位置和速度方向，更重要的是，假定裂变链中的所有代与源中子都相同。本工作的目的是在单速与空间有关的模型中得出相同的阶乘矩，其中考虑了中子的位置和方向，但是（类似于原始的Böhnel模型），没有假定能量依赖性。力矩的积分方程通过碰撞数展开进行数值求解。结果表明，与基于空间的计算相比，使用点模型的展开方法低估了裂变质量，而低估随着裂变质量和值的增加而增加。$\alpha$。