Abstract

In a previous paper by Pázsit and Pál [“Multiplicity Theory Beyond the Point Model,” Ann. Nucl. Energy, Vol. 154 (2021)], a general transport theory calculation of the factorial moments of the number of neutrons emitted spontaneously from a sample was elaborated. In contrast to the original derivations by Hage and Cifarelli [“On the Factorial Moments of the Neutron Multiplicity Distribution of Fission Cascades,” Nucl. Instrum. Meth. Phys. Res. A, Vol. 236 (1985)] and Böhnel [“The Effect of Multiplication on the Quantitative Determination of Spontaneously Fissioning Isotopes by Neutron Correlation Analysis,” Nucl. Sci. Eng., Vol. 90 (1985)], also referred to as the point model, in the transport model the spatial and angular dependence of the internal fission chain is taken into account with a one-speed transport theory treatment. Quantitative results were given for a spherical item, and the bias of the point model regarding the estimation of the fission rate as compared to the more exact space-dependent model was estimated as a function of the size of the sphere and the $\alpha$ factor.

In the present paper the formalism and the quantitative work are extended to the treatment of items with cylindrical shapes, which are more relevant in many practical applications. Results are presented for both square cylinders ($D=H$) and for tall ($H/D>1$) and flat ($H/D<1$) cylinders. This way the differences between the cylinder and the sphere on one hand and those between the various cylinder shapes on the other hand can be estimated. The results show that the bias depends on the geometry of the cylinder quite moderately, but similarly to the case of the sphere, the bias of the point model is quite significant for larger item sizes and $\alpha$ values, and it is nonconservative (underestimates the fissile mass) as well.

摘要

在 Pázsit 和 Pál 之前的一篇论文中 [“超越点模型的多重性理论”，Ann。核。能源，卷。154（2021）]，详细阐述了从样品中自发发射的中子数量的阶乘矩的一般输运理论计算。与 Hage 和 Cifarelli 的原始推导相反 [“关于裂变级联的中子多重性分布的阶乘矩”，Nucl。仪表。冰毒。物理。水库。A，卷。236 (1985)] 和 Böhnel [“乘法对通过中子相关分析定量测定自发裂变同位素的影响”，Nucl。科学。工程，卷。90（1985）]，也称为点模型，在传输模型中，内部裂变链的空间和角度相关性被考虑到单速传输理论处理。$\alpha$ 因素。

在本文中，形式主义和定量工作扩展到处理具有圆柱形形状的物品，这在许多实际应用中更为相关。结果显示为两个方形圆柱体（$D=H$) 和高 ($H/D>1$) 和平 ($H/D<1$) 气缸。这样，一方面可以估计圆柱体和球体之间的差异，另一方面可以估计各种圆柱体形状之间的差异。结果表明，偏差相当适度地取决于圆柱体的几何形状，但与球体的情况类似，点模型的偏差对于较大的项目尺寸和$\alpha$ 值，并且它也是非保守的（低估了裂变质量）。