An Alternative Method for Analyzing Active Multiplicity Data

We have developed a novel method for analyzing active neutron multiplicity data. The conventional method was derived from the standard passive multiplicity equations known as the point model. The approach was to substitute a term consisting of the product of the interrogation source strength, the coupling coefficient, and the sample mass for the product term of the sample mass and the fission rate: I m F m c 0 ? ? , where I is the source strength, c ? is the coupling coefficient, m is the sample mass and F is the fission rate. Note that the sample mass, m, refers to the fissile material (e.g. 235U) in the active case and fertile material (e.g. 240Pueff) in the passive case. In addition, the spontaneous fission multiplicity coefficients, s ? , were replaced with the induced fission multiplicity coefficients, i ? . This model has several drawbacks. The most significant is that the coupling coefficient, c ? , varies significantly with the multiplication. As a consequence, there is not a clear linear relationship between the doubles rate and the sample mass, nor is there a clear linear relationship between the multiplication-corrected doubles rate and the sample mass. This problem has limited the application of active neutron multiplicity counting. We propose here a novel approach to deriving the multiplicity equations. A different substitution is made in the point model equations. The value of alpha is replaced with a new term, alpha-prime: 0 s1 p Fm I ? ? a ?a ' =a + . There are several benefits to this approach, but most significant is that the new coupling coefficient, p ? , remains constant. In this paper we will establish the general physics justification why this different substitution is appropriate. We will derive the new point model equations for active neutron multiplicity starting from the original point model equations and making the substitution above, and we will compare the two models.