Space and energy dependent theoretical formula for the third order neutron correlation technique

We have studied measurement techniques of subcriticality by using the neutron correlation techniques. Among various techniques, we have paid attention to the third order neutron correlation technique, which was proposed by Furuhashi originally and utilizes the third order fluctuations of neutron counts. By using this technique, we can obtain the absolute value of subcriticality with the aid of factorial moments of fission neutron ν and external source neutron q, without prior knowledge of the prompt neutron decay constant at a reference state. However, in order to apply the third order neutron correlation technique to actual experiments, we must consider the spatial and neutron energy effects in this technique. For this purpose, we derived more generalized theoretical formulas of the third order neutron correlation technique that took account of the spatial and neutron energy effects by virtue of the α-eigenfunction expansion. Making use of the newly derived formulas, we propose the practical formulas and the experimental procedures based on the fundamental mode approximation.