Measurement of the effect of the lattice pitch on the effective resonance integral of natural uranium

The analytical theory of resonance absorption, as well as the numerical Monte Carlo method, allows calculation of the resonance integral. However, it is based on specific approximations so it may be used accurately enough in a limited number of cases. Likewise, insufficiently accurate know ledge of the basic nuclear constants (e.g. resonance parameters, etc.) used as input data in analytical calculation, leads to inaccurate determination of the resonance integral.. Therefore, experimental determination of the effective resonance integral is still indispensable. In some cases the experimental results are used as the exclusive source of information, or as the basis for the semiempirical technique of calculation, and in others as a check of the new theoretical procedures. There are several experimental methods of direct determination of the resonance integral: the activation method (1,2), the reactor oscillator and the danger coefficient method. Indirectly, using the results of critical experiments, it is possible to determine correlated values of the effective resonance integral. The present work investigates the dependence of the effective resonance integral on the lattice pitch. Theoretically, the dependence is determined starting from Wigner's rational approximation in which the lattice is characterized by the effective ratio (S/M) X. Later this allows correlation between the lattice resonance integral and the resonance integral of the single rod (the rod in infinite medium). Using two approximations for Dancoff's factor we give the measured functional dependence of the effective resonance integral on the effective (S/M)X ratio. To determine the resonance integral experimentally we used the activation method and the differential technique of measuring absorption distribution in U238. Since, because of the use of cadmium in determining the cadmium ratio in the fuel rod the effective lattice pitch cannot be defined with certain reliability, besides other perturbing effects, the method of comparing thermal activations of and a suitable thermal detector are used to determine the cadmium ratio (author)