Adjustment of Group Cross Sections by Means of Integral Data, (I)

Theoretical Study

Abstract

A theoretical treatment is developed for the adjustment of group cross sections making use of integral data such as critical mass, reaction rate ratio and sample worth ratio obtained from various fast critical experiments. The method of least squares is the usual practice in such treatment. In the present case, however, the total number of integral data available is usually smaller than that of the group cross sections to be adjusted. To overcome this difficulty, the observation equations for applying the least squares treatment are established by using both integral and differential data. In such treatment, the correlation between group cross sections can be easily taken into account. General formulas are presented on two kinds of such correlation, one based on nuclear theory and the other due to relative measurements of the cross sections. The χ²-test for the sum of squares of the residual is used as criterion to judge whether or not group cross sections carry systematic error. If systematic error exists, the sum of squares of the residual has a non-central Chi-square distribution. When the systematic error is included only in the group cross sections and not in the integral data, it is possible to remove this systematic error through use of the method of least squares.