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In this report we present an approach to deal with a problem encountered in different type of systems and specific configurations: the treatment of low density regions. This is the case of gas cooled reactors, voided configurations (evaluations of associated reactivity coefficients), beam region of external source driven systems, etc. The approach is to form the nodal response matrix using the first-order form of the transport equation, for then the cross section no longer appears in the denominator, as in the case of the standard formulation of the VARIANT code. Two different formulations are presented: the differential and integral ones. After applications to different difficult benchmark problems, it was concluded that the new formulations can treat low density regions

Fuel cycle methods : first-order spherical harmonics formulations capable of treating low density regions.