image: While reactivity is commonly understood to have a nonlinear relationship with nuclide concentration, typically requiring complex numerical calculations, we discovered that taking the reciprocal of uranium concentration reveals a linear relationship with reactivity.
Credit: Chang-Qing Yu
The 1/v Law as the Foundation
The nuclear reaction cross-sections of major nuclides obey the 1/v law in the thermal neutron region—that is, the cross-section is inversely proportional to velocity. This establishes the foundation for the theoretical derivation and serves as the basis for the general applicability of the linear relationship.
Two key conclusions
Two key conclusions can be drawn due to the 1/v law: the one-group cross-sections of nuclear reactions exhibit a linear relationship with each other, and the cross-section shows a linear relationship with the reciprocal of nuclide concentration.
Derivation of the Theoretical Relationship
Based on the two main conclusions mentioned above, the relationship between reactivity and uranium concentration can be derived through the neutron balance equation. “In this paper, we have derived the relationship specifically for fissile nuclides—uranium concentration. As can be seen, this formulation can be extended to non-fissile nuclides, thereby establishing a relationship between reactivity and the concentrations of all nuclides," explained Changqing Yu.
Potential Applications
The most direct application of this simple relationship is in criticality calculations. By knowing the reactivity at any two uranium concentrations, one can determine the reactivity at any other uranium concentration. In addition, it can be used for fuel loading prediction, reactivity measurement, and even burnup calculations.
Insights Gained
The primary path in the development of modern reactor physics lies in numerical computation, which is undoubtedly crucial, as advances in computing allow numerical results to become increasingly precise. However, theoretical research grounded in physical processes enables us to grasp the essence of physics. Discovering that results we typically understand as requiring complex numerical calculations can actually be described by a simple linear relationship is truly exciting.
The complete study is via by DOI: 10.1007/s41365-025-01854-6
Journal
Nuclear Science and Techniques
Method of Research
Computational simulation/modeling
Subject of Research
Not applicable
Article Title
Linear relationship between reactivity and the reciprocal of uranium concentration in thermal-spectrum molten salt reactors
Article Publication Date
3-Jan-2026