Which statement best describes the diffusion-adjoint eigenvalue problem used in reactor theory?

• A. It yields the time-dependent neutron distribution.
• B. It gives the relation between flux and k_eff without time dependence.
• C. It results in an eigenvalue equal to k_eff where φ is the eigenfunction.
• D. It is the equation for the thermal expansion of the reactor core.

Answer: (C)

Neutron diffusion in steady state is formulated as an eigenvalue problem that balances production and loss. The diffusion operator acting on the neutron flux, together with removal terms, is set up so that the production from fission is scaled by 1/k_eff. Solving this operator equation yields an eigenvalue that equals k_eff and an eigenfunction that is the spatial distribution of the scalar flux φ. The diffusion-adjoint form introduces an adjoint flux as well, but the eigenvalue you obtain remains k_eff, tying directly to the criticality condition: k_eff = 1 for critical, greater for supercritical, smaller for subcritical. This formulation describes a time-independent balance, not the time evolution of the neutron population.