Updating the Lambda modes of a nuclear power reactor

This problem is known as the Lambda Modes problem. The fundamental eigenvalue (the largest one) is called the effective multiplication, k-effective, of the reactor core. This eigenvalue and its corresponding eigenfunction describe the steady state neutron distribution in the core. On the other hand, to compute the dominant modes of the reactor core is useful to develop modal methods [2] to integrate the time dependent neutron diffusion equation and also for perturbative calculations.