On the perturbative calculation of the vibration noise by strong absorbers

I n two previous papers the neutron noise, induced by small vibrations of a strong absorber, was treated (pazsit 1984, 1988). In these, two different rod models and corresponding different linearization procedures were used. The first. called the Feinberg-Galanin-Williams (FGW) model, uses a 8-function approximation of both the static and the vibrating rod. This model corresponds to preserving the static boundary condition (logarithmic derivative) at the surface of the moving rod. The second, a perturbative approach called the Eld model, starts with a finite absorber and represents the vibration by two stationary absorbing layers with strengths fluctuating in opposite phase. It was found that these two models lead to differing results, indicating a contradiction. In this paper we show that the reason for this contradiction is that the previous results based on the Eld model are in error. The error is due to the fact that the effect of the static rod was neglected in the Greenʹs function. The correct Eld result is calculated here in both one and two dimensions and is shown to be equivalent to the FGW results. This serves also as a confirmation of the two-dimensional FGW result which had earlier been derived only by heuristic arguments