Lattice Eigenvalue as a Function of Buckling: Correction to First-Order Perturbation Theory

In earlier work by Gelbard and Lell, arguments based on perturbation theory were used to obtain relations between mean-square chord lengths and lattice eigenvalues for given bucklings. We show here that first-order perturbation theory does not give the lattice eigenvalue correctly to order B². When all missing terms in B² are inserted, the eigenvalue buckling relations remain formally unchanged, but the mean-square chord lengths must be redefined. The original and redefined mean-square chord lengths differ only insofar as events in successive fission generations are correlated. A reexamination of work based on the original relations indicates that earlier numerical results were substantially correct.