The asymptotic decay constant for the die-away experiment in which a moderator is poisoned with a non-l/ν absorber is expanded as the power series with λ0 the decay constant for the unpoisoned moderator and N the concentration of the non-l/ν absorber. The coefficients in the expansion are computed with the Mass-1 and the Nelkin scattering kernels for water poisoned with Cd, Gd and Sm. The computed coefficients δσeff/δ N are in significant disagreement with experimental values: the latter are some five times as large as the computed values.