  As a function of energy E, the average strength function S(E) of a doorway
state is commonly assumed to be Lorentzian in shape and characterized by two
parameters, the peak energy E_0 and the spreading width Gamma. The simple
picture is modified when the density of background states that couple to the
doorway state changes significantly in an energy interval of size Gamma. For
that case we derive an approximate analytical expression for S(E). We test our
result successfully against numerical simulations. Our result may have
important implications for shell--model calculations.
