Spreading widths of doorway states

As a function of energy E, the average strength function image of a doorway state is commonly assumed to be Lorentzian in shape and characterized by two parameters, the peak energy image and the spreading width image. 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 image. For that case we derive an approximate analytical expression for image. We test our result successfully against numerical simulations. Our result may have important implications for shell-model calculations.