Spreading widths of doorway states

As a function of energy E, the average doorway strength function S(E)-bar of a doorway state is commonly assumed to be Lorentzian in shape and characterized by two parameters, the peak energy E0 and the spreading width Γ↓. 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 Γ↓. For that case we derive an approximate analytical expression for S(E)-bar. We test our result successfully against numerical simulations. Our result may have important implications for shell-model calculations.