Abstract

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 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 ) ¯ . We test our result successfully against numerical simulations. Our result may have important implications for shell-model calculations.

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