Spreading Widths of Doorway States

TL;DR

This paper derives an analytical expression for the strength function of doorway states considering variable background state density, with implications for shell-model calculations, validated by numerical simulations.

Contribution

It introduces a new analytical formula for the strength function when background state density varies significantly, extending the standard Lorentzian model.

Findings

Derived an approximate analytical expression for S(E).

Validated the formula against numerical simulations.

Implications for shell-model calculations.

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 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.