Relationship between the Width for Decay from a Doorway State and the Ratio between the Numbers of the Correlating and Open Channels

Abstract

The width $〈{\ensuremath{\Gamma}}_{d}\ensuremath{\uparrow}〉$ for the decay out of the doorway state is derived as a function of the average total level width $〈{\ensuremath{\Gamma}}_{\ensuremath{\mu}}〉$, the channel correlation coefficient ${C}_{c{c}^{\ensuremath{'}}}$, the ratio between the number ${n}_{d}$ of the correlating channels and the number $n$ of the open channels, and the level-overlapping ratio $\frac{〈{\ensuremath{\Gamma}}_{\ensuremath{\mu}}〉}{D}$. Using the function, the relation between the ratio $\frac{{n}_{d}}{n}$ and (1) the width $〈{\ensuremath{\Gamma}}_{d}\ensuremath{\uparrow}〉$ and (2) the ratio $\frac{〈{\ensuremath{\Gamma}}_{\ensuremath{\mu}}〉}{D}$ are discussed. The results indicate that the latter relation is in agreement with the experiment of Shotter, Fisher, and Scott.