Resonance Width Distribution for Open Chaotic Quantum Systems

Recent measurements of resonance widths, $\Gamma$, for low-energy neutron scattering off heavy nuclei claim significant deviations from the standard chi-square $\chi^{2}_{1}(\Gamma)$, or the Porter-Thomas, distribution. The unstable nucleus is an open quantum system, where the intrinsic dynamics has to be supplemented by the coupling of chaotic internal states through the continuum. We propose a new resonance width distribution based on the random matrix theory for an open quantum system. For a single open channel, the new distribution is $P(\Gamma)=C\chi^{2}_{1}(\Gamma)\sqrt{\sinh{\kappa}/{\kappa}}$ where $\kappa={\pi\Gamma}/{2D}$ and $D$ is the mean energy level spacing. This result naturally recovers the Porter-Thomas distribution for small $\kappa$ and can be directly applied to a whole range of mesoscopic systems, and is invariant under $\Gamma\rightarrow{\eta-\Gamma}$, where$\eta$ is the total width. The realistic situation in nuclei is not that of a single neutron channel. Many photon channels are always opened which modifies the width distribution into $P(\Gamma,\gamma)=C\chi^{2}_{1}(\Gamma-\gamma)\sqrt{\sinh{\kappa_{\gamma}}/{\kappa_{\gamma}}}$ with $\kappa_{\gamma}={\pi(\Gamma-\gamma)}/{2D}$, and the whole distribution is shifted by $\gamma$, an average radiation width.