Distribution of Resonance Widths and Dynamics of Continuum Coupling

We analyze the statistics of resonance widths in a many-body Fermi system with open decay channels. Depending on the strength of continuum coupling, such a system reveals growing deviations from the standard chi-square (Porter-Thomas) width distribution. The deviations emerge from the process of increasing interaction of intrinsic states through common decay channels; in the limit of perfect coupling this process leads to the superradiance phase transition. The width distribution depends also on the intrinsic dynamics (chaotic versus regular). The results presented here are important for understanding the recent experimental data concerning the width distribution for neutron resonances in nuclei.

Figure 1

Normalized distribution of the widths for one open channel, $M=1$ (left panels), and for $M=2$ (right panels) for the GOE intrinsic Hamiltonian and different continuum coupling strength, $\kappa$. Numerical results are given by histograms; the expected PTD for $M=1$ and ${\chi }_{\nu =2}^2$ distribution for $M=2$ are shown by a smooth curve in all panels. Full squares stand for the best fit to a ${\chi }_{\nu }^2$ distribution. In the lowest panels, a straight line shows the power law $P(\Gamma /⟨\Gamma ⟩)\propto (\Gamma /⟨\Gamma ⟩{)}^{-2}$. In this Figure, the resonances in the energy interval $\pm 0.5$ for ${10}^3$ different ensemble realizations were considered.

Figure 2

Best fitted value of $\nu$ versus the coupling strength to the continuum, $\kappa$. Full circles refer to GOE intrinsic Hamiltonian, crosses stand for TBRE with $v_0=d_0/50$, and squares for TBRE with $v_0=0$ (no intrinsic chaos); the number of channels is one (upper panel) and two (lower panel). The inserts show the reduced ${\chi }_r^2$ as a function of $\kappa$.