Neutron Resonance Widths and the Porter-Thomas Distribution

Experimental evidence has recently put the validity of the Porter-Thomas distribution (PTD) for partial neutron widths into question. We identify two terms in the effective Hamiltonian that violate orthogonal invariance (the basis for the PTD). Both are due to the coupling to the decay channels. We show that realistic estimates for the coupling to the neutron channel and for nonstatistical $\gamma$ decays yield significant modifications of the PTD, similar to the observed ones.

Figure 1

Relative difference $[\mathcal{P}(x)/P(x)]-1$ as a function of $x$ for several values of $\kappa$ as indicated in the figure and for $N=1000$. The dashed-dotted lines are fits using expression (8).

Figure 2

Scaled fit coefficients: (a) $B/{\kappa }^2$ and (b) $A/{\kappa }^2$ with $A$ and $B$ defined in Eq. (8) are plotted as functions of $\kappa$ for GOE ensembles of different dimensions $N$ as indicated in the figure. For $N=1000$ the error in the fit is shown by error bars. The errors for the other curves are similar. The double-dot-dashed black line shows the linear fits [Eq. (9)] of $A/{\kappa }^2$ and $B/{\kappa }^2$ as functions of $\kappa$. Right: (c) The coefficient $\tau$ defined in Eq. (10) is plotted versus $\kappa$ for different widths of multiple random $\gamma$ channels as explained in the text. The scale on the right shows the corresponding $\nu$ values.