Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison

The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal cross sections in the Heidelberg approach, which is applicable to a wide range of quantum chaotic systems. Thus, eventually, we fully solve a problem that already arose more than half a century ago in compound-nucleus scattering. We compare our results with data from microwave and compound-nucleus experiments, particularly addressing the transition from isolated resonances towards the Ericson regime of strongly overlapping ones.

Figure 1

Bivariate characteristic function $R(k_1,k_2)$ in the frequency range 10–11 GHz. Analytical result (blue) and microwave data (orange).

Figure 2

As Fig. 1, but in the frequency range 24–25 GHz.

Figure 3

Joint probability density $P(x_1,x_2)$, analytical (surface), and microwave data (histogram) in the frequency range 24–25 GHz.

Figure 4

Distribution of normalized cross sections. Experimental data as histograms from microwave (left) and nuclear experiments (right), respectively. Analytical results as solid red lines.

Figure 5

Excitation functions for the reaction ${}^{37}\mathrm{Cl}(\mathit{p},\alpha ){}^{34}\mathrm{S}$ in the Ericson regime for scattering angles 31°, 110°, and 175° from top to bottom. Digitized from Ref. [66].

Figure 6

Excitation functions for the reaction ${}^{37}\mathrm{Cl}(\mathit{p},\alpha ){}^{34}\mathrm{S}$ in below the Ericson regime for scattering angle 90°. Digitized from Ref. [68].