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Title:
Application of RMT to Scattering Experiments with Microwave Billiards and Nuclear Data
Speaker:
Abstract:
In the first part of my talk I will review experiments with flat microwave resonators with induced time-reversal invariance violation of which the scattering matrix formalism is equivalent to that developed for the RMT description of compound nuclear reactions. The aim of the experiments was the derivation and experimental verifiation of a variety of statistical measures for the fluctuation properties in the spectra of the associated scattering matrix. Recently, we validated analytical expressions for the distribution of the off-diagonal cross sections based on these microwave data and then applied them to excitation functions of the compound-nuclear reaction $^{37}{\rm Cl}(p,\alpha)^{34}S$. In the second part of my talk I will speak about a thorough study of the fluctuation properties in the energy spectra of $^{\bf 208}${\bf Pb}. High resolution experiments have recently lead to a complete identification of the energy values, spin, and parity of 151 nuclear levels up to an excitation energy of $E_x= 6.20$~MeV in $^{\bf 208}${\bf Pb}. In a first approach we grouped states with the same spin and parity into subspectra, analyzed standard statistical measures for short- and long-range correlations in each sequence of unfolded energy levels and then computed their ensemble average and compared them to RMT results. In a second approach, following an idea of Rosenzweig and Porter, we considered the complete spectrum composed of the spacings between adjacent the unfolded energy levels of the independent subspectra. We analyzed their fluctuation properties using the method of Bayesian inference. We, furthermorem performed the same analysis with spectra computed on the basis of shell model calculations with different interactions (SDI, KB, M3Y).
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