Statistical Analysis of Composite Spectra

We consider nearest neighbor spacing distributions of composite ensembles of levels. These are obtained by combining independently unfolded sequences of levels containing only few levels each. Two problems arise in the spectral analysis of such data. One problem lies in fitting the nearest neighbor spacing distribution to the histogram of level spacings obtained from the data. We show that the method of Bayesian inference is superior to this procedure. The second problem occurs when one unfolds such short sequences. We show that the unfolding procedure generically leads to an overestimate of the chaoticity parameter. This trend is absent in the presence of long-range level correlations. Thus, composite ensembles of levels from a system with long-range spectral stiffness yield reliable information about the chaotic behavior of the system.Comment: 26 pages, 3 figures; v3: changed conclusions, appendix adde

Fusion and Binary-Decay Mechanisms in the 35^{35}Cl+24^{24}Mg System at E/A ≈\approx 8 MeV/Nucleon

Compound-nucleus fusion and binary-reaction mechanisms have been investigated for the $^{35}$Cl+$^{24}$Mg system at an incident beam energy of E$_{Lab}$= 282 MeV. Charge distributions, inclusive energy spectra, and angular distributions have been obtained for the evaporation residues and the binary fragments. Angle-integrated cross sections have been determined for evaporation residues from both the complete and incomplete fusion mechanisms. Energy spectra for binary fragment channels near to the entrance-channel mass partition are characterized by an inelastic contribution that is in addition to a fully energy damped component. The fully damped component which is observed in all the binary mass channels can be associated with decay times that are comparable to, or longer than the rotation period. The observed mass-dependent cross sections for the fully damped component are well reproduced by the fission transition-state model, suggesting a fusion followed by fission origin. The present data cannot, however, rule out the possibility that a long-lived orbiting mechanism accounts for part or all of this yield.Comment: 41 pages standard REVTeX file, 14 Figures available upon request -

Discrete structures in fusion-barrier distributions for vibrational nuclei

We obtain a closed-form expression for the distribution of fusion barriers for vibrational nuclei using a generalization of Dasso, Landowne, and Winther's model, which represents the nuclear surface vibrations as a number of harmonic oscillators, and allows the excitation of an arbitrary number of phonons in the target and/or projectile. We find that this expression is in reasonable agreement with the average trends of the empirical distributions for the fusion of $\mathsf{^{16}O}$ with $\mathsf{^{92}Zr}$, $\mathsf{^{144}Sm}$ and $\mathsf{^{208}Pb}$, but fails to reproduce the double peaking of the distribution for the $\mathsf{^{144}Sm}$ target. Only when we restrict the number of excited phonons to a limited number, we are able to reproduce such discrete structures. We show that limiting the number of coupled channels, particularly in the case of strong coupling, increases the spacings between the channel eigenvalues that determine the positions of the peaks of the barrier distribution and modifies their heights