Universal Correlations of Coulomb Blockade Conductance Peaks and the Rotation Scaling in Quantum Dots

We show that the parametric correlations of the conductance peak amplitudes of a chaotic or weakly disordered quantum dot in the Coulomb blockade regime become universal upon an appropriate scaling of the parameter. We compute the universal forms of this correlator for both cases of conserved and broken time reversal symmetry. For a symmetric dot the correlator is independent of the details in each lead such as the number of channels and their correlation. We derive a new scaling, which we call the rotation scaling, that can be computed directly from the dot's eigenfunction rotation rate or alternatively from the conductance peak heights, and therefore does not require knowledge of the spectrum of the dot. The relation of the rotation scaling to the level velocity scaling is discussed. The exact analytic form of the conductance peak correlator is derived at short distances. We also calculate the universal distributions of the average level width velocity for various values of the scaled parameter. The universality is illustrated in an Anderson model of a disordered dot.Comment: 35 pages, RevTex, 6 Postscript figure

Nuclear Level Density and the Determination of Thermonuclear Rates for Astrophysics

The prediction of cross sections for nuclei far off stability is crucial in the field of nuclear astrophysics. We discuss the model mostly employed for such calculations: the statistical model (Hauser-Feshbach). Special emphasis is put on the uncertainties arising from nuclear level density descriptions and an improved global description is presented. Furthermore, criteria for the applicability of the statistical model are investigated and a "map" for the applicability of the model to reactions of stable and unstable nuclei with neutral and charged particles is given.Comment: REVTeX paper + 7 B/W figures + 2 color figures; PRC, in press. Also available at http://quasar.physik.unibas.ch/preps.htm