Examination of experimental evidence of chaos in the bound states of Pb208

Abstract

We study the spectral fluctuations of the 208 Pb nucleus using the complete experimental spectrum of 151 states up to excitation energies of 6.20 MeV recently identified at the Maier-Leibnitz Laboratorium at Garching, Germany. For natural parity states the results are very close to the predictions of random matrix theory (RMT) for the nearest-neighbor spacing distribution. A quantitative estimate of the agreement is given by the Brody parameter ω, which takes the value ω = 0 for regular systems and ω 1 for chaotic systems. We obtain ω = 0.85 which is, to our knowledge, the closest value to chaos ever observed in experimental bound states of nuclei. By contrast, the results for unnatural parity states are far from RMT behavior. We interpret these results as a consequence of the strength of the residual interaction in 208 Pb, which, according to experimental data, is much stronger for natural than for unnatural parity states. In addition, our results show that chaotic and nonchaotic nuclear states coexist in the same energy region of the spectrum.

Resistivity scaling due to electron surface scattering in thin metal layers

“…Electron transport in thin metallic films including the prediction of the resistivity ρ as a function of layer thickness d continues to be of great scientific interest [1][2][3][4][5][6][7][8][9][10][11][12][13]. Electron scattering at film surfaces [14][15][16][17][18][19] is particularly important as it causes an increase in ρ with decreasing thickness [20][21][22][23][24][25][26] that has also garnered technological interest as it impedes integrated circuit downscaling [27,28].…”

“…This intrinsic limitation of the F-S model [3] originates from two approximations that are not necessarily satisfied at small thickness, in particular (i) the electronic structure is bulk like, and (ii) the surface scattering occurs exactly at the surface. Later studies have proposed other models to replace the F-S model [3,4,5,7,12]. They apply a two-dimensional transport description with quantized vertical wave vector components, leading to an electronic structure with sub-bands and an in-plane conductivity defined by the sum over all conduction channels [5].…”

Spreading widths of giant resonances in spherical nuclei: Damped transient response

“…Introducing a residual interaction in general implies a transition to the Gaussian orthogonal ensemble (GOE) -properties above some excitation energy [13]. In fact, recent analysis of 151 experimental nuclear levels up to excitation energy of E x = 6.2 MeV in 208 Pb indicates already that the spectral properties are described by the GOE due to a residual interaction, even though there is a small admixture of regular dynamics brought about by the low-lyings states [14].The quasiparticle-phonon model (QPM) [15] offers an attractive framework for such studies. We will use the modern development of the QPM, a finite rank separable approximation (FRSA) [16].…”

Structure of negative parity states at $${\mathbf {6}\,\lesssim \, \mathbf {E}_\mathbf {x} <{\mathbf {7.0}} }$$ MeV in $$\mathbf {^{208}}{} \mathbf{Pb}$$

“…The distance between two states with the same spin and parity is larger than 30 keV. It is explained by the chaoticity [62][63][64]. The state contributing dominantly to a certain level in the MPIK data could be identified by the high resolution Q3D data (Table 15).…”

“…The rather firm completeness of the sequence of states for most spins at E x < 6.2 MeV allowed to study the chaoticity among bound states in a heavy nucleus [62][63][64]. The rather complete orthonormal transformation matrices from one-particle one-hole configurations to states [34,49,50] for Table 1 Resonance energy E res and total width Γ tot for IARs L J in 209 Bi…”