Analysis of confinement potential fluctuation and band-gap renormalization effects on excitonic transition in GaAs/AlGaAs multiquantum wells grown on (1 0 0) and (3 1 1)A GaAs surfaces

The competition between confinement potential fluctuations and band-gap renormalization (BGR) in GaAs/Al_xGa_1−xAs$\mathrm{GaAs}/{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum wells grown on [1 0 0] and [3 1 1]A GaAs substrates is evaluated. The results clearly demonstrate the coexistence of the band-tail states filling related to potential fluctuations and the band-gap renormalization caused by an increase in the density of photogenerated carriers during the photoluminescence (PL) experiments. Both phenomena have strong influence on temperature dependence of the PL-peak energy (E_PL(T))$(E_{\mathit{PL}}(T))$. As the photon density increases, the E_PL can shift to either higher or lower energies, depending on the sample temperature. The temperature at which the displacement changes from a blueshift to a redshift is governed by the magnitude of the potential fluctuations and by the variation of BGR with excitation density. A simple band-tail model with a Gaussian-like distribution of the density of state was used to describe the competition between the band-tail filling and the BGR effects on E_PL(T).     

The mathematical relationship between Zipf’s law and the hierarchical scaling law

The empirical studies of city-size distribution show that Zipf’s law and the hierarchical scaling law are linked in many ways. The rank-size scaling and hierarchical scaling seem to be two different sides of the same coin, but their relationship has never been revealed by strict mathematical proof. In this paper, the Zipf’s distribution of cities is abstracted as a q$q$-sequence. Based on this sequence, a self-similar hierarchy consisting of many levels is defined and the numbers of cities in different levels form a geometric sequence. An exponential distribution of the average size of cities is derived from the hierarchy. Thus we have two exponential functions, from which follows a hierarchical scaling equation. The results can be statistically verified by simple mathematical experiments and observational data of cities. A theoretical foundation is then laid for the conversion from Zipf’s law to the hierarchical scaling law, and the latter can show more information about city development than the former. Moreover, the self-similar hierarchy provides a new perspective for studying networks of cities as complex systems. A series of mathematical rules applied to cities such as the allometric growth law, the 2ⁿ$2^n$ principle and Pareto’s law can be associated with one another by the hierarchical organization.     

Analysis of alpha-cluster transfer in O + C and C + O at energies near Coulomb barrier

The aim of this work is to track the phenomenon of α-cluster transfer mechanism at low energies 1.25, 1.5 and 1.75 MeV/n, close to the Coulomb barrier energy for ¹²C(¹⁶O, ¹²C)¹⁶O and ¹⁶O(¹²C, ¹⁶O)¹²C nuclear systems. The measurements of the angular distribution show a significant increase in the differential cross section at large angles due to alpha-transfer mechanism. The optical model code SPI-GENOA could be used effectively for fitting the experimental data with the theoretical predictions nearly up to angle 90°, where the differential cross section decreases steadily with increasing the scattering angle. For the second hemisphere, at angles greater than 100°, there is a large increase in cross section due to the contribution of α-transfer mechanism, and the Distorted Wave Born Approximation (DWBA) method could be used effectively for fitting the experimental data with the theoretical predictions at this region using (DWUCK5) code.     

Single- and double-pion production in nucleon collisions on the nucleon and on nuclei—the ABC effect and its origin in a dibaryonic resonance

The ABC effect-an intriguing low-mass enhancement in the ππ invariant mass spectrum-is known from inclusive measurements of two-pion production in nuclear fusion reactions. First exclusive measurements carried out at CELSIUS-WASA for the fusion reactions leading to d or ³He reveal this effect to be a σ-channel phenomenon associated with the formation of a ΔΔ system in the intermediate state and combined with a resonance-like behavior in the total cross-section. Together with the observation that the differential distributions do not change in shape over the resonance region the features fulfill the criteria of an isoscalar s-channel resonance in pn and NNππ systems, if the two emitted nucleons are bound. It obviously is robust enough to survive in nuclei as a dibaryonic resonance configuration. In this context also the phenomenon of NΔ resonances is reexamined.