New parametrization for optical model description of elastic α\alpha -particle scattering from heavy nuclei over a wide energy range

Differential cross sections for elastic scattering of $\alpha$-particle from $^{90}$Zr, $^{92}$Zr, $^{124}$Sn and $^{208}$Pb were analysed over available energy range in terms of the optical model. New parametrization of the energy dependence of the optical potential parameters was used. Satisfactory agreement of the model predictions and experimental data was obtained

Chaos induced by Pauli blocking

Dynamics of classical scattering in the system of fermions is studied. The model is based on the coherent state representation and the equations of motion for fermions are derived from the time-dependent variational principle. It is found that the antisymmetrization due to the Pauli exclusion principle, may lead to hyperbolic chaotic scattering even in the absence of interaction between particles. At low bombarding energies, the same effect leads to the screening of the hard, short-ranged component in the two particle interaction and thus regularizes the dynamics.Comment: 10 pages, LaTeX

Stochastic equation for a jumping process with long-time correlations

A jumping process, defined in terms of jump size distribution and waiting time distribution, is presented. The jumping rate depends on the process value. The process, which is Markovian and stationary, relaxes to an equilibrium and is characterized by the power-law autocorrelation function. Therefore, it can serve as a model of the 1/f noise as well as a model of the stochastic force in the generalized Langevin equation. This equation is solved for the noise correlations 1/t; the resulting velocity distribution has sharply falling tails. The system preserves the memory about the initial condition for a very long time.Comment: 7 pages, 5 Postscript figure

A study on whether the wood-saxon or the woods-saxon square parametrisation is appropriate for the phenomenological representation of different α \alpha -particle nucleus folding potentials

The Woods-Saxon (WS) and the squared Woods-Saxon (WS)$^{2}$ parametrisations for the single and double folding potentials were tested. We showed that the (WS)$^{2}$ form is appropriate for single as well as double folding approaches

Stochastic processes with finite correlation time: modeling and application to the generalized Langevin equation

The kangaroo process (KP) is characterized by various forms of the covariance and can serve as a useful model of random noises. We discuss properties of that process for the exponential, stretched exponential and algebraic (power-law) covariances. Then we apply the KP as a model of noise in the generalized Langevin equation and simulate solutions by a Monte Carlo method. Some results appear to be incompatible with requirements of the fluctuation-dissipation theorem because probability distributions change when the process is inserted into the equation. We demonstrate how one can construct a model of noise free of that difficulty. This form of the KP is especially suitable for physical applications.Comment: 22 pages (RevTeX) and 4 figure

Non-Markovian Levy diffusion in nonhomogeneous media

We study the diffusion equation with a position-dependent, power-law diffusion coefficient. The equation possesses the Riesz-Weyl fractional operator and includes a memory kernel. It is solved in the diffusion limit of small wave numbers. Two kernels are considered in detail: the exponential kernel, for which the problem resolves itself to the telegrapher's equation, and the power-law one. The resulting distributions have the form of the L\'evy process for any kernel. The renormalized fractional moment is introduced to compare different cases with respect to the diffusion properties of the system.Comment: 7 pages, 2 figure