Large deviations for random walks under subexponentiality: the big-jump domain

For a given one-dimensional random walk $\{S_n\}$ with a subexponential step-size distribution, we present a unifying theory to study the sequences $\{x_n\}$ for which $\mathsf{P}\{S_n>x\}\sim n\mathsf{P}\{S_1>x\}$ as $n\to\infty$ uniformly for $x\ge x_n$. We also investigate the stronger "local" analogue, $\mathsf{P}\{S_n\in(x,x+T]\}\sim n\mathsf{P}\{S_1\in(x,x+T]\}$. Our theory is self-contained and fits well within classical results on domains of (partial) attraction and local limit theory. When specialized to the most important subclasses of subexponential distributions that have been studied in the literature, we reproduce known theorems and we supplement them with new results.Comment: Published in at http://dx.doi.org/10.1214/07-AOP382 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

An evolution equation as the WKB correction in long-time asymptotics of Schrodinger dynamics

We consider 3d Schrodinger operator with long-range potential that has short-range radial derivative. The long-time asymptotics of non-stationary problem is studied and existence of modified wave operators is proved. It turns out, the standard WKB correction should be replaced by the solution to certain evolution equation.Comment: This is a preprint of an article whose final and definitive form has been published in Comm. Partial Differential Equations, available online at http://www.informaworld.co

Nuclear collective motion with a coherent coupling interaction between quadrupole and octupole modes

A collective Hamiltonian for the rotation-vibration motion of nuclei is considered, in which the axial quadrupole and octupole degrees of freedom are coupled through the centrifugal interaction. The potential of the system depends on the two deformation variables $\beta_2$ and $\beta_3$. The system is considered to oscillate between positive and negative $\beta_3$-values, by rounding an infinite potential core in the $(\beta_2,\beta_3)$-plane with $\beta_2>0$. By assuming a coherent contribution of the quadrupole and octupole oscillation modes in the collective motion, the energy spectrum is derived in an explicit analytic form, providing specific parity shift effects. On this basis several possible ways in the evolution of quadrupole-octupole collectivity are outlined. A particular application of the model to the energy levels and electric transition probabilities in alternating parity spectra of the nuclei $^{150}$Nd, $^{152}$Sm, $^{154}$Gd and $^{156}$Dy is presented.Comment: 25 pages, 13 figures. Accepted in Phys. Rev.

Alpha-nucleus potential for alpha-decay and sub-barrier fusion

The set of parameters for alpha-nucleus potential is derived by using the data for both the alpha-decay half-lives and the fusion cross-sections around the barrier for reactions alpha+40Ca, alpha+59Co, alpha+208Pb. The alpha-decay half-lives are obtained in the framework of a cluster model using the WKB approximation. The evaluated alpha-decay half-lives and the fusion cross-sections agreed well with the data. Fusion reactions between alpha-particle and heavy nuclei can be used for both the formation of very heavy nuclei and spectroscopic studies of the formed compound nuclei.Comment: 10 pages, 5 figure

Search for long-lived superheavy eka-tungsten with radiopure ZnWO4_4 crystal scintillator

The data collected with a radioactively pure ZnWO$_4$ crystal scintillator (699 g) in low background measurements during 2130 h at the underground (3600 m w.e.) Laboratori Nazionali del Gran Sasso (INFN, Italy) were used to set a limit on possible concentration of superheavy eka-W (seaborgium Sg, Z = 106) in the crystal. Assuming that one of the daughters in a chain of decays of the initial Sg nucleus decays with emission of high energy $\alpha$ particle ($Q_\alpha > 8$ MeV) and analyzing the high energy part of the measured $\alpha$ spectrum, the limit N(Sg)/N(W) < 5.5 $\times$ 10$^{-14}$ atoms/atom at 90% C.L. was obtained (for Sg half-life of 10$^9$ yr). In addition, a limit on the concentration of eka-Bi was set by analysing the data collected with a large BGO scintillation bolometer in an experiment performed by another group [L. Cardani et al., JINST 7 (2012) P10022]: N(eka-Bi)/N(Bi) < 1.1 $\times$ 10$^{-13}$ atoms/atom with 90% C.L. Both the limits are comparable with those obtained in recent experiments which instead look for spontaneous fission of superheavy elements or use the accelerator mass spectrometry.Comment: 9 pages, 2 figures; in press on Physica Script

Increase the strength characteristics of polymer films by radiation graft polymerization

The possibility of increasing the strength characteristics of polymer films based on polyethylene and polyamide by radiation graft polymerization was investigated. Two methods of graft polymerization (direct method and the method of polymer mixtures cross-linking) on the PMMA films surface were studied. The possibility of increasing the strength and elasticity of polymeric films by radiation modification of polymethyl methacrylate was shown