On the hexadecapole collective motion in spherical nuclei

The hexadecapole-collective motion in spherical nuclei is discussed. Numerical calculations are presented and compared with available experimental data.     

Anomaly in electron channeling due to imperfections produced thermally in a potassium chloride crystal

Lattice imperfections were produced in KCl crystals by a thermal process. The heat treated specimen was irradiated with 50 KeV electrons and the corresponding range of electrons in the crystal has been estimated. It was found that the electron range in the crystal depends upon the temperature of heat treatment, being a decreasing function of this temperature up to about 625 K, above which it becomes an increasing function. This anomaly has been explained in terms of dissolution of vacancies through dislocation loops.     

A study of the vestigial records of cosmic rays in lunar rocks using a thick section technique

An experimental technique has been developed for systematic measurements of fossil tracks along selected planes cut from grains and rocks. With controlled etching, the technique allows successive revelation of tracks in different minerals in the same section, a typical sequence being olivine, anorthite, clinopyroxene. It thus becomes possible to study precisely the cosmic ray track density variations over dimensions much greater than those of individual crystals. The technique also provides accurate information on the relative recording characteristics of different minerals present in a rock and cosmic ray tracks can be studied with a minimum interference of tracks due to spontaneous fission of uranium and transuranic elements. Continuous chains of sections, each section measuring approximately 1 cm., have been cut along several different planes in fifteen rocks from Mare Tranquillitatis, Oceanus Procellarum and Fra Mauro region. The cosmic ray track measurements from these sections have provided dramatic evidence for a number of processes affecting lunar rocks. The statistical, and non-uniform nature of erosion by micrometeorite bombardment can be seen in sections intersecting exposed surface which show regions of very steep track density gradients interspersed with eroded regions having lower track densities. The thick section technique permits determination of the energy spectrum of VH nuclei from track density gradients that extend over distances limited only by the dimensions of the rock, and, more important, in samples of identical orientation. The latter is particularly important in higher energy regions (deeper within the rock) where variations in crystal orientation cause track density differences of the same order as real changes in the gradient. Also in the near surface regions of rocks where low energy particles produce steep track density gradient, the thick section method has proved indispensable since it permits accurate depth determinations not possible in the spot sampling procedure. In this paper the technique of studying track profiles in thick sections is described. Although developed primarily for studying lunar samples, the thick section technique is also useful for similar studies in meteorites, particularly for gas-rich meteorites containing irradiated grains. In contrast to single grain studies, thick sections preserve the grain boundaries and permit accurate depth—density measurements. In addition thick section studies have revealed occasional large uniformly irradiated lithic fragments which would not have been possible to discover by spot sampling methods.     

A search for rare types of fission induced in silver and bromine nuclei

Ternary and quaternary fission produced in silver and bromine nuclei have been studied withK5 nuclear emulsion exposed to 1.8 GeV/cK ⁻ beams. The frequency of the ternary events is found to be ∼0.08 of that of the binary events produced in the same volume of the emulsion. The range ratio and range distribution of the fission fragments are studied and the angles between each pair of the fragments are determined. Ranges are found to vary from 5 to 40μ with a maximum number lying between 5 and 10μ. The angles between the fission fragments are found to form a broad distribution extending from 40° to 180°. A few of the events have also been analysed to give them a possible identity. A possible case of quaternary fission has also been reported. This paper was presented at the Symposium on 3rd High Energy Physics held at Bhubaneswar during November 1976.     

Self-assembly and odd-even effects of cis-unsaturated carboxylic acids on highly oriented pyrolytic graphite

The self-assembly of several cis-unsaturated carboxylic acids of the structure cis-CH3(CH2)p-1CH=CH(CH2)m-1COOH on highly oriented pyrolytic graphite (HOPG) was studied. The impact of the interior cis-CH=CH group and the molecular chain length on their self-assembled structures was considered. Due to the cis conformation of the -HC=CH- group in the interior of these molecules, they display self-assembled structures significantly different from saturated acids with all-trans configurations. As an example of the class of molecules cis-CH3(CH2)p-1CH=CH(CH2)2n-1COOH (p not equal 2n) (p=8, n=7), cis-CH3(CH2)7CH=CH(CH2)13COOH self-assembles into two kinds of enantiomer domains with opposite 2-D chirality. Due to the steric restriction of the interior cis-HC=CH group, all chains with acid groups are packed at the same side of a lamella, a head-to-head arrangement which is different from the head-to-tail packing of saturated all-trans acids. However, cis-CH3(CH2)7CH=CH(CH2)8COOH, considered as one example of the group cis-CH3(CH2)p-1CH=CH(CH2)2n-2COOH (p not equal 2n-1) (p=8, n=5), does not form any stable self-assembled domain, consistent with the molecular arrangement model. This difference in self-assembly behavior between cis-CH3(CH2)p-1CH=CH(CH2)2n-1COOH (p not equal 2n) and cis-CH3(CH2)p-1CH=CHC2n-2COOH (p not equal 2n-1) shows an odd-even chain-length effect of cis-CH3(CH2)p-1CH=CH(CH2)m-1COOH (p not equal m, m=2n or 2n-1). For another category of molecules, cis-unsaturated acids with equal numbers of all-trans carbon atoms on both sides of the cis-CH=CH group, cis-CH3(CH2)m-1CH=CH(CH2)m-1COOH (m=2n or 2n-1), display another odd-even effect. cis-CH3(CH2)7CH=CH(CH2)7COOH, one example of cis-CH3(CH2)2n-1-CH=CH(CH2)2n-1COOH (n=4), is predicted to form both an enantiomer and a nonchiral racemic structure, which is in accordance with the experimental observation of its self-assembled monolayer. However, cis-CH3(CH2)2n-2CH=CH(CH2)2n-2COOH does not form a stable self-assembled domain due to the same steric repulsion as that seen in the cis-CH3(CH2)7CH=CH(CH2)8COOH structure. These odd-even effects demonstrate that molecular self-assembly can be significantly tailored by slightly changing the molecular chain length.     

Imaging of atomic layer deposited (ALD) tungsten monolayers on alpha-TiO2(110) by X-ray standing wave Fourier inversion

A single atomic layer of tungsten grown by atomic layer deposition (ALD) on a single-crystal rutile TiO2(110) support is studied by the X-ray standing wave (XSW) technique. The surface structural and chemical properties were also examined using atomic force microscopy, X-ray photoelectron spectroscopy, and low-energy electron diffraction. The XSW measured set of hkl Fourier components for the W atomic distribution function are summed together to produce a model-independent 3D map of the W atoms relative to the rutile lattice. The 3D atomic image shows surface tungsten atoms equally occupying the two nonequivalent Ti sites with a slight outward displacement. This corresponds to the atop and bridge sites with respect to the underlying lattice oxygen atoms. These XSW measurements clearly show that ALD conformal layers can be highly coherent with respect to the substrate lattice.     

2540 km: bimagic baseline for neutrino oscillation parameters

We show that a source-to-detector distance of 2540 km, motivated recently [S. K. Raut, R. S. Singh, and S. U. Sankar, arXiv:0908.3741] for a narrow band superbeam, offers multiple advantages for a low energy neutrino factory with a detector that can identify muon charge. At this baseline, for any neutrino hierarchy, the wrong-sign muon signal is almost independent of CP violation and θ(13) in certain energy ranges. This allows the identification of the hierarchy in a clean way. In addition, part of the muon spectrum is also sensitive to the CP violating phase and θ(13), so that the same setup can be used to probe these parameters as well.     

On approximately monotone and approximately Hölder functions

Periodica Mathematica Hungarica - A real valued function f defined on a real open interval I is called $$\Phi $$ -monotone if, for all $$x,y\in I$$ with $$x\le y$$ it satisfies $$\begin{aligned}...     

Modified (22pi) smaragdyrins with large two-photon absorption cross section: a structure function correlation

[structure: see text] Two-photon absorption (TPA) cross-section values for a series of 22pi smaragdyrins bearing phenylacetylenylphenyl and [(phenylacetylenyl)phenylacetylenyl]phenyl meso links and their Rh(I) derivatives are reported.     

American option pricing under stochastic volatility: an efficient numerical approach

This paper develops a new numerical technique to price an American option written upon an underlying asset that follows a bivariate diffusion process. The technique presented here exploits the supermartingale representation of an American option price together with a coarse approximation of its early exercise surface that is based on an efficient implementation of the least-squares Monte–Carlo algorithm (LSM) of Longstaff and Schwartz (Rev Financ Stud 14:113–147, 2001). Our approach also has the advantage of avoiding two main issues associated with LSM, namely its inherent bias and the basis functions selection problem. Extensive numerical results show that our approach yields very accurate prices in a computationally efficient manner. Finally, the flexibility of our method allows for its extension to a much larger class of optimal stopping problems than addressed in this paper.